I also recently developed a SEIR model for COVID-19, with variables for the magnitude and timing of social distancing restrictions, as well a probabilistic variable for decaying immunity. The results were ominous and are not fully reflected in equity prices, especially after the very large rebound from the March 23rd lows in the last few months. I explained the Coronavirus model in an in-depth article titled: "New Coronavirus Model and the Economy," which I posted on April 1, 2020.

This article updates the diffusion indices, recession slack index, aggregate recession model, and aggregate peak-trough model through June 2020. The explanatory variables are now capturing the effects of COVID-19 on the market and on the U.S. economy.

The current *26-variable* model has a diverse set of explanatory variables and is quite robust. Each of the explanatory variables has predictive power individually; when combined, the group of indicators is able to identify early recession warnings from a wide range of diverse market-based, fundamental, technical, and economic sources.

Several of the explanatory variables are market-based. These variables are available in real-time (no lag), which means they respond very quickly to changing market conditions. In addition, they are never revised. This makes the Trader Edge recession model more responsive than many recession models. The current *and* historical data in this report reflect the current model configuration with all *26 variables*.

The Trader Edge diffusion index equals the percentage of independent variables indicating a recession. With the latest changes, there are now a total of 26 explanatory variables, each with a unique look-back period and recession threshold. The resulting diffusion index and the trend in the diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the diffusion index from 1/1/2006 to 7/1/2020 is presented in Figure 1 below (in red - left axis). The gray shaded regions in Figure 1 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

The U.S. economy flirted with entering a recession in early 2016, which was reflected in the deteriorating economic, fundamental, and especially market-based data. The diffusion index, slack index, and recession probability forecasts all captured the weakening conditions. However, the weakness proved to be temporary and the conditions and recession model forecasts improved rapidly.

Preliminary signs of weakness in the diffusion index reemerged in late 2018 and conditions deteriorated rapidly in December and January before rebounding in February through April of 2019 and stabilizing thereafter. However, the slack indices remained depressed throughout 2019.

The number of explanatory variables indicating a recession decreased from 18 (69.2%) to 16 (61.5%) in June, which is largely due to the continued rebound in the prices of risk assets.

Please note that past estimates and index values will change whenever the historical data is revised and/or whenever model improvements are implemented. All current and past forecasts and index calculations are based on the most recent models using the latest revised data from the current data set.

The Trader Edge 0.5-sigma diffusion Index equals the percentage of explanatory variables with Z-scores that are *less than 0.5 standard deviations* above their respective recession thresholds. This new diffusion index is much more sensitive than the standard (zero-sigma) diffusion index. As a result, it provides much more detail on the health of the U.S. economy. The new 0.5-sigma diffusion index and the trend in the new diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the 0.5-sigma diffusion index from 1/1/2006 to 7/1/2020 is presented in Figure 2 below (in red - left axis). The gray shaded regions in Figure 2 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

The percentage of explanatory variables with Z-scores below the 0.5-sigma early warning threshold declined from 84.6% to 76.9% in June. The additional level of detail provided by this more continuous and responsive metric is particularly valuable in the months leading up to a recession, especially given the infrequent and more discrete movements of the standard (zero-sigma) diffusion index.

As I noted in past months, the percentage of variables with Z-scores below their respective 0.5 sigma thresholds had been unusually high, especially with the standard diffusion index equal to zero. This significantly reduced the potential cushion to any adverse economic shocks and accelerated the decline due to the Coronavirus.

This new 0.5-sigma diffusion index and the trend in the new diffusion index are now both used directly in the neural network recession models. When combined with the recession slack indices, the new diffusion index provides even greater insight into rapidly changing conditions.

The Trader Edge recession slack index equals the median standardized deviation of the current value of the explanatory variables from their respective recession thresholds. The resulting value signifies the amount of slack or cushion relative to the recession threshold, expressed in terms of the number of standard deviations. Higher slack values signify larger cushions above recessionary threshold levels. While the *median* recession slack index is used in the recession models, I am now including the *mean* recession slack index in the graph as well. As I mentioned above, I am not capping the maximum standardized deviation for each explanatory variable before calculating the mean and median. I use both of these values in the neural network models and in the probit and logit models.

The gray shaded regions in Figure 3 below represent U.S. recessions as defined (after the fact) by the NBER. The *median* recession slack index is depicted in purple and is plotted against the right axis, which is expressed as the number of standard deviations above the recession threshold. The *mean* recession slack index is depicted in blue and is also plotted against the right axis.

The dark-red, horizontal line at 0.50 standard deviations denotes a possible warning threshold for the recession slack index. Many of the past recessions began when the recession slack index crossed below 0.50. Similarly, many of the past recessions ended when the recession slack index crossed back above 0.0.

In June 2020, the median recession slack index increased from -0.40 to -0.21. The mean recession slack index (affected more by outliers - even when capped) improved from -1.78 to -1.47. Similar to the situation with the 0.5-sigma diffusion index, the mean and median slack indices had been unusually low. This made the U.S. economy particularly vulnerable to any adverse economic shocks, which accelerated the decline due to the Coronavirus. Note, all of these values reflect the new smoothed trend data.

To gain further insight into the slack index, I provide the three-month moving average of the percentage of variables with increasing slack in Figure 4, but I personally monitor the monthly percentages as well.

Slack is a standardized value, so it is directly comparable across all variables. More slack indicates a larger cushion relative to a recessionary environment. As a result, we would like to see as many variables as possible with *increasing* slack. Given the diverse nature of the explanatory variables, it is unusual to see more than 60% of the variables with increasing slack or fewer than 40% of the variables with increasing slack. These extreme values are significant and predictive of the near-term direction of economic growth and *often the equity market*.

The 3-month moving average of the percentage of variables with *increasing* slack increased from 19.2% to 29.5% in June. New evidence of economic weakness (or strength) often shows up first in this timely metric.

The ability to track small variations and trend changes over time illustrates the advantage of monitoring the continuous recession slack index. The new slack variable provides additional insight into the near-term direction of the economy and should be used in conjunction with the median recession slack index.

While it is useful to track the actual recession slack index values and percentage of variables with increasing slack, the diffusion percentages and slack index values are also used to generate the more intuitive probit and logit probability forecasts.

The Trader Edge aggregate recession model averages the estimates from probit and logit models derived from the level and trend in a subset of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack. The aggregate recession model estimates from 1/1/2006 to 7/01/2020 are depicted in Figure 5 below (red line - left vertical axis). The gray shaded regions represent NBER recessions and the blue line reflects the value of the S&P 500 index (right vertical axis). I suggest using a warning threshold of between 20-30% for the aggregate recession model (green horizontal line).

The aggregate recession model probability estimate dropped from 97.1% to 82.5% in June. It is highly likely that the U.S. is *currently* in a recession, but there are signs of "growth" due to the relaxation of COVID-19 restrictions.

The peak-trough model forecasts are different from the recession model and are much more responsive. The peak-trough models estimate the probability of the S&P 500 being between the peak and trough associated with an NBER recession. The S&P 500 typically peaks before recessions begin and bottoms out before recessions end. As a result, it is far more difficult for the peak-trough model to fit this data and the model forecasts have larger errors than the recession model.

The Trader Edge aggregate peak-trough model is a weighted-average of the estimates from a number different neural network models, all of which use the levels and trends of the diffusion and slack indices described above.

The aggregate peak-trough model estimates from 1/1/2006 to 7/01/2020 are depicted in Figure 6 below, which uses the same format as Figure 5, except that the shaded regions represent the periods between the peaks and troughs associated with NBER recessions. The value of the S&P 500 index is also included (in blue - right axis).

The aggregate peak-trough model probability estimate for 7/01/2020 was 100.0%, which was unchanged from the prior month.

The probability forecasts are continuous, but when the probabilities are elevated, modest changes from month to month (even 10-15%) are not unusual. As a result, it can also be useful to use a discrete cutoff value (such as 40-50%) to make a discrete (0/1) recession or peak-trough determination.

I also wanted to note that all of the recession models were designed to identify "typical" recessions, with gradual weakening metrics preceding the recession and gradual strengthening metrics as the economy emerges from the recession. The models use trends in the data, but these trend changes *could be* more rapid due to the discrete nature of economic restrictions imposed by federal and state governments due to COVID-19. This could be a particular challenge for the models when exiting the current recession.

The diffusion indices, slack indices, and the recession model forecasts generally improved in June, with the exception of the peak-trough model. The diffusion index decreased from 18 (69.2%) to 16 (61.5%) in June. The new 0.5-sigma diffusion index dropped from 84.6% to 76.9%. The mean and median recession slack indices were -1.47 and -0.21 respectively. The moving average of explanatory variables with *increasing* slack increased from 19.2% to 29.5% in June. The aggregate recession probability dropped from 97.1% to 82.5%. The peak-trough recession probability remained constant at 100%.

Based on the most recent data, the equity allocation percentage regression model indicates that the expected *annual price return* of the S&P 500 index for the next 10 years remains extremely low at + 0.72% with an expected drawdown in that period of 33% (from 7/1/2020 levels). The low expected future return is due to the sharp rebound in equity prices since March 23rd. Expected future equity returns are still quite low in a historical context, especially given the near-term market, economic, and virus-related risks.

The "Buffett Indicator" regression model currently indicates that the expected *annual price return* of the S&P 500 index for the *next 10 years* is still alarmingly negative (-8.0%), with an expected drawdown in that 10-year period of 64% (from 7/1/2020 levels).

Given the unprecedented and ongoing effects of shutting down the U.S. and global economies, I used a forward estimate of negative 34% annualized GDP "growth" in Q2 (Atlanta GDPNow Cast) when calculating the most recent Buffet Indicator ratio. Similar forward-looking adjustments would be required when calculating P/E or other valuation ratios. The resulting Buffett ratio incorporates forward-looking near-term GDP estimates as well as market data as of 7/1/2020. The most recent Buffett Indicator value was higher than 99% of the historical Buffett Indicator ratios since 1951. History offers compelling evidence that bullish equity positions today will face reduced returns over the coming years.

On a related note, there is also a shocking disconnect between earnings estimates and equity prices. Earlier in the month of July, the S&P 500 Index was down less than 6% from its all-time high. At the same time, bottom-up S&P 500 earnings estimates for 2020 and 2021 had declined by 31% and 20% respectively. Given that earnings are the main drivers of long-term value in the equity market, this divergence adds another material element of risk to the market.

On a related note, in his recent article titled *"This is the simple reason you can’t believe the P/E ratio for the Russell 2000 right now*", Mark Hulbert reported that the current P/E ratio of the Russell 2000 Index (adjusted for negative earnings) was an astounding 132. In other words, Russell 2000 investors are currently paying $132 for every $1 of *forward* earnings (which have historically been notoriously overstated).

Unlike human prognosticators, the Trader Edge recession models are completely objective and have no ego. They are not burdened by the emotional need to defend past erroneous forecasts and will always consistently apply the insights gained from new data.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>I also recently developed a SEIR model for COVID-19, with variables for the magnitude and timing of social distancing restrictions, as well a probabilistic variable for decaying immunity. The results were ominous and are not fully reflected in equity prices, especially after the very large rebound from the March 23rd lows in April and May month-to-date. The growth rate in new Coronavirus cases is only slightly less than my model estimates during the social distancing phase. I documented the model results in an in-depth article titled: "New Coronavirus Model and the Economy," which I posted on April 1, 2020.

This article updates the diffusion indices, recession slack index, aggregate recession model, and aggregate peak-trough model through May 2020. The explanatory variables are now capturing the effects of COVID-19 on the market and on the U.S. economy.

The current *26-variable* model has a diverse set of explanatory variables and is quite robust. Each of the explanatory variables has predictive power individually; when combined, the group of indicators is able to identify early recession warnings from a wide range of diverse market-based, fundamental, technical, and economic sources.

Several of the explanatory variables are market-based. These variables are available in real-time (no lag), which means they respond very quickly to changing market conditions. In addition, they are never revised. This makes the Trader Edge recession model more responsive than many recession models. The current *and* historical data in this report reflect the current model configuration with all *26 variables*.

The Trader Edge diffusion index equals the percentage of independent variables indicating a recession. With the latest changes, there are now a total of 26 explanatory variables, each with a unique look-back period and recession threshold. The resulting diffusion index and the trend in the diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the diffusion index from 1/1/2006 to 6/1/2020 is presented in Figure 1 below (in red - left axis). The gray shaded regions in Figure 1 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

The U.S. economy flirted with entering a recession in early 2016, which was reflected in the deteriorating economic, fundamental, and especially market-based data. The diffusion index, slack index, and recession probability forecasts all captured the weakening conditions. However, the weakness proved to be temporary and the conditions and recession model forecasts improved rapidly.

Preliminary signs of weakness in the diffusion index reemerged in late 2018 and conditions deteriorated rapidly in December and January before rebounding in February through April of 2019 and stabilizing thereafter. However, the slack indices remained depressed throughout 2019.

The number of explanatory variables indicating a recession increased from 17 (65.4%) to 18 (69.2%) in May, which is the highest diffusion index value since the great recession - by far.

Please note that past estimates and index values will change whenever the historical data is revised and/or whenever model improvements are implemented. All current and past forecasts and index calculations are based on the most recent models using the latest revised data from the current data set.

The Trader Edge 0.5-sigma diffusion Index equals the percentage of explanatory variables with Z-scores that are *less than 0.5 standard deviations* above their respective recession thresholds. This new diffusion index is much more sensitive than the standard (zero-sigma) diffusion index. As a result, it provides much more detail on the health of the U.S. economy. The new 0.5-sigma diffusion index and the trend in the new diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the 0.5-sigma diffusion index from 1/1/2006 to 6/1/2020 is presented in Figure 2 below (in red - left axis). The gray shaded regions in Figure 2 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

The percentage of explanatory variables with Z-scores below the 0.5-sigma early warning threshold remained constant at 84.6% in May. The additional level of detail provided by this more continuous and responsive metric is particularly valuable in the months leading up to a recession, especially given the infrequent and more discrete movements of the standard (zero-sigma) diffusion index.

As I noted in past months, the percentage of variables with Z-scores below their respective 0.5 sigma thresholds had been unusually high, especially with the standard diffusion index equal to zero. This significantly reduced the potential cushion to any adverse economic shocks and accelerated the decline due to the Coronavirus.

This new 0.5-sigma diffusion index and the trend in the new diffusion index are now both used directly in the neural network recession models. When combined with the recession slack indices, the new diffusion index provides even greater insight into rapidly changing conditions.

The Trader Edge recession slack index equals the median standardized deviation of the current value of the explanatory variables from their respective recession thresholds. The resulting value signifies the amount of slack or cushion relative to the recession threshold, expressed in terms of the number of standard deviations. Higher slack values signify larger cushions above recessionary threshold levels. While the *median* recession slack index is used in the recession models, I am now including the *mean* recession slack index in the graph as well. As I mentioned above, I am not capping the maximum standardized deviation for each explanatory variable before calculating the mean and median. I use both of these values in the neural network models and in the probit and logit models.

The gray shaded regions in Figure 3 below represent U.S. recessions as defined (after the fact) by the NBER. The *median* recession slack index is depicted in purple and is plotted against the right axis, which is expressed as the number of standard deviations above the recession threshold. The *mean* recession slack index is depicted in blue and is also plotted against the right axis.

The dark-red, horizontal line at 0.50 standard deviations denotes a possible warning threshold for the recession slack index. Many of the past recessions began when the recession slack index crossed below 0.50. Similarly, many of the past recessions ended when the recession slack index crossed back above 0.0.

In May 2020, the median recession slack index was almost unchanged, increasing from -0.38 to -0.36. The mean recession slack index (affected more by outliers - even when capped) dropped sharply from -1.53 to -1.76. Similar to the situation with the 0.5-sigma diffusion index, the mean and median slack indices had been unusually low. This made the U.S. economy particularly vulnerable to any adverse economic shocks, which accelerated the decline due to the Coronavirus. Note, all of these values reflect the new smoothed trend data.

To gain further insight into the slack index, I provide the three-month moving average of the percentage of variables with increasing slack in Figure 4, but I personally monitor the monthly percentages as well.

Slack is a standardized value, so it is directly comparable across all variables. More slack indicates a larger cushion relative to a recessionary environment. As a result, we would like to see as many variables as possible with *increasing* slack. Given the diverse nature of the explanatory variables, it is unusual to see more than 60% of the variables with increasing slack or fewer than 40% of the variables with increasing slack. These extreme values are significant and predictive of the near-term direction of economic growth and *often the equity market*.

The 3-month moving average of the percentage of variables with *increasing* slack decreased from 25.6% to 17.9% in May. New evidence of economic weakness (or strength) often shows up first in this timely metric.

The ability to track small variations and trend changes over time illustrates the advantage of monitoring the continuous recession slack index. The new slack variable provides additional insight into the near-term direction of the economy and should be used in conjunction with the median recession slack index.

While it is useful to track the actual recession slack index values and percentage of variables with increasing slack, the diffusion percentages and slack index values are also used to generate the more intuitive probit and logit probability forecasts.

The Trader Edge aggregate recession model averages the estimates from probit and logit models derived from the level and trend in a subset of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack. The aggregate recession model estimates from 1/1/2006 to 6/01/2020 are depicted in Figure 5 below (red line - left vertical axis). The gray shaded regions represent NBER recessions and the blue line reflects the value of the S&P 500 index (right vertical axis). I suggest using a warning threshold of between 20-30% for the aggregate recession model (green horizontal line).

The aggregate recession model probability estimate remained constant at 97.1% in May. It is a virtual certainty that the U.S. is *currently* in a recession.

The peak-trough model forecasts are different from the recession model and are much more responsive. The peak-trough models estimate the probability of the S&P 500 being between the peak and trough associated with an NBER recession. The S&P 500 typically peaks before recessions begin and bottoms out before recessions end. As a result, it is far more difficult for the peak-trough model to fit this data and the model forecasts have larger errors than the recession model.

The Trader Edge aggregate peak-trough model is a weighted-average of the estimates from a number different neural network models, all of which use the levels and trends of the diffusion and slack indices described above.

The aggregate peak-trough model estimates from 1/1/2006 to 6/01/2020 are depicted in Figure 6 below, which uses the same format as Figure 5, except that the shaded regions represent the periods between the peaks and troughs associated with NBER recessions. The value of the S&P 500 index is also included (in blue - right axis).

The aggregate peak-trough model probability estimate for 6/01/2020 was 90.0%, which declined slightly from last month's revised value 97.8%. It is highly likely that the S&P 500 index is now between the peak and trough associated with a new U.S. recession.

The probability forecasts are continuous, but when the probabilities are elevated, modest changes from month to month (even 10-15%) are not unusual. As a result, it can also be useful to use a discrete cutoff value (such as 50%) to make a discrete (0/1) recession or peak-trough determination.

I also wanted to note that all of the recession models were designed to identify "typical" recessions, with gradual weakening metrics preceding the recession and gradual strengthening metrics as the economy emerges from the recession. The models use trends in the data, but these trends *could be* more rapid due to the discrete nature of economic restrictions imposed by federal and state governments due to COVID-19. This could be a particular challenge for the models when exiting the current recession.

The diffusion indices, slack indices, and the recession model forecasts were relatively stable in May. The diffusion index increased from 17 (65.4%) to 18 (69.2%) in May. The new 0.5-sigma diffusion index was unchanged at 84.6%. The mean and median recession slack indices were -1.76 and -0.36 respectively. The moving average of explanatory variables with *increasing* slack dropped from 25.6% to 17.9% in May. The aggregate recession probability remained at 97.1%. The peak-trough recession probability dropped from 97.8% to 90.0%.

Based on the most recent data, the equity allocation percentage regression model indicates that the expected *annual price return* of the S&P 500 index for the next 10 years remains extremely low at + 1.01% with an expected drawdown in that period of 32% (from 6/1/2020 levels). The low expected future return is due to the sharp rebound in equity prices since March 23rd. Expected future equity returns are still quite low in a historical context, especially given the near-term market, economic, and virus-related risks.

The "Buffett Indicator" regression model currently indicates that the expected *annual price return* of the S&P 500 index for the *next 10 years* is still alarmingly negative (-8.5%), with an expected drawdown in that 10-year period of 65% (from 6/1/2020 levels).

Given the unprecedented and ongoing effects of shutting down the U.S. and global economies, I used a forward estimate of negative 45% annualized GDP "growth" in Q2 when calculating the most recent Buffet Indicator ratio. Similar forward-looking adjustments would be required when calculating P/E or other valuation ratios. The resulting Buffett ratio incorporates forward-looking near-term GDP estimates as well as market data as of 6/1/2020. The most recent Buffett Indicator value was higher than 99% of the historical Buffett Indicator ratios since 1951. History offers compelling evidence that bullish equity positions today will face reduced returns over the coming years.

On a related note, there is also a shocking disconnect between earnings estimates and equity prices. Earlier in the month of June, the S&P 500 Index was down less than 6% from its all-time high. At the same time, bottom-up S&P 500 earnings estimates for 2020 and 2021 had declined by 31% and 20% respectively. Given that earnings are the main drivers of long-term value in the equity market, this divergence adds another material element of risk to the market.

Unlike human prognosticators, the Trader Edge recession models are completely objective and have no ego. They are not burdened by the emotional need to defend past erroneous forecasts and will always consistently apply the insights gained from new data.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>I also recently developed a SEIR model for COVID-19, with variables for the magnitude and timing of social distancing restrictions, as well a probabilistic variable for decaying immunity. The results were ominous and are not fully reflected in equity prices, especially after the very large rebound from the March 23rd lows in April and May month-to-date. The growth rate in new Coronavirus cases is only slightly less than my model estimates during the social distancing phase. I documented the model results in an in-depth article titled: "New Coronavirus Model and the Economy," which I posted on April 1, 2020.

This article updates the diffusion indices, recession slack index, aggregate recession model, and aggregate peak-trough model through April 2020. Most of the explanatory variables are now capturing the effects of COVID-19 on the market and on the U.S. economy - however, there are still a few data series that have more pronounced delays.

The current *26-variable* model has a diverse set of explanatory variables and is quite robust. Each of the explanatory variables has predictive power individually; when combined, the group of indicators is able to identify early recession warnings from a wide range of diverse market-based, fundamental, technical, and economic sources.

Several of the explanatory variables are market-based. These variables are available in real-time (no lag), which means they respond very quickly to changing market conditions. In addition, they are never revised. This makes the Trader Edge recession model more responsive than many recession models. The current *and* historical data in this report reflect the current model configuration with all *26 variables*.

The Trader Edge diffusion index equals the percentage of independent variables indicating a recession. With the latest changes, there are now a total of 26 explanatory variables, each with a unique look-back period and recession threshold. The resulting diffusion index and the trend in the diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the diffusion index from 1/1/2006 to 5/1/2020 is presented in Figure 1 below (in red - left axis). The gray shaded regions in Figure 1 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). Due to the typical NBER delay, I have *preliminarily* shaded the *likely* beginning of a new U.S. recession in March 2020. The value of the S&P 500 index is also included (in blue - right axis).

The U.S. economy flirted with entering a recession in early 2016, which was reflected in the deteriorating economic, fundamental, and especially market-based data. The diffusion index, slack index, and recession probability forecasts all captured the weakening conditions. However, the weakness proved to be temporary and the conditions and recession model forecasts improved rapidly.

Preliminary signs of weakness in the diffusion index reemerged in late 2018 and conditions deteriorated rapidly in December and January before rebounding in February through April of 2019 and stabilizing thereafter. However, the slack indices remained depressed throughout 2019.

Upon detailed examination of the individual economic data series, it is clear that the Government shutdown temporarily affected the economic data in early 2019. The most recent economic data is no longer affected, but the shutdown did temporarily affect the look-back data and the resulting trends.* I initially went back and smoothed the trend data for every economic variable, but the new trend calculation is even more effective at reducing the impact of outliers, which makes it more robust. *Smoothing the look-back data mitigates the impact of all such data outliers now and in the future.

The number of explanatory variables indicating a recession jumped from 11 (42.3%) to 16 (61.5%) in April, which is the highest diffusion index value since the great recession - by far.

*As explained above, it will take another month or so before the effects of the coronavirus are fully reflected in all of the explanatory variables, but most of these variables are already capturing these effects.
*

Please note that past estimates and index values will change whenever the historical data is revised and/or whenever model improvements are implemented. All current and past forecasts and index calculations are based on the most recent models using the latest revised data from the current data set.

The Trader Edge 0.5-sigma diffusion Index equals the percentage of explanatory variables with Z-scores that are *less than 0.5 standard deviations* above their respective recession thresholds. This new diffusion index is much more sensitive than the standard (zero-sigma) diffusion index. As a result, it provides much more detail on the health of the U.S. economy. The new 0.5-sigma diffusion index and the trend in the new diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the 0.5-sigma diffusion index from 1/1/2006 to 5/1/2020 is presented in Figure 2 below (in red - left axis). The gray shaded regions in Figure 2 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis). As explained above, I have *preliminarily* shaded the *likely* beginning of a new U.S. recession in March 2020.

The percentage of explanatory variables with Z-scores below the 0.5-sigma early warning threshold spiked from 73.1% to 80.8% in April, almost exclusively due to the economic effects of Coronavirus. The additional level of detail provided by this more continuous and responsive metric will be invaluable going forward, especially given the infrequent and more discrete movements of the standard (zero-sigma) diffusion index.

As I noted in past months, the percentage of variables with Z-scores below their respective 0.5 sigma thresholds had been unusually high, especially with the standard diffusion index equal to zero. This significantly reduced the potential cushion to any adverse economic shocks and accelerated the decline due to the Coronavirus.

This new 0.5-sigma diffusion index and the trend in the new diffusion index are now both used directly in the neural network recession models. When combined with the recession slack indices, the new diffusion index provides even greater insight into rapidly changing conditions.

The Trader Edge recession slack index equals the median standardized deviation of the current value of the explanatory variables from their respective recession thresholds. The resulting value signifies the amount of slack or cushion relative to the recession threshold, expressed in terms of the number of standard deviations. Higher slack values signify larger cushions above recessionary threshold levels. While the *median* recession slack index is used in the recession models, I am now including the *mean* recession slack index in the graph as well. I use both of these values in the neural network models and in the probit and logit models.

The gray shaded regions in Figure 3 below represent U.S. recessions as defined (after the fact) by the NBER. The *median* recession slack index is depicted in purple and is plotted against the right axis, which is expressed as the number of standard deviations above the recession threshold. The *mean* recession slack index is depicted in blue and is also plotted against the right axis.

The dark-red, horizontal line at 0.50 standard deviations denotes a possible warning threshold for the recession slack index. Many of the past recessions began when the recession slack index crossed below 0.50. Similarly, many of the past recessions ended when the recession slack index crossed back above 0.0.

In April 2020, the median recession slack index plunged from 0.10 to -0.23. The mean recession slack index (affected more by outliers) plummeted from -0.18 to -1.94. Similar to the situation with the 0.5-sigma diffusion index, the mean and median slack indices had been unusually low. This made the U.S. economy particularly vulnerable to any adverse economic shocks, which accelerated the decline due to the Coronavirus. Note, all of these values reflect the new smoothed trend data.

To gain further insight into the slack index, I provide the three-month moving average of the percentage of variables with increasing slack in Figure 4, but I personally monitor the monthly percentages as well.

Slack is a standardized value, so it is directly comparable across all variables. More slack indicates a larger cushion relative to a recessionary environment. As a result, we would like to see as many variables as possible with *increasing* slack. Given the diverse nature of the explanatory variables, it is unusual to see more than 60% of the variables with increasing slack or fewer than 40% of the variables with increasing slack. These extreme values are significant and predictive of the near-term direction of economic growth and *often the equity market*.

The 3-month moving average of the percentage of variables with *increasing* slack decreased sharply from 44.9% to 26.9% in April. The percentage of variables with increasing slack was only 11.5% in April - the lowest monthly value since November 2008. New evidence of economic weakness (or strength) often shows up first in this timely metric.

The ability to track small variations and trend changes over time illustrates the advantage of monitoring the continuous recession slack index. The new slack variable provides additional insight into the near-term direction of the economy and should be used in conjunction with the median recession slack index.

While it is useful to track the actual recession slack index values and percentage of variables with increasing slack, the diffusion percentages and slack index values are also used to generate the more intuitive probit and logit probability forecasts.

The Trader Edge aggregate recession model averages the estimates from probit and logit models derived from the level and trend in a subset of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack. The aggregate recession model estimates from 1/1/2006 to 5/01/2020 are depicted in Figure 5 below (red line - left vertical axis). The gray shaded regions represent NBER recessions and the blue line reflects the value of the S&P 500 index (right vertical axis). As explained above, I have *preliminarily* shaded the *likely* beginning of a new U.S. recession in March 2020. I suggest using a warning threshold of between 20-30% for the aggregate recession model (green horizontal line).

The aggregate recession model probability estimate jumped from 62.0% to 94.4% in April. It is now a virtual certainty that the U.S. is *currently* in a recession.

The peak-trough model forecasts are different from the recession model and are much more responsive. The peak-trough models estimate the probability of the S&P 500 being between the peak and trough associated with an NBER recession. The S&P 500 typically peaks before recessions begin and bottoms out before recessions end. As a result, it is far more difficult for the peak-trough model to fit this data and the model forecasts have larger errors than the recession model.

The Trader Edge aggregate peak-trough model is a weighted-average of the estimates from a number different neural network models, all of which use the levels and trends of the diffusion and slack indices described above.

The aggregate peak-trough model estimates from 1/1/2006 to 5/01/2020 are depicted in Figure 6 below, which uses the same format as Figure 5, except that the shaded regions represent the periods between the peaks and troughs associated with NBER recessions. Due the unavoidable NBER delay, I have *preliminarily* shaded the *likely* peak associated with the beginning of a new U.S. recession in February 2020. The value of the S&P 500 index is also included (in blue - right axis).

The aggregate peak-trough model probability estimate for 5/01/2020 was 96.3%, which is almost unchanged from last months revised value of 96.6%. It is highly likely that the S&P 500 index is now between the peak and trough associated with a new U.S. recession.

The probability forecasts are continuous, but when the probabilities are elevated, modest changes from month to month (even 10-15%) are not unusual. As a result, it can also be useful to use a discrete cutoff value (such as 50%) to make a discrete (0/1) recession or peak-trough determination.

The diffusion indices, slack indices, and the recession model forecasts continued to deteriorate in April. The diffusion index jumped from 11 (42.3%) to 16 (61.5%) in April. The new 0.5-sigma diffusion index climbed from 73.8% to 80.8%. The mean and median recession slack indices both plummeted this month (to -1.94 and -0.23 respectively). The moving average of explanatory variables with *increasing* slack dropped sharply from 44.9% to 26.9% in April. The aggregate recession probability vaulted from 62.0% to 94.4%. The peak-trough recession probability remained extremely high: 96.3%.

Based on the most recent data, the equity allocation percentage regression model indicates that the expected *annual price return* of the S&P 500 index for the next 10 years dropped from +2.0% last month back into negative territory (-0.1%), with an expected drawdown in that period of 35% (from 5/1/2020 levels). The decline in expected future returns is due to the sharp rebound in equity prices since March 23rd. Expected future equity returns are still quite low in a historical context, especially given the near-term market, economic, and geopolitical risks.

The "Buffett Indicator" regression model currently indicates that the expected *annual price return* of the S&P 500 index for the *next 10 years* is still alarmingly negative (-7.5%), with an expected drawdown in that 10-year period of 62% (from 5/1/2020 levels).

Given the unprecedented and ongoing effects of shutting down the U.S. and global economies, I used a forward estimate of negative 34% annualized GDP "growth" in Q2 when calculating the most recent Buffet Indicator ratio. Similar forward-looking adjustments would be required when calculating P/E or other valuation ratios. The resulting Buffett ratio incorporates forward-looking near-term GDP estimates as well as market data as of 5/1/2020. The most recent Buffett Indicator value was higher than 99% of the historical Buffett Indicator ratios since 1951. History offers compelling evidence that bullish equity positions today will face reduced returns over the coming years.

Unlike human prognosticators, the Trader Edge recession models are completely objective and have no ego. They are not burdened by the emotional need to defend past erroneous forecasts and will always consistently apply the insights gained from new data.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>I also recently developed a SEIR model for COVID-19, with variables for the magnitude and timing of social distancing restrictions, as well a probabilistic variable for decaying immunity. The results were ominous and are not fully reflected in equity prices, especially after the 31% rebound from the March 23rd lows to late April. The growth rate in new Coronavirus cases very closely matches my model estimates during the social distancing phase. I documented the model results in an in-depth article titled: "New Coronavirus Model and the Economy," which I posted on April 1, 2020.

This article updates the diffusion indices, recession slack index, aggregate recession model, and aggregate peak-trough model through March 2020. When interpreting the results, please be aware that the economic effects of COVID-19 will not be fully reflected in *all* of the explanatory variables (due to reporting lags in the economic data) until May or even June. However, a number of the variables are already capturing these effects, particularly the market-based variables.

*26-variable* model has a diverse set of explanatory variables and is quite robust. Each of the explanatory variables has predictive power individually; when combined, the group of indicators is able to identify early recession warnings from a wide range of diverse market-based, fundamental, technical, and economic sources.

*and* historical data in this report reflect the current model configuration with all *26 variables*.

The graph of the diffusion index from 1/1/2006 to 4/1/2020 is presented in Figure 1 below (in red - left axis). The gray shaded regions in Figure 1 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). Due to the typical NBER delay, I have *preliminarily* shaded the *likely* beginning of a new U.S. recession in March 2020. The value of the S&P 500 index is also included (in blue - right axis).

Upon detailed examination of the individual economic data series, it is clear that the Government shutdown temporarily affected the economic data. The most recent economic data is no longer affected, but the shutdown did temporarily affect the look-back data and the resulting trends.* I initially went back and smoothed the trend data for every economic variable, but the new trend calculation is even more effective at reducing the impact of outliers, which makes it more robust. *Smoothing the look-back data mitigates the impact of all such data outliers now and in the future. The number of explanatory variables indicating a recession jumped from one (3.8%) to 11 (42.3%) in March, which is the highest diffusion index value since the great recession - by far.

*As explained above, it will take another one to two months before the effects of the coronavirus are fully reflected in all of the explanatory variables, but a number of these variables are already capturing these effects.
*

*less than 0.5 standard deviations* above their respective recession thresholds. This new diffusion index is much more sensitive than the standard (zero-sigma) diffusion index. As a result, it provides much more detail on the health of the U.S. economy. The new 0.5-sigma diffusion index and the trend in the new diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the 0.5-sigma diffusion index from 1/1/2006 to 4/1/2020 is presented in Figure 2 below (in red - left axis). The gray shaded regions in Figure 2 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis). As explained above, I have *preliminarily* shaded the *likely* beginning of a new U.S. recession in March 2020.

The percentage of explanatory variables with Z-scores below the 0.5-sigma early warning threshold spiked from 30.8% to 73.1% in March, almost exclusively due to the economic effects of Coronavirus. The additional level of detail provided by this more continuous and responsive metric will be invaluable going forward, especially given the infrequent and more discrete movements of the standard (zero-sigma) diffusion index.

The Trader Edge recession slack index equals the median standardized deviation of the current value of the explanatory variables from their respective recession thresholds. The resulting value signifies the amount of slack or cushion relative to the recession threshold, expressed in terms of the number of standard deviations. Higher slack values signify larger cushions above recessionary threshold levels. While the *median* recession slack index is used in the recession models, I am now including the *mean* recession slack index in the graph as well. I use both of these values in the neural network models and in the probit and logit models.

*median* recession slack index is depicted in purple and is plotted against the right axis, which is expressed as the number of standard deviations above the recession threshold. The *mean* recession slack index is depicted in blue and is also plotted against the right axis.

In March 2020, the median recession slack index plunged from 0.79 to 0.10. The mean recession slack index (affected more by outliers) plummeted from 0.87 to -0.34. Similar to the situation with the 0.5-sigma diffusion index, the mean and median slack indices had been unusually low. This made the U.S. economy particularly vulnerable to any adverse economic shocks, which accelerated the decline due to the Coronavirus. Note, all of these values reflect the new smoothed trend data.

*increasing* slack. Given the diverse nature of the explanatory variables, it is unusual to see more than 60% of the variables with increasing slack or fewer than 40% of the variables with increasing slack. These extreme values are significant and predictive of the near-term direction of economic growth and *often the equity market*.

The 3-month moving average of the percentage of variables with *increasing* slack decreased sharply from 50.3% to 41.0% in March. The percentage of variables with increasing slack was only 19.2% in March. New evidence of economic weakness (or strength) often shows up first in this timely metric. The sharp decline in February (the previous month) provided the first glimpse of the eventual effects of the coronavirus.

The Trader Edge aggregate recession model averages the estimates from probit and logit models derived from the level and trend in a subset of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack. The aggregate recession model estimates from 1/1/2006 to 4/01/2020 are depicted in Figure 5 below (red line - left vertical axis). The gray shaded regions represent NBER recessions and the blue line reflects the value of the S&P 500 index (right vertical axis). As explained above, I have *preliminarily* shaded the *likely* beginning of a new U.S. recession in March 2020. I suggest using a warning threshold of between 20-30% for the aggregate recession model (green horizontal line).

The aggregate recession model probability estimate jumped from 0.1% to 59.7% in March, which is almost double the suggested early warning level of 30%. Given the lag in many of the economic data series, the probability that the U.S. is *currently* in a recession is now extremely high.

The Trader Edge aggregate peak-trough model is a weighted-average of the estimates from a number of 12 different neural network models, all of which use the levels and trends of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack.

The aggregate peak-trough model estimates from 1/1/2006 to 4/01/2020 are depicted in Figure 6 below, which uses the same format as Figure 5, except that the shaded regions represent the periods between the peaks and troughs associated with NBER recessions. Due the unavoidable NBER delay, I have *preliminarily* shaded the *likely* peak associated with the beginning of a new U.S. recession in February 2020. The value of the S&P 500 index is also included (in blue - right axis).

The aggregate peak-trough model probability estimate for 4/01/2020 was 98.1%, which exploded from last months revised value of 12.4%. Even with the effects of the Coronavirus not fully reflected in the economic data, it is extremely likely that the S&P 500 index is now between the peak and trough associated with a new U.S. recession.

The Coronavirus can be spread by asymptomatic individuals, limiting the effectiveness of precautionary actions. Despite the projected risks of opening the economy too soon, many U.S. states and foreign countries are already relaxing some or even all restrictions on social interaction, even before adequate testing programs have been implemented. With immunity levels far below the 65% threshold required to limit the spread of the virus, this could result in a very large spike in new cases and a new round of restrictions.

Similarly, there is no guarantee that those who have been infected will have or will retain immunity to subsequent infections. I have also read that there are already over 30 different Coronavirus mutations, which could dramatically limit the potential development or effectiveness of a vaccine. The Coronavirus may not be a short-term problem.

Even if the economies were opened prudently and safely, consumers would not return to their past behavior immediately (due to economic and health-related self preservation). Consumer behavior in some products or services will eventually return to some semblance of normalcy, but others may never recover. The generation that lived through the great depression was forever changed by the experience.The longer the Coronavirus pandemic lasts, the more likely we will see similar permanent behavioral changes in consumers.

Finally, the recent negative price of crude oil and the ongoing depressed demand raises the possibility of instability in several countries that are unusually dependent on crude oil. Of particular concern are many countries in the Middle East and Russia.

The March 2020 changes in the diffusion indices, slack indices, and the recession model forecasts were alarming and unprecedented - even with the Coronavirus effects not fully reflected in the economic data. The diffusion index jumped from one (3.8%) to 11 (42.3%) in March. The new 0.5-sigma diffusion index spiked from 30.8% to 73.1%. The mean and median recession slack indices both plummeted this month (to -0.34 and 0.10 respectively). The moving average of explanatory variables with *increasing* slack dropped sharply from 51.3% to 41.0% in March. The aggregate recession probability vaulted from 0.1% to 59.7%. The peak-trough recession probability exploded from 12.4% to 98.1%.

Based on the most recent data, the equity allocation percentage regression model indicates that the expected *annual price return* of the S&P 500 index for the next 10 years moved into positive territory (+2.0%), with an expected drawdown in that period of 30% (from 4/1/2020 levels). Expected price returns are still low in a historical context, especially given the near-term market, economic, and geopolitical risks.

The "Buffett Indicator" regression model currently indicates that the expected *annual price return* of the S&P 500 index for the *next 10 years* is still alarmingly negative (-7.3%), with an expected drawdown in that 10-year period of 62% (from 4/1/2020 levels).

Given the unprecedented and ongoing effects of shutting down the U.S. and global economies, I used forward estimates of annualized GDP declines of 4% in Q1 and 34% in Q2 when calculating the most recent Buffet Indicator ratio. Similar forward-looking adjustments would be required when calculating P/E or other valuation ratios. The resulting Buffett ratio incorporates forward-looking near-term GDP estimates as well as market data as of 4/1/2020. Even with the large equity declines through the end of March, the most recent Buffett Indicator value was higher than 99% of the historical Buffett Indicator ratios since 1951. As is evidenced by the data, a large decline in equity prices does not necessarily imply that stocks are undervalued. History offers compelling evidence that bullish equity positions today will face reduced returns over the coming years.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>I am not an expert on epidemiology, but I have done extensive modeling work. That said, it was far easier to tweak an existing model, rather than starting from scratch. A simple web search yielded a very promising starting point. The article was titled “Social Distancing to Slow the Coronavirus” by Christian Hubbs. I chose this article/model as a starting point because the author included Python code, which expedited the modeling process and allowed me to cross check my results.

Hubbs used a SEIR model, which is an acronym for *Susceptible, Exposed, Infected, Recovered*, which breaks a fixed population down into the above four categories (which sum to 100%). The susceptible group has not yet been exposed to the virus and has no immunity. Exposed and Infected are self-explanatory, but the Recovered group actually includes people who have recovered from the virus (and have immunity), plus the people who have died from the virus. A more appropriate name for this group would probably be “Resolved.” Fortunately, given the relatively low mortality rate for the COVID-19 (1-2%), it is not necessary to separate deaths from the recovered group for modeling purposes.

I will not repeat the Hubbs formulas here, but they use a series of input parameters that are specific to the Coronavirus to describe how the population transitions from one group to the next: Susceptible to Exposed, to Infected, to Recovered. Hubbs also explains how each of these input values are used to calculate the values of intermediate variables that are used directly in the formulas. Please review the Hubbs article if you would like more detail on the exact formulation. I will include the input and intermediate values in the scenario tables below, but I will not provide the formulas here.

As implied by the title of his article, Hubbs cleverly added a social distancing parameter to his model, which reduces social interactions and slows the spread of the virus. This is essential for modeling the effects of social distancing policies and restrictions across the globe.

I made two significant improvements to the Hubbs SEIR model. First, Hubbs applied the social distancing adjustment in perpetuity, which is not practical or realistic. I added an end date variable for the social distancing adjustment, which allowed me to simulate social distancing restrictions of different durations. My social distancing parameter ranges from 0% (standard SEIR model with no social distancing) to 100% (no social interaction). I found this formulation more intuitive, but it is the reverse of the social distancing formulation in the Hubbs article. The effects are the same. However, adding the end date makes a dramatic difference.

Second, I added an immunity period variable, which allows the recovered group to become re-infected probabilistically after a specified period. Preliminary research reports indicate that some patients who have recovered from the Coronavirus have already become re-infected, even though the first *official* reports of the virus date back only two months. This immunity period variable is particularly important in modeling future outbreaks of the virus as the population eventually transitions from Recovered back to Susceptible. These simulations are critical in determining the maximum time period for the development and distribution of a COVID-19 vaccine globally.

There are a number of characteristics that are specific to the Coronavirus, all of which affect how quickly the population transitions from Susceptible to Exposed, to Infected, to Recovered. These values also affect the eventual peak in each of these groups, which is critical to determining whether global health resources would be overrun. The spreadsheet is particularly valuable for simulating alternative virus assumptions, but here are the values I assumed for the initial simulations (see Table 1 below):

Incubation Period: 5 Days

Infectious Period: 10 Days

Hospitalization Rate: 10% of infected population

R0 (pronounced “R Naught:” 3.5 (slightly less than SARS (4.0))

R0 quantifies the contagiousness of an infectious disease. It represents the number of people (without immunity) who will become infected by a single contagious person. The initial SEIR population conditions (S:99.9859%, E:0.0038%, I:0.0076%, R:0.0027%) were estimated from the global Coronavirus population values on March 31, 2020. Finally, I begin by assuming all people in the Recovered group have perpetual immunity and no social distancing.

The results of the above simulation are shown in Graph 1 below. The horizontal or X-axis represents the number of days into the future, with zero representing March 31, 2020. The left-hand (vertical) Y-axis represents the percentage of the global population for each of the SEIR groups, as well as the hospital beds available (bright red) and required (blue). In reality, the hospital bed variables (required and available) to treat Coronavirus patients are proxies for all of the necessary resources in the health care system: gloves, gowns, masks, hospital beds, medication, test kits, ventilators, lab technicians, nurses, doctors, etc. If the *required* resources exceed the *available* resources at any point, people would die in very large numbers. The primary goals in social distancing policy is to ensure these limited health-care resources are not exceeded, and to buy time to develop and distribute a vaccine.

Orange is used to show the percentage of the global population in the Exposed group (left-hand vertical axis) and dark red is used to show the percentage of the population in the infected group (left-hand vertical axis). Finally, the green line (right-hand vertical Y-axis) represents the percentage of the population in the susceptible group (with no immunity). The susceptible value is extremely important in determining whether the virus has been controlled.

The first simulation in Graph 1 above does not include any social distancing; the effects are extreme. The infected group (dark red) peaks on day 87 with almost 24% of the population infected simultaneously. The resulting peak requirement of hospital beds equals 2.39% (blue line) of the population, which exceeds the assumed available beds (bright red line) of 1% by 1.39% (Table 1). The cumulative bed shortage (sum of bed shortage over all scenario days) equals 33.12% (Table 1). This would result in catastrophic loss of life.

The percentage of the population Exposed begins to decline on day 81 and the Susceptible percentage drops below 35% on day 82. This is not a coincidence. The population remains at risk until the percentage of the population Susceptible (without immunity) drops below approximately 35%. There are only two ways this could happen: the population develops immunity in response to infection, or from a successful vaccine.

The percentage of the population Infected begins to decline on day 88, shortly after the peak in Exposures. However, the infected population does not drop below 1% until day 139. To put that in perspective, 1% of the population being infected would still represent over 100 times the current Infected group (0.0076%). Even without direct governmental restrictions on social interaction, healthy individuals would shelter at home out of self-preservation and sick individuals would be forced into quarantine or hospitalization as appropriate. Disruptions to commerce would persist for five brutal months and loss of life would be severe.

The Federal Government has proposed an extension of shelter at home until April 30, 2018, 30 days into the future. Scenario II uses the same assumptions as Scenario I above, but adds 50% social distancing (reducing social interaction by 50%) for a period of 30 days (Table 2 below).

The simulation in Graph 2 below includes 50% social distancing for 30 days. It may surprise you, but the effects are still extreme. In fact, the results are almost identical to Scenario I, they are just delayed. The infected group (dark red) now peaks on day 107 with almost 24% of the population infected simultaneously. The resulting peak requirement of hospital beds still equals 2.39% (blue line) of the population, which again exceeds the assumed available beds (bright red line) of 1% by 1.39% (Table 2). The cumulative bed shortage (sum of bed shortage over all scenario days) equals 33.09% (Table 2). This would still result in catastrophic loss of life.

Short-term social distancing does allow some additional time to increase resources, but does not reduce the Susceptible population significantly. Even after 30 days, the virus would still be lingering in the population and would quickly infect the unprotected Susceptible population after social distancing rules were relaxed. Remember, the global pandemic originated with a single patient zero in China.

In Scenario II, the percentage of the population Exposed begins to decline on day 100 and the Susceptible percentage drops below 35% on day 100 as well.

The percentage of the population Infected begins to decline on day 107, shortly after the peak in Exposures. However, the infected population does not drop below 1% until day 158. Even with 30 days of direct governmental restrictions on social interaction, for the next 128 days, healthy individuals would choose to shelter at home out of self-preservation and sick individuals would be forced into quarantine or hospitalization. Disruptions to commerce would persist for over five months, and the loss of life would be no less severe (barring a vaccine breakthrough or weather-related slowing of virus transmission).

Since 30 days was not sufficient to limit the spread of the virus and loss of life, I tried 120 days. Scenario III uses the same assumptions as Scenario II above, but extends 50% social distancing (reducing social interaction by 50%) for a period of 120 days (Table 3 below).

The simulation in Graph 3 below includes 50% social distancing for 120 days. The results are still almost identical to Scenario II, the peaks are just delayed. The infected group (dark red) now peaks on day 163 with just over 23% of the population infected simultaneously. The resulting peak requirement of hospital beds equals 2.31% (blue line) of the population, which again exceeds the assumed available beds (bright red line) of 1% by 1.31% (Table 3). The cumulative bed shortage (sum of bed shortage over all scenario days) equals 31.07% (Table 3). This would still result in catastrophic loss of life.

Short-term social distancing does allow some additional time to increase resources, but does not reduce the Susceptible population significantly. Even after 120 days, the virus would still be lingering in the population and would quickly infect the unprotected Susceptible population.

In Scenario III, the percentage of the population Exposed begins to decline on day 157 and the Susceptible percentage drops below 35% on day 157 as well.

The percentage of the population Infected begins to decline on day 164, shortly after the peak in Exposures. However, the infected population would not drop below 1% until day 215. Even with 120 days of direct governmental restrictions on social interaction, for the following 95 days, healthy individuals would choose to shelter at home out of self-preservation and sick individuals would be forced into quarantine or hospitalization. Disruptions to commerce would persist for over seven months, and the loss of life would be no less severe.

Since 120 days was still not sufficient, I extended the social distancing period to 215 days. Scenario IV uses the same assumptions as Scenario I-III above, but extends 50% social distancing (reducing social interaction by 50%) for a period of 215 days (Table 4 below).

The simulation in Graph 4 below includes 50% social distancing for 215 days. This time the results are different. The infected group (dark red) is bimodal with the second (higher) peak occurring on day 236 with only 8.2%% of the population infected simultaneously. The resulting peak requirement of hospital beds equals 0.82% (blue line) of the population, which remains under the assumed available beds (bright red line) of 1% by 0.18% (Table 4). The cumulative bed shortage (sum of bed shortage over all scenario days) equals 0.0% (Table 4). This is the first scenario where all patients would have full access to all health care resources, minimizing the loss of life.

In Scenario IV, the percentage of the population Exposed initially begins to decline on day 189, but spikes after the social distancing rules are relaxed on day 215. The Exposed percentage begins to decline again (the second time) on day 228 and the Susceptible percentage drops below 35% on day 225.

The percentage of the population Infected initially begins to decline on day 198, but also spikes after the social distancing rules are relaxed on day 215. The Infected percentage begins to decline again (the second time) on day 237, shortly after the second peak in Exposures. However, the infected population would not drop below 1% until day 295.

Finally, with 215 days of forced governmental restrictions on social interaction, the progression of the virus could be slowed long enough to provide care for all Coronavirus patients. However, disruptions to commerce would persist for almost 10 months.

Scenario V uses the same assumptions as Scenario IV above, but gradually reduces immunity for the Recovered group. As I explained earlier, there is already evidence of reinfection after a few short months.

The simulation in Graph 5 below includes 50% social distancing for 215 days, plus a probabilistic loss of immunity over an average period of two years (730 days). The horizontal axis in Graph 5 now extends out four years (1460 days). The left and right vertical axes are unchanged.

During the initial wave of the virus, the values and progression of the Susceptible, Exposed, and Infected groups are very similar to Simulation IV. However, we now see additional waves of infection occur in subsequent years as the population gradually loses its immunity and the Susceptible percentage grows above the minimum threshold required for the virus to propagate. Based on these assumptions, if a successful vaccine was developed and distributed in the next 500 days or so (directly reducing the Susceptible population and increasing the Recovered or immune population), that should be sufficient to prevent subsequent waves of infection.

It is important to realize that very little is known about COVID-19. As a result, different scenarios should be evaluated based on alternative input assumptions. Scenario VI uses the same assumptions as Scenario V above, except for increasing the infectious period from 10 to 15 days.

The simulation in Graph 6 below includes 50% social distancing for 215 days, plus gradual loss of immunity, with a longer infectious period (15 days). Even with 50% social distancing, the longer infectious period would be catastrophic.

The infected group (dark red) now peaks on day 253 with just over 22% of the population infected simultaneously. The resulting peak requirement of hospital beds equals 2.23% (blue line) of the population, which again exceeds the assumed available beds (bright red line) of 1% by 1.23% (Table 6). The cumulative bed shortage (sum of bed shortage over all scenario days) equals 41.54% (Table 6). This would result in catastrophic loss of life. If a vaccine was not developed, we would again see subsequent waves of infection, but they would be less severe. While the sensitivity to a longer infectious period is startling, it might offer a clue to managing the war against the virus.

While we cannot change the nature of the Coronavirus, it might be possible to take external actions to artificially reduce the infectious period. Scenario VII uses the same assumptions as Scenario VI above, except for decreasing the infectious period to only 5 days.

The simulation in Graph 7 below includes 50% social distancing for 215 days, plus gradual loss of immunity, with a shorter infectious period (5 days). With 50% social distancing for 215 days and a shorter infectious period, the virus is much more manageable. In fact, it would probably be possible to significantly shorten the social distancing period.

The infected group (dark red) now peaks on day 134 with only 5.62% of the population infected simultaneously. The resulting peak requirement of hospital beds equals 0.6% (blue line) of the population, which is well below the assumed available beds (bright red line) of 1%. As a result, the cumulative bed shortage (sum of bed shortage over all scenario days) equals 0.0% (Table 7).

If a vaccine was not developed in time, we would again see subsequent waves of infection, but they would be far less severe. This is clearly the best-case scenario I have presented, but what steps could be taken to artificially shorten the infectious period from 10 days to five days?

Initially, widespread social distancing (shelter at home requirements) would be necessary to reduce growth rate and the number of infected cases. Once this was accomplished, it could be possible to shorten the infectious period by using widespread (universal) and repeated testing, followed by *selective* quarantine of infected individuals, and all people who have come in close contact with them. In other words, if the virus could be discovered much faster, the infectious period could be artificially reduced by immediately placing all affected people in quarantine. This is very similar to the initial approach successfully implemented in South Korea. It would require a massive and efficient testing effort, but it would cost far less than two trillion dollars.

If this approach was effective, it could also eliminate the requirement for widespread shelter at home requirements, allowing individuals to return to work and school. This would minimize the impact on the economy, corporate profits, and job losses.

Unfortunately, the initial reaction of many communities has been to restrict testing to the most at-risk segments of the population (over 65, those with pre-existing health conditions, those requiring hospitalization, etc.). This is the worst possible approach. It will lead to longer infectious periods as many Infected but asymptomatic people continue to interact with the Susceptible population, rapidly spreading the disease. In addition, failing to conduct adequate testing would eliminate the ability to even estimate the percentage of the population in the SEIR groups, which would make it even more challenging to manage the disease through policy and health care initiatives.

Simulation results are only as good as the inputs used and the accuracy of the underlying models. The SEIR model with social distancing is a reasonable representation of virus transmission. However, there is room for improvement. For example, there are really multiple populations, each with different social distancing requirements, demographics, and SEIR population percentages.

If I worked for the CDC or the WHO, I would create separate SEIR models for each county, city, state, and region, each of which would have variable connections to every other entity. As travel limitations were implemented and removed, this would restrict or allow model interaction in real-time between various cities and states, etc. It would also be possible to change the social distancing restrictions in real-time or even model dynamic changes in response to the population percentages of the Infected or Susceptible groups.

For example, it is unreasonable to assume that social distancing in NYC will be as effective as in Alaska, Wyoming, or Montana. It is simply not practical for residents on the 20^{th} floor of a high-rise in NYC to walk up and down 20 flights of stairs, and it is not possible to maintain social distancing in an elevator.

In practice, the social distancing model parameter will equal the *greater* of the federal, state, and local restrictions, and the aggregate personal protective measures adopted by individuals and families. These parameters will change on a daily basis in response to the evolving virus statistics in each location and could be modeled dynamically. The resulting group of SEIR models would be far more realistic, with specific social distancing values that evolve and are specific to each location.

However, for purposes of understanding the duration, breadth, and severity of the global pandemic (and the economic and financial consequences), the SEIR model with social distancing is sufficient.

Before I built my version of the SEIR model with variable social distancing, I was (and am still) calculating the growth rates of Coronavirus cases daily for every county and for the world. While this information is useful, it is backward-looking. To understand how the coronavirus will affect the economy and asset prices, it is essential to use a forward-looking approach that integrates judgement with simulation tools. It is obvious that the markets are currently responding to the daily virus statistics as they become available, but this is short-sighted and ill-advised.

As the SEIR simulation model shows, it is possible to contain the virus temporarily by severely limiting social interaction. However, the if the limits were not maintained for an extended period of time, the benefit would only be temporary and the virus would return with a vengeance (because the Susceptible percentage would still be very high).

Similarly, it is also possible that warmer weather could dramatically slow the spread of the virus. However, even if that is true, the growth rates would explode in the southern Hemisphere in the next few months. Unless we restricted all travel out of the southern Hemisphere in the fall, the virus would return to the northern Hemisphere again late this year (because the Susceptible percentage would still be very high).

The virus will not be completely contained until there is widespread distribution of a successful vaccine or a sufficient percentage of the population becomes immune through infection. In both of these scenarios, the percentage of the Susceptible population would be reduced below the required threshold.

I did not adequately understand the potential evolution of the Coronavirus until I built this model. The model is very basic and only requires six formulas, all of which are provided in the Hubbs article. If you would like to understand and experiment with plausible virus scenarios (and the effect on asset prices), I strongly encourage you to build a similar model in a spreadsheet for experimentation and analysis. Programming is not required and you do not need to use the Python code from the article. I have found this spreadsheet to be invaluable and highly instructive. It is particularly valuable to be able to objectively evaluate different assumptions and policy actions in real-time.

While I hope the model results turn out to be overly pessimistic, I have not been able to construct a more benign scenario using reasonable model assumptions. Instead, the scenarios paint a bleak picture, but offer a glimmer of hope by potentially using widespread and repeated testing to reduce the infectious period until a vaccine could be developed. Knowledge of the virus is growing rapidly and new developments are also unfolding, so there is always some hope.

Barring unforeseen developments, the most likely conclusion is that the severe economic effects resulting from containing the spread of the virus could continue for six months to a year, with possible subsequent waves in the future. This would result in devastating and extended global declines in GDP, widespread business failures, extensive job losses, and long-lasting changes to supply chains, public policies, trade policies, and deficits. This possibility does not appear to be reflected in current asset prices.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>

Before proceeding with the model results this month, I need to explain how and when the coronavirus (COVID-19) will affect the recession model forecasts. The coronavirus is an unprecedented, discrete, exogenous event that will severely affect the global economy and has already roiled the financial markets. While quantitative models like the recession models are invaluable, they are unable to model unique external events, especially one of this speed, breadth, and magnitude. *Even under normal circumstances, integrating judgement with quantitative analysis is essential; in this case, it is even more critical. *

While the World Health Organization (WHO) was the last to know, COVID-19 is a global pandemic. According to experts, there are only two ways to slow the spread of the virus: widespread quarantine and restricting travel and social interaction (China), or widespread testing and selective quarantine / intervention (South Korea). Unfortunately, few countries took these early steps, and the growth rates have exploded. In a single day (March 13^{th} to March 14^{th}), the number of new cases increased by over 10% in 54 different countries and by over 20% in 38 different countries.

In other countries (such as the U.S.) delayed testing suggests that cases are significantly underreported, which has slowed containment efforts. Some countries may be intentionally underreporting the spread of disease for political purposes. COVID-19 is particularly difficult to contain because it apparently can be spread by individuals who are asymptomatic.

Given the limited number of hospital beds, health care professionals, respirators, etc., the only viable plan appears to be to slow the spread of the disease as much as possible to avoid overburdening the limited health care resources and buy additional time for the development of a vaccine. There is also some hope that warmer weather could help contain the virus.

To buy more time, unprecedented steps have already been implemented in various locations across the globe to enforce social distancing and limit human interaction: suspension of cruise ship travel, suspension of air traffic between the U.S. and Europe, suspension of NBA, NHL, and NCAA sports seasons, immediate shift of University classes to online, closing K-12 schools, movie theaters, restaurants, and all indoor gatherings of more than a given number of people, etc.

While these steps are necessary, they will all have serious economic consequences. Corporate revenues have already dropped and will continue to fall further as these steps become more widespread. Unfortunately, many corporate costs are fixed, which means that the effects on corporate earnings will be even more pronounced. Even more serious, many corporations have taken advantage of 10+ years of very low interest rates by greatly expanding their use of debt. This financial engineering inflated earnings (and stock values) when times were good, but many of these companies would be unable to cover their interest payments if this situation persists. This would lead to corporate defaults, job losses, a self-reinforcing downward spiral, and a global recession.

Finally, a 25% decline in equity markets in a little over a month will probably result in a wealth effect, further dampening economic growth. The coronavirus and the market meltdown are the lead stories on every news site and broadcast. This reduces consumer and business confidence, increases uncertainty and risk premiums, which reduces spending and investment, which reduces GDP and corporate earnings, which leads to more layoffs and further market declines.

The economic impact of the containment efforts is real. “Buying the dip” is a popular and effective strategy in a healthy and growing economy, but not in the early stages of a recession. Hypothetically, if stock prices declined by 25% and earnings declined by 50%, equities would not be cheaper; they would be twice as expensive.

Several economists have increased their probability estimates of a U.S. recession to 75% in the next six months. *Unless the coronavirus is contained in the very near future* (eliminating the need for global containment measures), that probability estimate may be too low; a U.S. and global recession would probably be unavoidable. As you will see in the recession model update below, the effects of the coronavirus are not yet evident in the model forecast – and will not be fully captured in the explanatory variables for a number of months.

Furthermore, in a typical recession scenario, several of the economic variables usually lead the market and the overall trend in economy by many months, but that does not happen if the recession is triggered by a large exogenous shock. The unusual immediate reversal of the economic and market trends also limits the effectiveness of the market-sensitive explanatory variables, several of which typically have long lead times.

In the case of the coronavirus, the recession model forecasts can be used to confirm and quantify the impact on the economy, but only with a lag. However, if we do enter a recession and eventually contain the coronavirus, the recession model should be useful in evaluating the probable end of the recession. If containment efforts, warmer temperatures, and/or a vaccine are immediately effective in containing the virus, the recession model would also be useful in quantifying the magnitude of the near-term economic impact and the speed of the recovery. Integration of qualitative factors outside the model will continue to be critically important in the investment process.

I made a number of significant improvements to the recession model in January of 2020. If you missed the January recession model post, or if you would like to review the improvements to the models, please revisit the Recession Model Forecast: 01-01-2020.

This article updates the diffusion indices, recession slack index, aggregate recession model, and aggregate peak-trough model through February 2020. The current *26-variable* model has a diverse set of explanatory variables and is quite robust. Each of the explanatory variables has predictive power individually; when combined, the group of indicators is able to identify early recession warnings from a wide range of diverse market-based, fundamental, technical, and economic sources.

*and* historical data in this report reflect the current model configuration with all *26 variables*.

The graph of the diffusion index from 1/1/2006 to 3/1/2020 is presented in Figure 1 below (in red - left axis). The gray shaded regions in Figure 1 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

Preliminary signs of weakness reemerged in late 2018 and conditions deteriorated rapidly in December and January before rebounding in February through April of 2019 and stabilizing thereafter. Upon detailed examination of the individual economic data series, it is clear that the Government shutdown temporarily affected the economic data. The most recent economic data is no longer affected, but the shutdown did temporarily affect the look-back data and the resulting trends.* I initially went back and smoothed the trend data for every economic variable, but the new trend calculation is even more effective at reducing the impact of outliers, which makes it more robust. *Smoothing the look-back data mitigates the impact of all such data outliers now and in the future. The number of explanatory variables indicating a recession remained at zero (0.0%) in February.

*As explained above, it will take a number of months before the long-term effects of the coronavirus are fully reflected in the trends of the explanatory variables.*

*less than 0.5 standard deviations* above their respective recession thresholds. This new diffusion index is much more sensitive than the standard (zero-sigma) diffusion index. As a result, it provides much more detail on the health of the U.S. economy. The new 0.5-sigma diffusion index and the trend in the new diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the 0.5-sigma diffusion index from 1/1/2006 to 3/1/2020 is presented in Figure 2 below (in red - left axis). The gray shaded regions in Figure 2 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

The percentage of explanatory variables with Z-scores below the 0.5-sigma early warning threshold increased from 30.8% to 34.6% in February. The additional level of detail provided by this more continuous and responsive metric will be invaluable going forward, especially given the infrequent and more discrete movements of the standard (zero-sigma) diffusion index.

As I noted in past months, the percentage of variables with Z-scores below their respective 0.5 sigma thresholds is unusually high, especially with the standard diffusion index equal to zero. I used the entire history to calculate the average 0.5-sigma diffusion index percentage when the zero-sigma diffusion index was zero. The resulting average was only 8.1% - compared to 34.6% at the end of February.

In other words, the percentage of explanatory variables with Z-scores that are within 0.5 sigma of their respective recession thresholds is currently over four times the historical average. This increased vulnerability could significantly accelerate the economic decline if the coronavirus continues to spread.

This new 0.5-sigma diffusion index and the trend in the new diffusion index are now both used directly in the new recession models. When combined with the recession slack indices, the new diffusion index provides even greater insight into rapidly changing conditions.

The Trader Edge recession slack index equals the median standardized deviation of the current value of the explanatory variables from their respective recession thresholds. The resulting value signifies the amount of slack or cushion relative to the recession threshold, expressed in terms of the number of standard deviations. Higher slack values signify larger cushions above recessionary threshold levels. While the *median* recession slack index is used in the recession models, I am now including the *mean* recession slack index in the graph as well.

*median* recession slack index is depicted in purple and is plotted against the right axis, which is expressed as the number of standard deviations above the recession threshold. The *mean* recession slack index is depicted in blue and is also plotted against the right axis.

In February 2020, the median recession slack index decreased from 0.80 to 0.76. The mean recession slack index declined from 0.91 to 0.81. The mean and median slack indices remain relatively close to the 0.5-sigma early warning threshold. This is consistent with the fact that a surprising 34.6% of the explanatory variables are below the 0.5-sigma threshold.

Similar to the situation with the 0.5-sigma diffusion index, the median slack index is unusually low, especially with the standard diffusion index equal to zero. I used the entire history to calculate the average median slack index when the zero-sigma diffusion index was zero. The resulting average was 1.39 standard deviations above the recession threshold - compared to a median slack index of only 0.76 standard deviations at the end of February.

In other words, median slack index is only 0.26 above the early warning threshold - compared to a typical spread of 0.89 standard derivations. As a result, the cushion above the 0.5-sigma early warning threshold is a fraction of its typical value when the diffusion index equals zero.

The slack indices and the trend in the slack indices are now both used directly in the latest recession models. Note, all of these values reflect the new smoothed trend data. The mean and median slack indices would both be expected to decline as the effects of the coronavirus become more evident in the coming months.

To gain further insight into the slack index, I provide the three-month moving average of the percentage of variables with increasing slack in Figure 4, but I personally monitor the monthly percentages as well. The moving average of the percentage of variables with increasing slack and the trend in that moving average are two of the variables used to estimate the probit, logit, and neural network model forecasts.

*increasing* slack. Given the diverse nature of the explanatory variables, it is unusual to see more than 60% of the variables with increasing slack or fewer than 40% of the variables with increasing slack. These extreme values are significant and predictive of the near-term direction of economic growth and *often the equity market*.

The 3-month moving average of the percentage of variables with *increasing* slack decreased sharply from 60.3% to 48.7% in February. The percentage of variables with increasing slack was only 34.6% in February. New evidence of economic weakness (or strength) often shows up first in this timely metric. The sharp decline in February is the first glimpse of the eventual effects of the coronavirus.

The Trader Edge aggregate recession model averages the estimates from probit and logit models derived from the level and trend in a subset of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack. The aggregate recession model estimates from 1/1/2006 to 3/01/2020 are depicted in Figure 5 below (red line - left vertical axis). The gray shaded regions represent NBER recessions and the blue line reflects the value of the S&P 500 index (right vertical axis). I suggest using a warning threshold of between 20-30% for the aggregate recession model (green horizontal line).

The aggregate recession model probability estimate increased from 0.0% to 0.1% in February. Normally, that would indicate that the probability that the U.S. is *currently* in a recession is extremely remote. However, as explained above, that is not the case given the unprecedented exogenous shock of the coronavirus, which is not yet evident in the data.

The Trader Edge aggregate peak-trough model is a weighted-average of the estimates from a number of different neural network models, all of which use the levels and trends of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack.

The aggregate peak-trough model estimates from 1/1/2006 to 3/01/2020 are depicted in Figure 6 below, which uses the same format as Figure 5, except that the shaded regions represent the periods between the peaks and troughs associated with NBER recessions.

The aggregate peak-trough model probability estimate for 3/01/2020 was 0.8%, which decreased by 0.3% from last month's revised value of 1.1%. As explained above, this probability estimate does not reflect the effects of the coronavirus.

Despite the persistent low slack index values, the recession model probability estimates of a U.S. recession have remained quite low, but the effects of the coronavirus are not yet evident in the model forecast – and will not be fully captured in the explanatory variables for a number of months. With that caveat, the diffusion index has remained at zero (0.0%) since the end of April 2019. The new 0.5-sigma diffusion index increased from 30.8% to 34.6% in February. The mean and median recession slack indices both decreased slightly this month; the slack indices remain close to the 0.5-sigma early warning threshold and both are now decreasing. The moving average of explanatory variables with increasing slack dropped sharply from 60.3% to 48.7% in February. The aggregate recession probability increased from 0.0% to 0.1%. The peak-trough recession probability decreased from 1.1% to 0.8%. Again, these probability estimates do not include the effects of the coronavirus.

Even with the low recession model probabilities, there is has been lingering concern with the relatively low recession slack index values and the elevated 0.5-sigma diffusion index, especially given the uncertainty associated with the ongoing trade war, the coronavirus, and the November election. This increased vulnerability is particularly problematic now that the coronavirus has become a global pandemic.

Based on the most recent data, the equity allocation percentage regression model indicates that the expected *annual price return* of the S&P 500 index for the next 10 years is still negative (-0.7%), with an expected drawdown in that period of 36% (from 3/1/2020 levels). Expected price returns are still extremely low in a historical context, especially given the near-term market, economic, and geopolitical risks.

The "Buffett Indicator" regression model currently indicates that the expected *annual price return* of the S&P 500 index for the *next 10 years* is materially negative (-6.5%), with an expected drawdown in that 10-year period of 59% (from 3/1/2020 levels).

History offers compelling evidence that bullish equity positions today will face significant headwinds over the coming years.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>This article updates the diffusion indices, recession slack index, aggregate recession model, and aggregate peak-trough model through January 2019. The current *26-variable* model has a diverse set of explanatory variables and is quite robust. Each of the explanatory variables has predictive power individually; when combined, the group of indicators is able to identify early recession warnings from a wide range of diverse market-based, fundamental, technical, and economic sources.

*and* historical data in this report reflect the current model configuration with all *26 variables*.

The graph of the diffusion index from 1/1/2006 to 2/1/2020 is presented in Figure 1 below (in red - left axis). The gray shaded regions in Figure 1 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

Preliminary signs of weakness reemerged in late 2018 and conditions deteriorated rapidly in December and January before rebounding in February through April and stabilizing thereafter. Upon detailed examination of the individual economic data series, it is clear that the Government shutdown temporarily affected the economic data. The most recent economic data is no longer affected, but the shutdown did temporarily affect the look-back data and the resulting trends.

*less than 0.5 standard deviations* above their respective recession thresholds. This new diffusion index is much more sensitive than the standard (zero-sigma) diffusion index. As a result, it provides much more detail on the health of the U.S. economy. The new 0.5-sigma diffusion index and the trend in the new diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the 0.5-sigma diffusion index from 1/1/2006 to 2/1/2020 is presented in Figure 2 below (in red - left axis). The gray shaded regions in Figure 2 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

The percentage of explanatory variables with Z-scores below the 0.5-sigma early warning threshold remained constant at 26.9% in January. The additional level of detail provided by this more continuous and responsive metric will be invaluable going forward, especially given the infrequent and more discrete movements of the standard (zero-sigma) diffusion index.

As I noted in past months, the percentage of variables with Z-scores below their respective 0.5 sigma thresholds is unusually high, especially with the standard diffusion index equal to zero. I used the entire history to calculate the average 0.5-sigma diffusion index percentage when the zero-sigma diffusion index was zero. The resulting average was only 8.1% - compared to 26.9% at the end of January.

In other words, the percentage of explanatory variables with Z-scores that are within 0.5 sigma of their respective recession thresholds is currently over three times the historical average. This new 0.5-sigma diffusion index and the trend in the new diffusion index are now both used directly in the new recession models.

When combined with the recession slack indices, the new diffusion index provides even greater insight into rapidly changing conditions.

The Trader Edge recession slack index equals the median standardized deviation of the current value of the explanatory variables from their respective recession thresholds. The resulting value signifies the amount of slack or cushion relative to the recession threshold, expressed in terms of the number of standard deviations. Higher slack values signify larger cushions above recessionary threshold levels. While the *median* recession slack index is used in the recession models, I am now including the *mean* recession slack index in the graph as well.

*median* recession slack index is depicted in purple and is plotted against the right axis, which is expressed as the number of standard deviations above the recession threshold. The *mean* recession slack index is depicted in blue and is also plotted against the right axis.

In early-2014, the revised median recession slack index peaked at 1.41, far above the warning level of 0.50. The recession slack index declined significantly in 2015 and reached a low of 0.59 in March 2016, before rebounding over the next few months. For most of 2017 and 2018, the median recession slack index was quite strong, but declined sharply in the fall of 2018. In 2019, the median recession slack index continued to decline, reaching a low of 0.67 at the end of December.

In January 2020, the median recession slack index increased from 0.76 to 0.83. The mean recession slack index increased from 0.90 to 0.93. The mean and median slack indices remain relatively close to the 0.5-sigma early warning threshold. This is consistent with the fact that a surprising 26.9% of the explanatory variables are below the 0.5-sigma threshold.

Similar to the situation with the 0.5-sigma diffusion index, the median slack index is unusually low, especially with the standard diffusion index equal to zero. I used the entire history to calculate the average median slack index when the zero-sigma diffusion index was zero. The resulting average was 1.39 standard deviations above the recession threshold - compared to a median slack index of only 0.83 standard deviations at the end of January.

In other words, median slack index is only 0.33 above the early warning threshold - compared to a typical spread of 0.89 standard derivations. As a result, the cushion above the 0.5-sigma early warning threshold is a fraction of its typical value when the diffusion index equals zero. On a positive note, the short-term trend in the recession slack indices is favorable.

The slack indices and the trend in the slack indices are now both used directly in the latest recession models. Note, all of these values reflect the new smoothed trend data.

To gain further insight into the slack index, I provide the three-month moving average of the percentage of variables with increasing slack in Figure 4, but I personally monitor the monthly percentages as well. The moving average of the percentage of variables with increasing slack and the trend in that moving average are two of the variables used to estimate the probit, logit, and neural network model forecasts.

*increasing* slack. Given the diverse nature of the explanatory variables, it is unusual to see more than 60% of the variables with increasing slack or fewer than 40% of the variables with increasing slack. These extreme values are significant and predictive of the near-term direction of economic growth and *often the equity market*.

The 3-month moving average of the percentage of variables with *increasing* slack increased from 57.7% to 61.5% in January. New evidence of economic weakness (or strength) often shows up first in this timely metric.

The Trader Edge aggregate recession model averages the estimates from probit and logit models derived from the level and trend in a subset of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack. The aggregate recession model estimates from 1/1/2006 to 2/01/2020 are depicted in Figure 5 below (red line - left vertical axis). The gray shaded regions represent NBER recessions and the blue line reflects the value of the S&P 500 index (right vertical axis). I suggest using a warning threshold of between 20-30% for the aggregate recession model (green horizontal line).

The aggregate recession model probability estimate remained constant at 0.0% in January. According to the model, the probability that the U.S. is *currently* in a recession is extremely remote.

The Trader Edge aggregate peak-trough model is a weighted-average of the estimates from a number of different neural network models, all of which use the levels and trends of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack.

The aggregate peak-trough model estimates from 1/1/2006 to 2/01/2020 are depicted in Figure 6 below, which uses the same format as Figure 5, except that the shaded regions represent the periods between the peaks and troughs associated with NBER recessions.

The aggregate peak-trough model probability estimate for 2/01/2020 was 0.9%, which decreased by 1.7% from last month's revised value of 2.6%.

January and February 2016 marked a potential tipping point in U.S. recession risk, but those conditions proved to be temporary. Conditions improved significantly since early 2016, but many explanatory variables remain only marginal above their early warning thresholds.

Despite the low slack index values, U.S. recession risk remains quite low. The diffusion index has remained at zero (0.0%) since the end of April 2019. The new 0.5-sigma diffusion index remained constant at 26.9% in January. The mean and median recession slack indices both increased slightly; the slack indices remain close to the 0.5-sigma early warning threshold, but both are increasing. The moving average of explanatory variables with increasing slack increased from 57.7% to 61.5% in January. The aggregate recession probability remained constant at 0.0%. The peak-trough recession probability decreased from 2.6% to 0.9%.

Even with the low recession model probabilities, there is still some concern with the relatively low recession slack index values and the elevated 0.5-sigma diffusion index, especially given the uncertainty associated with the ongoing trade war, the coronavirus, and the November election. Fortunately, the slack index values and the 0.5-sigma diffusion index values are now used directly in the new recession models and any further deterioration would be captured immediately by the new recession models.

Based on the most recent data, the equity allocation percentage regression model indicates that the expected *annual price return* of the S&P 500 index for the next 10 years is still negative (-0.4%), with an expected drawdown in that period of 36% (from 2/1/2020 levels). Expected price returns are still extremely low in a historical context, especially given the near-term market, economic, and geopolitical risks.

The "Buffett Indicator" regression model currently indicates that the expected *annual price return* of the S&P 500 index for the *next 10 years* is materially negative (-5.7%), with an expected drawdown in that 10-year period of 57% (from 2/1/2020 levels).

Overvalued markets can *always* become more overvalued - especially in the near-term. That said, history offers compelling evidence that bullish equity positions today will face significant headwinds over the coming years.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>I did **NOT** write this book and I have asked Amazon to remove it from my author's page. If you purchased this book in error, please contact Amazon.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>

After completing my MBA derivatives class in December, I devoted the last six weeks to implementing new improvements to the recession models and to setting up a new high-powered Windows 10 laptop to replace my two Windows 7 desktop computers. Due to compatibility issues with Windows 10, this required new neural network software, which I use to make recession forecasts.

I began designing neural networks over 20 years ago, but I do not create new neural network models on a regular basis. As a result, I took this opportunity to get up to speed on the latest developments in AI, particularly deep learning and the corresponding new types of network layers, activation functions, and optimization algorithms. I also took two online classes and experimented with several different software packages. After researching AI platforms, I purchased one AI software suite and am also using a separate deep learning package that is currently available for free (and integrates with Python).

I have made several important improvements to the recession forecasting models. Over the past several years, I added a number of new explanatory variables and dropped a few others. As a result, I did not need to add any new variables at this time. However, I did implement a new approach to quantifying the trend in every explanatory variable. This approach smooths the trend calculation, which further reduces the impact of data outliers – an issue I discussed after the most recent Government shutdown. It also makes all of the trend calculations more robust by reducing the potential for over-fitting.

The original peak-trough neural network models were derived from the initial diffusion index. All of the new models are based on four explanatory variables: the original diffusion index, the 0.5 sigma diffusion index, the median recession slack index, and a moving average of the percentage of explanatory variables with increasing slack. I have discussed each of these metrics in past recession model reports. In addition to the latest values for each of these variables, the trends in these four variables (using the same approach used for the individual variables) are also input into the models. This results in a maximum of eight variables used in the new neural network peak-trough models.

Due to the complexity of the problem, I used neural network models exclusively to build the peak-trough models. As is always advisable with neural networks, I aggregate the results from a number of different neural network models to arrive at the peak-trough forecast. Each neural network has a different architecture, training set, activation function, or optimization algorithm, etc. In addition, I went to great pains to prevent the neural network models from over-fitting the data, including withholding validation and testing data sets and limiting the size of the network.

I also re-estimated the probit and logit functions (from a subset of the eight variables used as inputs for the neural networks) for the standard recession model (which forecasts the probability the U.S. economy is *currently* in a recession). This is a much easier problem than the peak-trough estimation. As a result, neural networks are not required for the standard recession model. The probit and logit functions were sufficiently powerful.

I am excited about the recession model improvements, which combine all of the new metrics I have implemented over the past few years, plus a number of new cutting-edge tools and techniques. All of the current and historical forecasts presented going forward will be based on the new models.

This article updates the diffusion indices, recession slack index, aggregate recession model, and aggregate peak-trough model through December 2019. The current *26-variable* model has a diverse set of explanatory variables and is quite robust. Each of the explanatory variables has predictive power individually; when combined, the group of indicators is able to identify early recession warnings from a wide range of diverse market-based, fundamental, technical, and economic sources.

*and* historical data in this report reflect the current model configuration with all *26 variables*.

The graph of the diffusion index from 1/1/2006 to 1/1/2020 is presented in Figure 1 below (in red - left axis). The gray shaded regions in Figure 1 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

Preliminary signs of weakness reemerged in late 2018 and conditions deteriorated rapidly in December and January before rebounding in February through April and stabilizing thereafter. Upon detailed examination of the individual economic data series, it is clear that the Government shutdown temporarily affected the economic data. The most recent economic data is no longer affected, but the shutdown did temporarily affect the look-back data and the resulting trends.

*less than 0.5 standard deviations* above their respective recession thresholds. This new diffusion index is much more sensitive than the standard (zero-sigma) diffusion index. As a result, it provides much more detail on the health of the U.S. economy. The new 0.5-sigma diffusion index and the trend in the new diffusion index are two of the variables used to estimate the probit, logit, and neural network model forecasts.

The graph of the 0.5-sigma diffusion index from 1/1/2006 to 1/1/2020 is presented in Figure 2 below (in red - left axis). The gray shaded regions in Figure 2 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

The percentage of explanatory variables with Z-scores below the 0.5-sigma early warning threshold increased from 30.8% to 34.6% in December. The additional level of detail provided by this more continuous and responsive metric will be invaluable going forward, especially given the infrequent and more discrete movements of the standard (zero-sigma) diffusion index.

As I noted in past months, the percentage of variables with Z-scores below their respective 0.5 sigma thresholds is unusually high, especially with the standard diffusion index equal to zero. I used the entire history to calculate the average 0.5-sigma diffusion index percentage when the zero-sigma diffusion index was zero. The resulting average was only 8.1% - compared to 34.6% at the end of December.

In other words, the percentage of explanatory variables with Z-scores that are within 0.5 sigma of their respective recession thresholds is currently over four times the historical average. This new 0.5-sigma diffusion index and the trend in the new diffusion index are now both used directly in the new recession models.

When combined with the recession slack indices, the new diffusion index provides even greater insight into rapidly changing conditions.

The Trader Edge recession slack index equals the median standardized deviation of the current value of the explanatory variables from their respective recession thresholds. The resulting value signifies the amount of slack or cushion relative to the recession threshold, expressed in terms of the number of standard deviations. Higher slack values signify larger cushions above recessionary threshold levels. While the *median* recession slack index is used in the recession models, I am now including the *mean* recession slack index in the graph as well.

*median* recession slack index is depicted in purple and is plotted against the right axis, which is expressed as the number of standard deviations above the recession threshold. The *mean* recession slack index is depicted in blue and is also plotted against the right axis.

In early-2014, the revised median recession slack index peaked at 1.42, far above the warning level of 0.50. The recession slack index declined significantly in 2015 and reached a low of 0.59 in March 2016, before rebounding over the next few months. For most of 2017 and 2018, the median recession slack index was quite strong, but declined sharply in the fall of 2018. In 2019, the median recession slack index continued to decline, reaching a low of 0.64 at the end of November.

In December 2019, the median recession slack index increased from 0.64 to 0.75. The mean recession slack index increased from 0.85 to 0.86. As I mentioned above, the mean and median slack indices remain relatively close to the 0.5-sigma early warning threshold. This is consistent with the fact that a surprising 34.6% of the explanatory variables are below the 0.5-sigma threshold.

Similar to the situation with the 0.5-sigma diffusion index, the median slack index is unusually low, especially with the standard diffusion index equal to zero. I used the entire history to calculate the average median slack index when the zero-sigma diffusion index was zero. The resulting average was 1.39 standard deviations above the recession threshold - compared to a median slack index of only 0.75 standard deviations at the end of December.

In other words, median slack index is only 0.25 above the early warning threshold - compared to a typical spread of 0.89 standard derivations. As a result, the cushion above the 0.5-sigma early warning threshold is a fraction of its typical value when the diffusion index equals zero. On a positive note, the short-term trend in the recession slack indices is favorable.

The slack indices and the trend in the slack indices are now both used directly in the latest recession models. Note, all of these values reflect the new smoothed trend data.

To gain further insight into the slack index, I provide the three-month moving average of the percentage of variables with increasing slack in Figure 4, but I personally monitor the monthly percentages as well. The moving average of the percentage of variables with increasing slack and the trend in that moving average are two of the variables used to estimate the probit, logit, and neural network model forecasts.

*increasing* slack. Given the diverse nature of the explanatory variables, it is unusual to see more than 60% of the variables with increasing slack or fewer than 40% of the variables with increasing slack. These extreme values are significant and predictive of the near-term direction of economic growth and *often the equity market*.

The 3-month moving average of the percentage of variables with *increasing* slack decreased from 59.0% to 56.4% in December. New evidence of economic weakness (or strength) often shows up first in this timely metric.

The Trader Edge aggregate recession model averages the estimates from probit and logit models derived from the level and trend in a subset of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack. The aggregate recession model estimates from 1/1/2006 to 1/01/2020 are depicted in Figure 5 below (red line - left vertical axis). The gray shaded regions represent NBER recessions and the blue line reflects the value of the S&P 500 index (right vertical axis). I suggest using a warning threshold of between 20-30% for the aggregate recession model (green horizontal line).

The aggregate recession model probability estimate remained constant at 0.1% in December. According to the model, the probability that the U.S. is *currently* in a recession is extremely remote.

The Trader Edge aggregate peak-trough model is a weighted-average of the estimates from a number of different neural network models, all of which use the levels and trends of the four variables described above: the original diffusion index, the 0.5-sigma diffusion index, the slack indices, and the percentage of variables with increasing slack.

The aggregate peak-trough model estimates from 1/1/2006 to 1/01/2020 are depicted in Figure 6 below, which uses the same format as Figure 5, except that the shaded regions represent the periods between the peaks and troughs associated with NBER recessions.

The aggregate peak-trough model probability estimate for 1/01/2020 was 3.0%, which increased by 0.3% from last month's revised value of 2.7%. While this value is now low, note the recent spike to 18.9% at the end of October.

January and February 2016 marked a potential tipping point in U.S. recession risk, but those conditions proved to be temporary. Conditions improved significantly since early 2016, but many explanatory variables remain only marginal above their early warning thresholds.

Despite the low slack index values, U.S. recession risk remains low and relatively stable. The diffusion index has remained at zero (0.0%) since the end of March 2019. The new 0.5-sigma diffusion index increased from 30.8% to 34.6% in December. The mean and median recession slack indices both increased slightly; both slack indices remain marginally above the early warning threshold. The moving average of explanatory variables with increasing slack decreased from 59.0% to 56.4% in December. The aggregate recession probability remained constant at 0.1%. The peak-trough recession probability increased from 2.7% to 3.0%.

Even with the relatively low recession model probabilities, the limited protection offered by the levels of the recession slack indices continues to be a concern, especially with the weak global economy and ongoing trade war. Fortunately, the slack index values are now used directly in the new recession models and any further deterioration would be captured immediately by the new recession models.

Based on the most recent data, the equity allocation percentage regression model indicates that the expected *annual price return* of the S&P 500 index for the next 10 years is still negative (-0.4%), with an expected drawdown in that period of 36% (from 1/1/2020 levels). Expected price returns are still extremely low in a historical context, especially given the near-term market, economic, and geopolitical risks.

The "Buffett Indicator" regression model currently indicates that the expected *annual price return* of the S&P 500 index for the *next 10 years* is materially negative (-5.9%), with an expected drawdown in that 10-year period of 57% (from 12/1/2019 levels).

Overvalued markets can *always* become more overvalued - especially in the near-term. That said, history offers compelling evidence that bullish equity positions today will face significant headwinds over the coming years.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

]]>*and* historical data in this report reflect the current model configuration with all *26 variables*.

The Trader Edge diffusion index equals the percentage of independent variables indicating a recession. With the latest changes, there are now a total of 26 explanatory variables, each with a unique look-back period and recession threshold. The resulting diffusion index and changes in the diffusion index are used to calculate the probit, logit, and neural network model forecasts.

The graph of the diffusion index from 1/1/2006 to 12/1/2019 is presented in Figure 1 below (in red - left axis). The gray shaded regions in Figure 1 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

However, preliminary signs of weakness reemerged in late 2018 and conditions deteriorated rapidly in December and January before rebounding in February through April and stabilizing thereafter. Upon detailed examination of the individual economic data series, it is clear that the Government shutdown temporarily affected the economic data. The most recent economic data is no longer affected, *but the shutdown was recently affecting the look-back data and the resulting trends, which is why I smoothed the data for every explanatory variable*. Smoothing the look-back data mitigates the impact of all such data outliers now and in the future. The number of explanatory variables indicating a recession dropped from one (3.8%) to zero (0.0%) in November.

Please note that past estimates and index values will change whenever the historical data is revised. All current and past forecasts and index calculations are based on the latest revised data from the current data set.

The Trader Edge 0.5-sigma diffusion Index equals the percentage of explanatory variables with Z-scores that are *less than 0.5 standard deviations* above their respective recession thresholds. This new diffusion index is much more sensitive than the standard (zero-sigma) diffusion index. As a result, it provides much more detail on the health of the U.S. economy. The new diffusion index is not currently being used in any of the regression models.

The graph of the 0.5-sigma diffusion index from 1/1/2006 to 12/1/2019 is presented in Figure 2 below (in red - left axis). The gray shaded regions in Figure 2 below represent U.S. recessions as defined (after the fact) by the National Bureau of Economic Research (NBER). The value of the S&P 500 index is also included (in blue - right axis).

The percentage of explanatory variables with Z-scores below the 0.5-sigma early warning threshold dropped from 30.8% to 23.1% in November. The additional level of detail provided by this (more continuous and responsive) metric will be invaluable going forward, especially given the infrequent and more discrete movements of the standard (zero-sigma) diffusion index.

For example, the percentage of variables below their respective 0.5 sigma thresholds seems unusually high, especially with the standard diffusion index equal to zero. To test this hypothesis, I used the entire history to calculate the average 0.5-sigma diffusion index percentage when the zero-sigma diffusion index was zero. The resulting average was only 8.1% - compared to 23.1% at the end of November. In other words, the percentage of explanatory variables that are within 0.5 sigma of their respective recession thresholds is almost three times the historical average. As I alluded to before, this implies that the the recession probability forecasts derived from the zero-sigma diffusion index are understated; however, the downward trend is favorable. This is an area of promising future research.

When combined with the recession slack indices, the new diffusion index will provide even greater insight into rapidly changing conditions.

*median* recession slack index is used in the recession models, I am now including the *mean* recession slack index in the graph as well.

*median* recession slack index is depicted in purple and is plotted against the right axis, which is expressed as the number of standard deviations above the recession threshold. The *mean* recession slack index is depicted in blue and is also plotted against the right axis.

In early-2014, the revised median recession slack index peaked at 1.48, far above the warning level of 0.50. The recession slack index declined significantly in 2015 and reached a low of 0.53 in February 2016, before rebounding over the next few months. For most of 2017 and 2018, the median recession slack index was quite strong, but declined sharply in the fall. In early 2019, the median recession slack index dropped to a low of 0.54, but that was partially due to the temporary and artificial effects of the Government shutdown.

In November 2019, the median recession slack index increased from 0.75 to 0.78. The mean recession slack index increased from 0.87 to 0.94. As I mentioned above, the mean and median slack indices remain relatively close to the 0.5-sigma early warning threshold. This is consistent with the fact that a surprising 23.1% of the explanatory variables are below the 0.5-sigma threshold.

Similar to the situation with the 0.5-sigma diffusion index, the median slack index seems unusually low, especially with the standard diffusion index equal to zero. To test this hypothesis, I used the entire history to calculate the average median slack index when the zero-sigma diffusion index was zero. The resulting average was 1.40 standard deviations above the recession threshold - compared to a median slack index of only 0.78 standard deviations at the end of November. In other words, median slack index is only 0.28 above the early warning threshold - compared to a typical spread of 0.90 standard derivations. As a result, the cushion above the 0.5-sigma early warning threshold is a fraction of its typical value when the diffusion index equals zero. This provides additional evidence that the recession probability forecasts derived from the zero-sigma diffusion index are understated.

Note, all of these values reflect the new smoothed look-back data. It is important to recognize that median is more reliable than the mean, because it is not affected by extreme values. On a positive note, the trend in the recession slack indices is favorable.

*increasing* slack. Given the diverse nature of the explanatory variables, it is unusual to see more than 60% of the variables with increasing slack or fewer than 40% of the variables with increasing slack. These extreme values are significant and predictive of the near-term direction of economic growth and *often the equity market*.

The 3-month moving average of the percentage of variables with *increasing* slack increased from 51.3% to 56.4% in November. New evidence of economic weakness (or strength) often shows up first in this timely metric.

The ability to track small variations and trend changes over time illustrates the advantage of monitoring the continuous recession slack index. The new slack variable will provide additional insight into the near-term direction of the economy and should be used in conjunction with the median recession slack index.

The Trader Edge aggregate recession model is the average of four models: the probit and logit models based on the diffusion index and the probit and logit models based on the recession slack index. The aggregate recession model estimates from 1/1/2006 to 12/01/2019 are depicted in Figure 5 below (red line - left vertical axis). The gray shaded regions represent NBER recessions and the blue line reflects the value of the S&P 500 index (right vertical axis). I suggest using a warning threshold of between 20-30% for the aggregate recession model (green horizontal line).

The aggregate recession model probability estimate remained decreased from 0.1% to 0.0% in November. According to the model, the probability that the U.S. is *currently* in a recession is extremely remote.

The Trader Edge aggregate peak-trough model equals the weighted-average of nine different models: the probit and logit models based on the diffusion index, the probit and logit models based on the recession slack index, and five neural network models.

The aggregate peak-trough model estimates from 1/1/2006 to 12/01/2019 are depicted in Figure 6 below, which uses the same format as Figure 6, except that the shaded regions represent the periods between the peaks and troughs associated with NBER recessions.

The aggregate peak-trough model probability estimate for 12/01/2019 was 4.3%, which decreased slightly from last month's revised value of 5.2%.

January and February 2016 marked a potential tipping point in U.S. recession risk, but those conditions proved to be temporary. Conditions improved significantly since early 2016, but deteriorated due to the Government shutdown before rebounding in the last few months. The recession risk appeared to increase in January of 2019, but this was largely due to the effects of the Government shutdown.

U.S. recession risk improved slightly in November. The diffusion index decreased from one (3.8%) to zero (0.0%) and the new 0.5-sigma diffusion index declined from 30.8% to 23.1%. The mean and median recession slack indices both increased slightly. Both slack indices remain marginally above the early warning threshold. The moving average of explanatory variables with increasing slack increased from 51.3% to 56.4% in November. The aggregate recession probability dropped from 0.1% to 0.0%. The peak-trough recession probability decreased from 5.2% to 4.3%.

Even with the relatively low recession model probabilities, the limited protection offered by the levels of the recession slack indices continues to be a concern, especially with the weak global economy and ongoing trade war.

Based on the most recent data, the equity allocation percentage regression model indicates that the expected *annual price return* of the S&P 500 index for the next 10 years is still negative (-0.1%), with an expected drawdown in that period of 35% (from 12/1/2019 levels). Expected price returns are still extremely low in a historical context, especially given the near-term market, economic, and geopolitical risks.

The "Buffett Indicator" regression model currently indicates that the expected *annual price return* of the S&P 500 index for the *next 10 years* is materially negative (-5.3%), with an expected drawdown in that 10-year period of 56% (from 12/1/2019 levels).

Overvalued markets can *always* become more overvalued - especially in the near-term. That said, history offers compelling evidence that bullish equity positions today will face significant headwinds over the coming years.

Unlike human prognosticators, the Trader Edge recession model is completely objective and has no ego. It is not burdened by the emotional need to defend past erroneous forecasts and will always consistently apply the insights gained from new data.

Brian Johnson

Copyright 2019 Trading Insights, LLC. All rights reserved.

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