Travel•Music•News•Sports•Money•Tech•Fashion
Saturday February 24th 2018

Evaluation of Stock Market Forecasting Models: CAPE Model

Dana Point Harbor, Dana Point CA USA. Mar 2015.
Photo by Standard Travel Fotos

In the last article we evaluated the CER (Constant Expected Return) Model. In this article, we evaluate the CAPE Model.

CAPE Model
CAPE, Cyclically-Adjusted Price Earnings Ratio, is the P/E developed by Robert Shiller of Yale University. CAPE uses the average of the past ten years worth of earnings, P/E10. The forecasting model that we will evaluate actually uses the inverse E10/P, which is the smoothed earnings yield.

This webspage shows the latest value of CAPE: Shiller PE Ratio. For example, when this article was written, P/E10 = 25.22 and the the inverse E10/P = 0.0396511.

The CAPE Model accounts for valuations when predicting stock market returns. The earnings yield varies over time, so the expected return of stocks varies over time. The idea that expected returns, or discount rates, vary over time is more in line with current thinking by financial economists than the Constant Expected Return model. See Presidential Address: Discount Rates by Professor John H. Cochrane.

Validating the CAPE Model
The model is typically presented as the statement: the long-term expected real return of the stock market is the smoothed earnings yield.

Applying the six grading rubrics:

  1. The CAPE model makes a prediction of the discount rate. 1 pt.
  2. The prediction does NOT specify a definite time frame. 0 pts.
  3. There is NO measure of uncertainty or precision. 0 pts.
  4. It does not use future data for earlier predictions, 1 pts.
  5. The prediction is reproducible. 1 pt.
  6. No computational errors. 1 pt.

The total score is only 4 of 6 points, so the CAPE model as typically stated fails validation. What is lacking is a definite time frame and a level of precision.

We will add time frame and precision to make a valid model. To start, choose a time frame of 20 years and add error bars.

Measuring CAPE Model Performance
The CAPE model was coded up in R and the tests run.

20-Year Forecast Performance
For 20-year forecasts, we chose +/-4 percent prediction interval.

Measured Accuracy
Number of Samples = 786 , Trueness = 0.800452 , Precision = 1.64144
Measured Confidence Level
At interval width 8 , passed 412 out of 424 tests. Confidence Level 97.1698 per cent
Figure of Merit
Confidence Level = 97.1698 , Interval Width = 8 , F.O.M = 12.1462

A plot of showing predicted and actual 20-year returns with lower and upper error bars for the period 1950-2014

Predicted and Actual 20-Year Return from 1950 to 2015 for model CAPE.

Over 20-year periods, 97% of the outcomes fell within the +/-4% prediction interval. The performance is fairly good considering the great uncertainty in stock returns. The good performance is reflected in the Figure-of-Merit of 12.15.

10-Year Forecast Performance
Since no time frame is typically specified for CER Model, we’ll test both 10 years and 30 years.

For 10-year forecasts, we kept the same +/-4 percent prediction interval.

Measured Accuracy
Number of Samples = 786 , Trueness = 0.956727 , Precision = 4.49009
Measured Confidence Level
At interval width 8 , passed 317 out of 544 tests. Confidence Level 58.2721 per cent
Figure of Merit
Confidence Level = 58.2721 , Interval Width = 8 , F.O.M = 7.28401

A plot showing predicted and actual 10-year returns with lower and upper error bars for the period 1950-2014

Predicted and Actual 10-Year Return from 1950 to 2015 for model CAPE.

The 10-year forecast is much worse than the 20-year forecast. Only 58% of the outcomes fall with in the prediction interval. Many outcomes were far below the prediction. For forecasts made in 1990, many outcomes far exceeded the predictions thanks to the stock market bubble of the late 1990s.

The lower Figure-of-Merit=7.28 shows the poor performance of the CAPE Model over 10-year periods.

30-Year Forecast Performance
For the 30-year forecast, we used the same +/- 4 percent error bars.

Measured Accuracy
Number of Samples = 786 , Trueness = 0.949083 , Precision = 2.15035
Measured Confidence Level
At interval width 8 , passed 268 out of 304 tests. Confidence Level 88.1579 per cent
Figure of Merit
Confidence Level = 88.1579 , Interval Width = 8 , F.O.M = 11.0197

A plot showing predicted and actual 30-year returns with lower and upper error bars for the period 1950-2014.

Predicted and Actual 30-Year Return from 1950 to 2015 for model CAPE.

The CAPE Model performs worse over 30-year periods than over 20 year periods. Only 88% of the outcomes fell in the +/-4 percent prediction interval.

Summary and Conclusion
The CAPE Forecasting Model was evaluated. The model performed poorly over 10-year periods, but performance improved over 20-year periods. Over 30-year periods, the forecasting model was less successful.

It would appear that taking into account valuations works best at around a 20-year horizon. At shorter periods, the outcomes can vary widely; at longer periods the outcome is less dependent on the initial earnings yield.

Applying the CAPE model to today’s valuation: P/E10 = 25.22, E10/P = 3.97%. With about 97% confidence, CAPE forecasts a 20-year real return of stocks from about 0% to 8% per annum.

Previous Topic: Avivii: Hey Brother

More from category

Evaluation of Stock Market Forecasting Models: Constant Expected Return Model
Evaluation of Stock Market Forecasting Models: Constant Expected Return Model

How well does CER Model forecast stock market returns. [Read More]

Evaluating Stock Market Forecasting Models
Evaluating Stock Market Forecasting Models

A blueprint for evaluating stock market forecasting models. [Read More]

Is the Dividend Discount Model Useful for Forecasting Stock Returns? Part 2
Is the Dividend Discount Model Useful for Forecasting Stock Returns? Part 2

It is unlikely to be useful for forecasting stock returns. [Read More]

Is the Dividend Discount Model Useful for Forecasting Stock Returns?
Is the Dividend Discount Model Useful for Forecasting Stock Returns?

It's useful for understanding the relationship between price, dividends, growth rate and expected return. [Read More]

Advertisement