## New Probit Models: U.S. Recession Risk is Currently Low

Last week I wrote about using statistical tools to forecast recessions and referenced James Picerno, who provided the inspiration for this idea through his articles on the Capital Spectator Economic Trend Index (CS-ETI) and the use of probit models to estimate the probability of a recession.  I used Picerno's explanatory variables as a starting point for developing two new recession forecasting models, which I will describe in this article.

## Review of the Capital Spectator Framework

Before discussing the new models, let's review the Capital Spectator (CS) framework.  Picerno uses 18 variables (see Figure 1 below) to construct a diffusion index. The CS diffusion index represents the percentage of the 18 independent variables that are increasing, which is indicative of an expansion.  If all of the variables were trending higher, the value of the diffusion index would be 1.0 or 100 percent.  If nine of the 18 variable were rising, the value of the diffusion index would be 0.50 or 50 percent.

Figure 1: Capital Spectator Economic Trend Variables

Picerno then uses a probit model to convert the diffusion index values into actual recession probability estimates.  Picerno explains his process:

"I'm using a standard probit model that uses the monthly data for the 3-month average of CS-ETI as the independent variable and NBER's monthly recession readings (0=no recession, 1=recession). I estimate the cumulative normal distribution of the alpha and beta coefficients via a maximum likelihood technique in both Excel and R. It's all relatively conventional statistics."

## Motivation for New Models

As I mentioned last week, I was intrigued by the power of these tools and wanted to experiment with a number of different variable combinations. I was also interested in the possibility of using the recession probability estimates with my existing trading strategies, which are based primarily on technical analysis.

I also have a more practical reason for wanting to develop my own objective, systematic recession forecasting models. Over the past year, I placed undue weight on ECRI's fall 2011 recession call, which caused me to overrule subsequent buy signals from my systematic trading strategies - all of which would have been quite profitable. While these decisions did not generate any actual losses, there were definitely opportunity costs.

ECRI has an excellent reputation and track record, but their methodology is proprietary and it now appears that their 2011 recession call for the U.S. was premature at best and possibly unwarranted. Given my experience over the past year, I could no longer justify relying solely on ECRI's proprietary black box for recession forecasts.  I needed to develop my own systematic, transparent model for forecasting recessions to augment my existing technical strategies.

## New Model Construction

Picerno's work was an excellent place to start.  His model was easy to understand and has performed very well historically.  Nevertheless, I had a few ideas for improvements.  First, instead of building one model, I created two.  The first model predicts the probability of being in a recession, as defined by the National Bureau of Economic Research (NBER).  This is the same dependent variable used by Picerno at CapitalSpectator.com.

The second model was more difficult to estimate, but is potentially more useful.  Markets typically peak before recessions begin and reach their troughs before recessions end.  As a result, the second model attempts to forecast the probability of being between the peak and trough of an NBER-defined recession. Peaks and troughs not associated with NBER recessions were ignored.

To calculate the diffusion index, Picerno uses a 12-month look-back period for every variable, which eliminates possible seasonal adjustment biases, but does not necessarily minimize forecasting errors.  Instead, I calculated the optimal look-back period and threshold for each independent variable in isolation - to best explain the behavior of the dependent variables.  Based on this research, I discarded  several of Picerno's variables and added two new variables that were derived from leading economic indicators.

Picerno's diffusion index (CS-ETI) represents the percentage of independent variables that are trending higher.  I reversed this convention for my models.  My diffusion index represents the percentage of independent variables that are indicating a recession.  Both of my new models use the same diffusion index, which is based on a common set of 15 independent or explanatory variables.

Picerno's probit model uses a single independent variable: "the 3-month average of CS-ETI." Instead, I use the most recent value of the diffusion index, which allows the model to respond faster.

I also added a second independent variable to both of my probit models: the change in the diffusion index over the past several months.  This means that the models can differentiate between entering a recession (when the diffusion index is increasing) and exiting a recession (when the diffusion index is decreasing).  This allows the probit models to respond directly to changes in the diffusion index, which was especially advantageous in estimating the peak-trough model.

## Diffusion Model Results

Figure 2 below is a graph of the resulting diffusion index from 1960 to early November 2012.  The red line is the value of the diffusion index, which uses the left vertical axis.  The gray shaded regions denote the NBER recessions.  Finally, the blue line represents the S&P 500 index, which uses a log scale on the right vertical axis.

The values of the diffusion index are not as intuitive as the probit model probability forecasts, but the historical diffusion index data suggest a possible rule-of-thumb: the probability of an NBER recession is high when the value of the diffusion index exceeds 40 percent. This threshold also eliminates some false signals.  Currently only one out of 15 variables is indicating a recession; the resulting diffusion index value is only 6.7 percent (1/15).

Figure 2: Diffusion Index - Percentage of Variables Indicating Recession

## Recession Probit Model Results

The first probit model uses the value of the diffusion index and the change in the diffusion index over the past few months to estimate the probability that the U.S. economy is currently in a recession.  The historical probit model estimates are depicted in Figure 3 below (red line - left vertical axis).  Again, the gray shaded regions represent NBER recessions and the blue line represents the log value of the S&P 500 index.

The model fits the data extremely well, but you will notice the NBER recessions begin after the S&P 500 peaks and end after the S&P 500 bottoms.  Nevertheless, the model is still a very useful tool.  When the recession probability estimate exceeds 50 percent, a U.S. recession is a virtual certainty. Based on the most recent probit model forecast, the probability that the U.S. is currently in a recession is less than 1.0 percent.

Figure 3: Probit Recession Model 11/2012

## Peak-Trough Probit Model Results

The peak-trough probit model (Figure 4 below) does not fit the data as well as the recession model.  As you would expect, it is much more difficult to predict market peaks and troughs using economic data.  However, a 40-50 percent threshold would eliminate most of the false signals, but would still provide more warning than the probit recession model.

The peak-trough estimates (red line - left vertical axis) represent the probability that the S&P 500 is currently between a peak and trough associated with a NBER recession. These probability estimates should increase before a recession begins and fall before a recession ends.

The gray shaded regions in Figure 4 below represent the peak-trough periods associated with NBER recessions - NOT the recession periods that were depicted in the previous charts.  To determine the peak-trough periods, I identified the highs and lows of the S&P 500 within 6-9 months of the NBER recession periods.

The probability that the S&P 500 is currently between a peak and trough associated with a NBER recession in the U.S. is only 11.1 percent, well below the suggested warning threshold.

Figure 4: Probit Peak-Trough Model 11/2012

## Practical Considerations

I have been careful to note that the above models forecast U.S. recessions, not global recessions.  Until I analyzed the worldwide economic data in more detail, I did not fully appreciate the importance of this distinction.

I have written several posts about the JP Morgan's Global Manufacturing PMI, which is an excellent leading indicator for global recessions.  The weakness in the Global Manufacturing PMI has been prophetic; the majority of OECD (Organization for Economic Co-operation and Development) countries are currently undergoing contractions.

While that raises the risk of a U.S. recession, it is not a foregone conclusion.  Every U.S. recession in the past 50 years occurred during an OECD global recession, but not every OECD global recession resulted in a U.S. recession.  Given the precarious state of the global economy, if a U.S. recession were to occur, it could come on quickly and it could be severe.  As a result, the probit models should be monitored closely for signs of any deterioration.

The above models use revised economic data, which means the forecasts will change when new data revisions are released.   It also means that the historical forecasts presented above would have been different in real-time.  However, I did incorporate appropriate lags into the data, accounting for the release dates for each data series.

The other important caveat is that significant equity market pullbacks are not limited to recessionary environments.  On Black Monday in October 1987, the S&P 500 Index declined by over 20 percent in a single day. And the economy was not in a recession at the time.  Even if cycle forecasts were perfect, they could not prevent trading losses.  However, when combined with technical analysis and market sentiment, they represent a formidable arsenal of decision-making resources.

## Conclusion

Here are several examples of how recession probability forecasts could be combined with technical tools and strategies:

• Verifying recession probabilities are low when entering bullish trend-following trades
• Ensuring recession probabilities are high when entering bearish trend-following trades
• Buying pullbacks when recession risk is low
• Selling market spikes when recession risk is high

I am pleased with the initial models, but I plan to continue to research new explanatory variables that could lead to improved performance.  Now that I have the historical data, it would be very easy to add new variables and re-estimate the model coefficients.

I have also developed neural network (NN) models in the past and would like to attempt to create a NN model to forecast the peak-trough probabilities.  Unfortunately, my previous NN development platform is incompatible with the Windows operating system on my new computer.  If I can find a reasonably-priced NN software package with an adequate feature set, I may pursue this approach as well.

I will closely monitor the forecasts for both of the new probit models going forward and I also plan to continue to track the CS-ETI.  The advantages of having continual U.S. recession and peak-trough probability estimates cannot be overstated.

The effects of recessions are not limited to equities.  Recessions affect all markets: equities, bonds, currencies, energy, metals, grains, meats, and softs. These tools have the potential to increase returns and reduce risk across all sectors and strategies.

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Brian Johnson

I have been an investment professional for over 30 years. I worked as a fixed income portfolio manager, personally managing over \$13 billion in assets for institutional clients. I was also the President of a financial consulting and software development firm, developing artificial intelligence based forecasting and risk management systems for institutional investment managers. I am now a full-time proprietary trader in options, futures, stocks, and ETFs using both algorithmic and discretionary trading strategies. In addition to my professional investment experience, I designed and taught courses in financial derivatives for both MBA and undergraduate business programs on a part-time basis for a number of years. I have also written four books on options and derivative strategies.

### 5 Responses to New Probit Models: U.S. Recession Risk is Currently Low

1. Pete Kasper says:

According to the Congressional Budget Office the probability of a near term recession is directly related to the outcome of the current sequestration problem. Would the probit model address that kind of circumstance.

Best regards

Pete Kasper

• Pete,

Thanks for the insightful and timely question. The answer to your question is both yes and no. The beginning and end of NBER recessions are defined (after the fact) by the trends in the economic data, which should be captured by the probit recession model.

However, if the recession were triggered by an instantaneous rise in taxes and a discrete drop in spending (the fiscal cliff), it would be very difficult if not impossible for the peak-trough probit model to provide any advance warning of the market decline.

A failure to resolve the fiscal cliff would greatly accelerate the normal cyclical transition from expansion to contraction, which would compromise the performance of the peak-trough model and reduce the value of the recession model. Nevertheless, if the recession were long and severe (which it could be given the fragile state of the global economy), both models should still provide some downside protection. They would also be useful in timing the end of the recession, regardless of the cause.

Unfortunately, forecasting models in general cannot deal with exogenous shocks that are not directly captured by the data. This includes terrorist attacks, conflict in the Middle East, political disruptions, exits from the Euro, country defaults, etc.

I should have covered this more fully in the article. Thanks for the question and for your continued interest in Trader Edge.

Regards,

Brian Johnson