### The S&P 500 Is Not Expensive According to the Kasriel Valuation Model

In each of the first three quarters of 2017, there have been double-digit year-over-year percentage increases in the quarterly average level of the S&P 500 stock-price index – 19.3% in Q1, 15.5% in Q2 and 14.2% in Q3. Although there were year-over-year contractions in the S&P 500 index of 5.6% in Q1:2016 and 1.3% in Q2:2016, there has not been a year-over-year contraction of 10% or more since Q3:2009. With the S&P 500 stock-price index hitting record highs in recent weeks and no contraction of 10% or more in it in eight years, one could reasonably wonder if large cap stocks have gotten expensive. In terms of the Kasriel stock market valuation model, the S&P 500 stock price index was *not* expensive in an historical context as of this past third quarter.

The essence of the Kasriel stock market valuation model is a calculated *theoretical* market capitalization of a group of stocks compared with the *actual* market capitalization. If the actual market cap is larger than the theoretical market cap, then the stock market group is overvalued. If the actual market cap is less than the theoretical market cap, then the stock market group is undervalued.

The theoretical market cap is calculated by discounting corporate earnings by a corporate bond yield. Thus, the theoretical market cap varies positively with the level of earnings and negatively with the level of bond yields. For corporate earnings, I have used quarterly observations of aggregate S&P 500 *reported* earnings, starting in 1964:Q1. (I would have preferred to use *operating *earnings, earnings adjusted for one-time special events. But in my database, operating earnings data do not begin until 1988:Q1.) I smooth the earnings series with some highfalutin econometric technique called the Hodrick-Prescott filter. The Hodrick-Prescott filter is supposed to remove the cyclical component of a series. Think of it as less arbitrary technique than a moving average, such as Shiller’s use of a 10-year moving average. Why 10 years? Why not 9 or 11 years? So, my theoretical S&P 500 market cap is Hodrick-Prescott filtered quarterly aggregate S&P earnings discounted by the quarterly average level of the corporate BAA bond yield. After calculating the theoretical market cap of the S&P 500 stocks, I calculate the percentage that the actual S&P market cap is over or under the theoretical S&P 500 market cap.

The results of these calculations are plotted in Chart 1. According to the Kasriel model, S&P 500 stocks in the aggregate were overvalued by 4.4% in 2017:Q3. Compared to the average overvaluation of 36.1% over the entire sample period, a 4.4% overvaluation is small potatoes. The level of the corporate bond yield used to discount smoothed annualized earnings of $899.1 billion in this past third quarter was 4.35%. Given the same level of annualized earnings, a 100 basis point increase in the corporate bond yield would put third-quarter S&P 500 stocks 28.4% overvalued, still short of the sample average of 36.1% overvaluation.

**Chart 1**

Testing the lead/lag relationship between the Kasriel valuation model and the year-over-year percent change in the S&P 500 stock price index shows that the highest negative correlation (-.20) between the two series is obtained when the over/under valuation measure is *lagged* by five quarters. So, the *current* quarter’s over/under valuation estimate has its greatest effect on the year-over-change in the S&P 500 stock price index five quarters in the *future*. Let’s plot the year-over-year percent change in the quarterly average of the S&P 500 stock price index against the Kasriel model of over/under valuation estimates *lagged five quarters *to see how the Kasriel model comports with the behavior of stock prices. These data are plotted in Chart 2.