The post Trading Option Volatility Now Available on Amazon first appeared on Trader Edge.

]]>The Kindle and Print versions of my new in-depth options book "*Trading Option Volatility: A Breakthrough in Option Valuation - Yielding Practical Insights into Strategy Design, Simulation, Optimization, Risk Management, and Profits*", are now both available on Amazon. *Trading Option Volatility* represents a breakthrough in option valuation, which has profound implications for option strategy design, option and volatility trading, and even for calculating accurate and reliable option risk metrics (Greeks).

I have developed a practical new analytical framework that *eliminates the invalid constant volatility and interest rate assumptions of the Black-Scholes and binomial options models, *and generates theoretically correct and internally consistent, current and future option prices, volatility index futures prices, and risk metrics (Greeks), across all term structures of volatilities and all term structures of interest rates - providing an exploitable edge for option traders.

If you enjoy the new book, please take a few minutes to provide a brief review on Amazon. It would be greatly appreciated. Thank you.

Brian Johnson

Copyright 2021 Trading Insights, LLC. All rights reserved.

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]]>The post Temporary Suspension of Recession Model Posts first appeared on Trader Edge.

]]>Please see TraderEdge.Net for updates on the status of the new book.

Brian Johnson

Copyright 2021 Trading Insights, LLC. All rights reserved.

**AI Volatility Edge Platform: E-Subscription**** **

**Option Income Strategy (OIS) Universal Filter: E-Subscription**

The post Temporary Suspension of Recession Model Posts first appeared on Trader Edge.

]]>The post Recession Model Forecast: 12-01-2020 first appeared on Trader Edge.

]]>Unfortunately, I have been unable to publish the recession model update for the last two months. I have been swamped finalizing and rolling out 32-bit and 64-bit versions of a new comprehensive option volatility forecasting platform called AI Volatility Edge (AIVE). I devoted the last year to designing *AI Volatility Edge* - which is an integrated collection of AI models based on the latest machine-learning (ML) algorithms. The AI Volatility Edge platform is available on a subscription basis for professional and non-professional option traders. Please see my initial post for more information about AI Volatility Edge.

This article updates the diffusion indices, recession slack index, aggregate recession model, and aggregate peak-trough model through November 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.

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 12/1/2020 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 NBER has not yet called the end of the 2020 recession, so I have entered a temporary end date in all graphs below*. The value of the S&P 500 index is also included (in blue - right axis).

COVID-19 and the resulting carnage from closing the economy hit the market in full-force in late February of 2020. The market plummeted in March, but has since staged the fastest recovery on record - surpassing the pre-COVID all-time highs in the S&P 500 and NASDAQ 100 Index.

The number of explanatory variables indicating a recession decreased from 3 (11.5%) to 1 (3.8%) in November, which was due to the continued rebound in the prices of risk-assets as well as the continued improvement in most economic indicators - as the U.S. economy continued to expand.

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 12/1/2020 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 36.4% to 24.1% in November. The additional level of detail provided by this more continuous and responsive metric is particularly valuable in the months leading up to or emerging from 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 before the recession, 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 now 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 November 2020, the median recession slack index increased from +1.63 to +1.79. The mean recession slack index (affected more by outliers - even when capped) jumped from +2.04 to +2.34. Similar to the situation with the 0.5-sigma diffusion index, the mean and median slack indices had been unusually low before the recession. 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 declined slightly from 78.2% to 75.6% in November. These values are remarkably high, reflecting the sharp rebound in the economy. 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 12/01/2020 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 at 0.0% in November. It is highly likely that the U.S. economy has bottomed and already emerged from the recession - albeit at a significantly lower level of economic output.

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 12/01/2020 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 12/01/2020 was 0.0%, which remained constant in November.

It is important 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 *in the COVID-19 recession were much more rapid* due to the discrete nature of economic restrictions imposed by federal and state governments to limit the spread of COVID-19. I was initially concerned that this could be a particular challenge for the models when exiting the current recession, but the models have been much more responsive than initially anticipated and have performed remarkably well in this very unique environment.

The November diffusion indices, slack indices, and the recession model forecasts all indicate the COVID-19 recession is over. The diffusion index decreased from 3 (11.5%) to 1 (3.8%) in November. The new 0.5-sigma diffusion index dropped from 36.4% to 24.1%. The median and mean recession slack indices were +1.79 and +2.34 respectively. The moving average of explanatory variables with *increasing* slack dropped very slightly from a very elevated 78.2% to 75.6 in November. The aggregate recession probability and aggregate peak-trough probabilities were both unchanged in November at 0.0%.

Typically, the environment after emerging from a recession offers very attractive buying opportunities for equities with high risk-adjusted expected returns. Valuation levels are usually very low due to elevated risk premiums. In addition, near-term growth rates following a recession are usually high. Unfortunately, the current environment is very different.

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 -1.26% with an expected drawdown in that period of 38% (from 12/1/2020 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, political, economic, and virus-related uncertainty.

The "Buffett Indicator" is widely followed as an equity valuation metric. I read a recent article that reported the Buffett Indicator is now higher than it has ever been in the past. My own calculations support this conclusion, even when applying the aggressive Atlanta GDP Now Cast growth rate of 11% for Q4 2020 to the indicator calculation. It is never a good idea to extrapolate outside the historical sample data with a regression model. As a result, we cannot put a lot of confidence in the estimated *annual price return* of -11% and estimated drawdown of 73% (from 12/1/2020 levels) for the S&P 500 index over the next 10 years, but the estimates are still alarming.

History offers compelling evidence that bullish equity positions today will face depressed 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.

**AI Volatility Edge Platform: E-Subscription**** **

**Option Income Strategy (OIS) Universal Filter: E-Subscription**

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]]>The post 64-Bit AI Volatility Edge Platform Now Available! first appeared on Trader Edge.

]]>The original AIVE platform is available for use with 32-bit versions of Excel (even if installed on a 64-bit version of Microsoft Windows).

For additional information on the AI Volatility Edge platform, please see the initial AIVE announcement post or the more detailed AI Volatility Edge product page. Both of these pages include links to two AIVE demonstration videos.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

**AI Volatility Edge Platform: E-Subscription**** **

**Option Income Strategy (OIS) Universal Filter: E-Subscription**

The post 64-Bit AI Volatility Edge Platform Now Available! first appeared on Trader Edge.

]]>The post Recession Model Updates Resume Next Month: 12-01-2020 first appeared on Trader Edge.

]]>The AI Volatility Edge Platform required a full year of research and development. This new tool uses the latest in machine learning algorithms to identify and quantify real-time volatility pricing anomalies that can be exploited with strategies based on SPX, NDX, and RUT index options, VIX futures, and VIX options. The platform provides real-time forecasts and relative value analysis across the entire term structure of volatilities.

I plan to resume publishing the monthly recession model in December.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

The post Recession Model Updates Resume Next Month: 12-01-2020 first appeared on Trader Edge.

]]>The post New AI Volatility Edge Platform first appeared on Trader Edge.

]]>Why is volatility so important? Because volatility is synonymous with the value of the option. If you could forecast the future distribution of returns, you would be able to estimate the current value of every option. If you could forecast implied volatility (IV - the market’s estimate of volatility) in the future, you would be able to estimate the future value of volatility indices and the future value of every option. If your estimates of the future return distribution and future implied volatilities diverged materially from the market’s estimates, you could design option and volatility index futures strategies to exploit those targeted pricing anomalies and earn excess risk-adjusted returns.

I have studied, researched, and modeled volatility for my entire 30+ year career as an investment professional: institutional investment manager, Professor of Practice, and proprietary trader. Forecasting future volatility is an extremely complex challenge.

I have devoted the last year to designing a comprehensive
option volatility forecasting platform called *AI Volatility Edge* - which
is an integrated collection of AI models based on the latest machine-learning
(ML) algorithms. The AI Volatility Edge platform is available on a subscription
basis for professional and non-professional traders.

Please see the AI Volatility Edge product page for a comprehensive explanation of the AI Volatility Edge platform, detailed analysis of AIVE forecasts, additional trade examples, and ordering links.

I have extensive experience with Artificial Intelligence (AI) models, dating back to the late-1990s. During that time, I developed and licensed a suite of neural network models (including a volatility model) used by professional investment managers, including hedge funds, international banks, and mutual fund companies.

AI models are extremely powerful – perhaps too powerful. Without expert oversight and design, they will overfit the training data – essentially memorizing the data, rather than generalizing the underlying data relationships. The resulting models will fail in practice, which is very costly in financial modeling. I used the insights gained from 20+ years of AI modeling to force the AIVE models to generalize (and not simply memorize the data):

- Limited number of cause-and-effect explanatory variables (fewer than 10),
- Same variables for every model,
- Testing/Validation data set much larger than training set,
- Single aggregate model for SPX, NDX, and RUT (tripled size of data set),
- Severely limited number of training/optimization iterations, and
- Volatility forecasts are weighted-averages of several AI models.

The interpretation of the AIVE volatility forecasts is straightforward. If volatility forecasts were higher than anticipated, volatility would be expected to rise (suggesting long volatility strategies) and vice versa.

The AI Volatility Edge platform forecasts four different types of future volatility (explained in detail below): annualized Realized Volatility (RV), Volatility index prices (VX), Realized Terminal Volatility (RTV), and Realized Extreme Volatility (REV), each for a specific number of trade days into the future: 0, 5, 10, 15, 21, 31, 42, 63, 84, 105, 126, 189, 252, and 504. The RV, VX, and RTV forecasts are derived from 80 different AI models (three for each time period and type of volatility). The Realized Extreme Volatility forecast is estimated using a regression model based on the AI model forecasts.

Realized Volatility (RV) is the annualized volatility derived from the daily returns of the underlying equity index over a specified number of trading days in the future. It can be compared directly to the implied volatility of at-the-money (ATM) options.

If realized volatility
forecasts were *higher* than the at-the-money (ATM) volatilities of the
equity index options, then ATM options would potentially be *undervalued. *In
this environment, positive Gamma strategies would be desirable to capitalize on
higher than expected realized volatility. If the realized volatility forecasts
were *lower* than the volatilities of ATM equity index options, then ATM
options would potentially be *overvalued*, which would suggest negative
Gamma/Positive Theta strategies.

The AI Volatility Edge platform also forecasts the volatility index prices (VX) a specified number of trading days into the future. These values are directly comparable to the current prices of volatility index futures contracts on the corresponding expiration dates.

If volatility index forecasts
were *higher* than volatility index futures prices, then volatility index
futures would potentially be *undervalued*. Since volatility index prices
are derived from actual options, this is equivalent to saying that implied volatilities
would be expected to rise more than anticipated, which would advocate positive
Vega strategies. If the volatility index forecasts were *lower* than
volatility index futures prices, then volatility index futures would
potentially be *overvalued*. In this environment, future implied
volatilities would be lower than expected, which would suggest negative Vega
strategies. Obviously, volatility index futures or options on volatility index
futures could also be used to capitalize on these prospective VX anomalies as
well.

The AI Volatility Edge platform
also forecasts Realized Terminal Volatility (RTV), which represents the
expected continuously compounded percentage price change of the underlying
equity index from the analysis date to the end of the specified period in the
future. These return forecasts are not annualized and are not directional. In
other words, a 21-trade day RTV forecast of 4% would imply an expected price
change of *plus or minus* 4% (continuously compounded) from now until the
close, 21 trading days in the future.

The Realized Extreme Volatility
(REV) is an estimate of the maximum percentage price change of the underlying
equity index *at any time during the specified period* in the future. As
was the case with the Realized Terminal Volatility, the Realized Extreme
Volatility forecasts are not annualized and are not directional. If the
Realized Terminal Volatility forecast was plus or minus 4% for the next 21
days, the Realized Extreme Volatility forecast might be plus or minus 5.6%
(continuously compounded). The RTV and REV are extremely useful when designing
option strategies, especially selecting strike prices.

There are only four steps in the AI Volatility Edge Analysis: 1) import the input data, 2) generate the model forecasts, 3) enter the current IV and VX futures data, and 4) analyze the results. I have provided links to two demonstration videos of the AI Volatility Edge Analysis below and I strongly encourage you to review the first video before reading the remainder of this document. Seeing a dynamic demonstration of the spreadsheet, while listening to an explanation would help provide a foundation for the written description that follows.

The AI Volatility Edge models use proprietary variables derived from current and historical equity price and volatility index data to generate their forecasts. The AIVE spreadsheets have macros to import previously downloaded data files from Yahoo and the CBOE or from Commodity Systems Inc. (CSI), the data-vendor that I use for all of my trading and research. There is also an option to enter the *intra-day* price and volatility index data, to generate *real-time* volatility forecasts. All of these import options are fully automated with push-button macros in the spreadsheets.

The next step is to choose an analysis date (current or historical) and calculate all of the volatility forecasts – again using a simple push-button macro. The user could quickly compare the volatility forecasts to a specific market implied volatility or volatility index futures price of interest, but it is much more valuable to evaluate the entire term structure of volatilities.

This requires current at-the-money (ATM) implied volatilities for equity options and current volatility index futures data (if available) for the specific equity volatility index

Finally, the Analysis worksheet compares the market IV and futures data with the AI Volatility Edge forecasts in graphical and tabular format to help identify prospective pricing anomalies.

The easiest way to understand the AI Volatility Edge platform is through specific examples (using static screen shots below and in the dynamic video demos). The tables and graphs shown below are an incomplete sample of those available in the AI Volatility Edge spreadsheets. Please see the AIVE product page for more detailed information and for a comprehensive interpretation of the AIVE forecasts with numerous specific trade examples.

The first example uses closing prices from October 1, 2019. Figure 3 below compares the 10/1/2019 AI Realized Volatility forecasts to the implied volatilities for actual S&P 500 equity index options with a range of expiration dates. Using the highlighted row as an example, the ATM S&P 500 option expires on 12/20/2019, 57 trading days in the future. The annualized implied volatility of that option was 16.70% and the annualized Realized Volatility (RV) forecast was only 12.45%. The resulting option was overpriced by 4.25%. Given a standard error of 5.47%, this error equates to a z-score of + 0.78. In other words, the actual implied volatility exceeded the forecast Realized Volatility by 0.78 standard errors. Calculating z-scores for every instrument allows us to compare the relative value across instruments. Finally, a z-score of 0.78 translates to a one-tailed probability (assuming a normal distribution) of 21.9%.

What observations can we make so far? First, the actual implied volatilities exceeded the Realized Volatility forecasts for every ATM option. The entire term structure of ATM implied volatilities was overpriced. Second, the 12/20/2019 expiration was the most overvalued with a z-score of + 0.78. The ATM IV information above is also shown graphically in the AIVE spreadsheets.

This example uses the S&P 500 index, so we also have reliable data for the futures contracts on the corresponding 30-day volatility index – the VIX. Figure 5 below compares the 10/1/2019 AI Volatility Index (VX) forecasts to the VIX futures prices over a range of expiration dates. Using the highlighted row as an example, the VIX futures contract expires on 11/20/2019, 36 trading days in the future. The VIX futures price was 19.18% and the annualized VIX forecast was only 15.90%. The resulting VIX futures contract was overpriced by 3.28%. Given a standard error of 5.14%, this error equates to a z-score of + 0.64. In other words, the actual November 2019 VIX futures price exceeded the 2019 VIX forecast by 0.64 standard errors. Calculating z-scores for every instrument allows us to compare the relative value across instruments. Finally, a z-score of 0.64 translates to a one-tailed probability (assuming a normal distribution) of 26.1%.

Our observations regarding the VIX futures contracts are similar to the ATM IV analysis. The VIX futures contract prices exceeded the AI VIX futures forecasts for six out of seven futures contracts. The current VIX index value (top row – zero days into the future) also exceeded its forecast. The entire term structure of VIX futures contracts was overpriced. The VIX futures contract expiring on 11/20/2019 was the most overpriced with a z-score of + 0.64. Actually, the current VIX index was more overvalued (higher z-score), but the VIX index itself is not directly tradable. The VX forecast analysis above is also shown graphically in the AIVE spreadsheets.

Before we explore specific trades to exploit these prospective pricing anomalies, let’s briefly review the AIVE Historical Volatilities as of 10/1/2019. The historical volatilities for the past five to 504 trade days are illustrated graphically in Figure 7. The values are all annualized, so they are directly comparable. As you can see from the graph, historical volatilities peaked over the past 42 trading days (2 months), then declined sharply before picking up slightly in the last five trading days. Recent volatility had been much lower than the volatilities reflected in ATM options and VIX futures.

The above analysis strongly suggests that the level of volatility priced into ATM equity options and volatility index (VIX) futures on 10/01/2019 was too high – relative to historical relationships between price, implied volatility, and future volatility. This suggests we should attempt to construct trades that have negative Gamma (and therefore positive Theta), which would benefit from a lower than expected level of Realized Volatility, and negative Vega, which would benefit from a prospective decline in implied volatility.

A detailed analysis of trade entries and exits for several trades is available on the AIVE product page, but below is a brief example of a trade appropriate for the overpriced volatility environment on 10/01/2019.

We have identified S&P 500 options expiring on 12/20/2019 and the VIX futures contract expiring on 11/20/2019 as particularly overvalued, so our proposed strategies will focus on these expiration dates in our example strategies.

Let’s begin with an options trade, a simple broken-wing butterfly (BWF), constructed with a put spread and a call spread. The OptionVue Greeks and graphical analysis as of 10/01/2019 are shown in Figures 8 and 9 below, respectively.

The BWF trade required $19,386 of capital (Reg-T margin) and had the desired negative gamma (-0.13), negative Vega (-464.6) and positive Theta (+25.67), which was consistent with the volatility pricing anomalies implied by the AI Volatility Edge Analysis. You will note the Delta was also slightly positive (+10.4). That was intentional. Volatility and equity prices are strongly negatively correlated. Given that we are forecasting a decline in volatility, that implies the bias will be toward higher equity prices. This is why I constructed a slightly bullish broken-wing butterfly trade, to be consistent with our volatility forecast. However, keep in mind that the volatility models are not directional; they forecast volatility, not price direction. It is up to the individual trader to determine how or when to leverage the historical relationship between price and volatility.

I used the AIVE Realized Terminal and Extreme Volatility price chart (Figure 10) below to estimate the potential magnitude of the price changes when selecting the strikes and designing the BWF strategy.

A comprehensive AIVE analysis of the proposed trade exit on 11/01/2019 with updated volatility forecasts is provided on the AIVE product page. In the interest of brevity, I will not include the full 11/01/2019 AIVE analysis here. In short, the AIVE models on 11/01/2019 indicated that the volatility pricing anomalies had corrected materially, which significantly reduced the upside in the trade.

In addition, if we look at OptionVue’s graphical analysis (Figure 13) and Greeks (Figure 14) for the BWF trade on 11/01/2019, we also see that we were at the top-end of the sweet-spot of the payoff distribution (which is undesirable) and Delta had turned negative (-14.61), which was inconsistent with the initial overpriced volatility environment.

When our edge is gone, we should exit the trade. In this case, the trade would have generated a $3,189 profit over the one-month holding period, representing a return on required capital of 16.45%.

A comprehensive analysis of an underpriced volatility environment, including analysis of trade entries and exits for several trades is also included on the AI Volatility Edge product page.

Volatility is arguably the single most important option concept, effectively determining the price of every derivatives instrument. The AI Volatility Edge platform uses the latest in machine learning algorithms to identify and quantify real-time volatility pricing anomalies that can be exploited with strategies based on SPX, NDX, and RUT index options, VIX futures, and VIX options. The AI Volatility Edge platform provides forecasts and relative value analysis across the entire term structure of volatilities.

Comprehensive AI Volatility platforms are rare, even at the institutional level. I am not aware of any other AI Volatility platforms designed by experienced investment professionals that are available on a subscription basis to professional or non-professional investors.

*If you have previously registered on the Trader Edge site, please use the email link you receive after ordering to register again. Please use a different email address during registration to ensure your AIVE PayPal payment profile is linked to your new registration. *

*Please note that a NEW version of the AIVE platform is now available and IS compatible with 64-bit versions of Excel! *

The original AIVE platform is available for use with 32-bit versions of Excel (even if installed on a 64-bit version of Microsoft Windows).

Please see the AI Volatility Edge product page for a comprehensive explanation of the AI Volatility Edge platform, detailed analysis of AIVE forecasts, additional trade examples, and ordering links.

If you have any questions about the AI Volatility Edge e-subscription, or you encounter any problems during the payment or registration process, please contact me via email: BJohnson@TraderEdge.Net.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

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]]>The post No Recession Model Post this Month (10-01-2020) first appeared on Trader Edge.

]]>I hope to release the new AI Volatility model very soon. Please see TraderEdge.Net for updates.

I plan to resume publishing the monthly recession model in November.

Brian Johnson

Copyright 2020 Trading Insights, LLC. All rights reserved.

The post No Recession Model Post this Month (10-01-2020) first appeared on Trader Edge.

]]>The post Recession Model Forecast: 09-01-2020 first appeared on Trader Edge.

]]>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 August 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 9/1/2020 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.

COVID-19 and the resulting carnage from closing the economy hit the market in full-force in late February of 2020. The market plummeted in March, but has since staged the fastest recovery on record - surpassing the pre-COVID all-time highs in the S&P 500 and NASDAQ 100 Index.

The number of explanatory variables indicating a recession decreased from 11 (42.3%) to 10 (38.5%) in August, which was due to the continued rebound in the prices of risk-assets as well as the bottoming of several economic indicators as the U.S. economy continued to expand.

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 9/1/2020 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 69.2% to 50.0% in August. The additional level of detail provided by this more continuous and responsive metric is particularly valuable in the months leading up to or emerging from 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 now 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 August 2020, the median recession slack index increased from +0.04 to +0.63. When this indicator moves from negative to positive, it has historically indicated the end of a recession. The mean recession slack index (affected more by outliers - even when capped) jumped from -0.84 to -0.12. Similar to the situation with the 0.5-sigma diffusion index, the mean and median slack indices had been unusually low before the recession. 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 51.3% to 66.7% in August. In the months of July and August, the percentage of variables with increasing slack spiked to 73.1%. 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 9/01/2020 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 49.1% to 2.7% in August. It is highly likely that the U.S. economy has bottomed and already emerged from the recession - albeit at a significantly lower level of economic output.

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 9/01/2020 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 9/01/2020 was 10.8%, which declined dramatically from the updated July reading of 89.2%.

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. I was initially concerned that this could be a particular challenge for the models when exiting the current recession, but the models appear to be much more responsive than initially anticipated.

The diffusion indices, slack indices, and the recession model forecasts generally improved substantially in August. The diffusion index decreased from 11 (42.3%) to 10 (38.5%) in August. The new 0.5-sigma diffusion index dropped from 69.2% to 50.0%. The mean and median recession slack indices were +0.63 and -0.12 respectively. The moving average of explanatory variables with *increasing* slack increased from 51.3% to 66.7% in August. The aggregate recession probability dropped from 49.1% to 2.7%. The peak-trough recession probability declined from 89.2% to 10.8%.

Typically, the environment after emerging from a recession offers very attractive buying opportunities for equities with high risk-adjusted expected returns. Valuation levels are usually very low due to elevated risk premiums. In addition, near-term growth rates following a recession are usually high. Unfortunately, the current environment is very different.

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 -0.7% with an expected drawdown in that period of 37% (from 9/1/2020 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, political, 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 (-8.3%), with an expected drawdown in that 10-year period of 65% (from 9/1/2020 levels).

Given the unprecedented and ongoing effects of shutting down and partially re-opening the U.S. and global economies, I am using the Atlanta GDPNow Cast when calculating the most recent Buffet Indicator ratio. The latest annualized estimate for Q3 is +31%. 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 9/1/2020. 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 depressed returns over the coming years.

I wrote last month that there was a shocking disconnect between earnings estimates and equity prices. The S&P 500 Index was above its pre-COVID all-time high at the end of July, and jumped another 7% in August. At the same time, the latest bottom-up S&P 500 earnings estimates for 2020 and 2021 had declined by 27% and 16% respectively from their pre-COVID highs. In other words, equity market participants were paying substantially higher prices for dramatically lower earnings - with all of the ongoing risks of COVID-19. This is one of the largest disparities between price and fundamentals that I had ever seen and was reminiscent of the tech bubble in 2000. Given that earnings are the main drivers of long-term value in the equity market, this unprecedented divergence adds another material element of risk to the market. In the month of September, the equity markets have already started to show a few cracks, but the U.S. equity markets remain overvalued.

This type of multiple expansion is typically associated with a reduction in risk premiums, the expectation of extremely rapid growth, or both. Given the near-term risks of COVID-19 and the uncertainty of the upcoming presidential election, it is difficult to defend compressed risk premiums. While near-term earnings growth should be rapid as the U.S. economy reopens, it is much more difficult to make the case that this rapid earnings growth would continue *after* earnings eventually reach their pre-COVID 2021 estimates. The long-term health, behavioral, budgetary, default, educational, productivity, and economic effects of COVID are unknown, but it seems likely that all of these effects could create a drag on future growth, potentially for many years. However, I acknowledge that the level of liquidity the Fed has injected into the market is unprecedented.

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 were paying $132 for every $1 of *forward* earnings (which have historically been notoriously overstated). The true P/E ratio of an equity market index (adjusted for negative earnings) is rarely published and is not typically available to most market participants.

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.

The post Recession Model Forecast: 09-01-2020 first appeared on Trader Edge.

]]>The post Recession Model Forecast: 08-01-2020 first appeared on Trader Edge.

]]>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 July 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 8/1/2020 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.

COVID-19 and the resulting carnage from closing the economy hit the market in full-force in late February of 2020. The market plummeted in March, but has since staged the fastest recovery on record - surpassing the pre-COVID all-time highs in the S&P 500 and NASDAQ 100 Index.

The number of explanatory variables indicating a recession decreased from 16 (61.5%) to 9 (34.6%) in July, which was due to the continued rebound in the prices of risk-assets as well as the bottoming of several economic indicators as the U.S. economy continued to re-open.

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 8/1/2020 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 76.9% to 65.4% in July. The additional level of detail provided by this more continuous and responsive metric is particularly valuable in the months leading up to or emerging from 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 July 2020, the median recession slack index increased from -0.23 to +0.15. When this indicator moves from negative to positive, it has historically indicated the end of a recession. The mean recession slack index (affected more by outliers - even when capped) jumped from -1.41 to -0.43. Similar to the situation with the 0.5-sigma diffusion index, the mean and median slack indices had been unusually low before the recession. 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 30.8% to 52.6% in July. In the month of July alone, the percentage of variables with increasing slack spiked to 76.9%. 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 8/01/2020 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 82.5% to 32.6% in July. It is becoming increasingly likely that the U.S. economy has bottomed and may have already emerged from the 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 8/01/2020 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 8/01/2020 was 76.4%, which declined significantly from the June reading of 100%.

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. I was concerned that this could be a particular challenge for the models when exiting the current recession, but the models appear to be more responsive than initially anticipated.

The diffusion indices, slack indices, and the recession model forecasts generally improved substantially in July. The diffusion index decreased from 16 (61.5%) to 9 (34.6%) in July. The new 0.5-sigma diffusion index dropped from 76.9% to 65.4%. The mean and median recession slack indices were +0.15 and -0.43 respectively. The moving average of explanatory variables with *increasing* slack increased from 30.8% to 52.6% in July. The aggregate recession probability dropped from 82.5% to 32.6%. The peak-trough recession probability declined from 100% to 76.4%.

Typically, the environment after emerging from a recession offers very attractive buying opportunities for equities with high risk-adjusted expected returns. Valuation levels are usually very low due to elevated risk premiums. In addition, near-term growth rates following a recession are usually high. Unfortunately, the current environment is very different.

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 -0.02% with an expected drawdown in that period of 35% (from 8/1/2020 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 (-7.7%), with an expected drawdown in that 10-year period of 63% (from 8/1/2020 levels).

Given the unprecedented and ongoing effects of shutting down and partially re-opening the U.S. and global economies, I am using the Atlanta GDPNow Cast when calculating the most recent Buffet Indicator ratio. The latest annualized estimate for Q3 is +25.6%. 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 8/1/2020. 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 depressed returns over the coming years.

On a related note, there is also a shocking disconnect between earnings estimates and equity prices. As I write this, the S&P 500 Index is above its pre-COVID all-time high. At the same time, the latest bottom-up S&P 500 earnings estimates for 2020 and 2021 have declined by 27% and 16% respectively from their pre-COVID highs. In other words, equity market participants are currently paying a higher price for dramatically lower earnings, with all of the ongoing risks of COVID-19. This is one of the largest disparities between price and fundamentals that I have ever seen and is reminiscent of the tech bubble in 2000. Given that earnings are the main drivers of long-term value in the equity market, this unprecedented divergence adds another material element of risk to the market.

This type of multiple expansion is typically associated with a reduction in risk premiums, the expectation of extremely rapid growth, or both. Given the near-term risks of COVID-19 and the uncertainty of the upcoming presidential election, it is difficult to defend compressed risk premiums. While near-term earnings growth should be rapid as the U.S. economy reopens, it is much more difficult to make the case that this rapid earnings growth would continue *after* earnings eventually reach their pre-COVID 2021 estimates. The long-term health, behavioral, budgetary, default, productivity, and economic effects of COVID are unknown, but it seems likely that all of these effects could create a drag on future growth, potentially for many years. However, I acknowledge that the level of liquidity the Fed has injected into the market is unprecedented - and bubbles can continue for extended periods before they pop.

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). The true P/E ratio of an equity market index (adjusted for negative earnings) is rarely published and is not typically available to most market participants.

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.

The post Recession Model Forecast: 08-01-2020 first appeared on Trader Edge.

]]>The post Recession Model Forecast: 07-01-2020 first appeared on Trader Edge.

]]>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.

*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 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.

*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.

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.

*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 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.

*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 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 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).

Brian Johnson

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