Practical Statistics

This week we are discussing ways that we could use regression analysis in our work place. I am in the investment business so I decided put an idea to the test. When figuring out an appropriate valuation for the stock market, many use what is called a price to earnings ratio (P/E ratio). This attempts to value a company based on a multiple of its earnings. This can also be aggregated up into a benchmark. That is what I will be discussing today, the aggregated-up P/E multiple for the S&P 500 Index.

I believe market valuation is a function of future earnings potential, interest rates, and inflation. I will be concentrating on the relationship between inflation and market value today.

In SPSS I imported 50 years’ worth of 12-month trailing non-GAAP (adjusted for one-time items) earnings for the S&P 500 that I sourced from Bloomberg. I also imported the monthly CPI (inflation index) from 1970 to today from the U.S. Bureau of Labor Statistics (Consumer Price Index, n.d.).

What we should see is an inverse relationship between the two with CPI being my independent variable and valuation (P/E ratio) as my dependent variable. So, the higher (lower) CPI, the lower (higher) the P/E ratio.

I ran a linear regression analysis in SPSS and received the following results.

Figure 1: Linear Regression analysis. Source: SPSS

It has an r-squared of .461. The F score is 516.963 and p<0.01. Looking at the scatterplot, it seems that the relationship between the two is non-linear. So, I ran a few more tests and found that by using the exponential regression function in SPSS had given me better results. Below are the results.

Figure 2: Exponential Regression analysis. Source: SPSS

It would seem that using an exponential regression model with an r-squared of .572 is a better fit. The F score increased to 808.057 and p<.01. If I am interpreting the results correctly, I could use the formula:

Where x is CPI Inflation

So, if the CPI inflation rate went to 5%, then based on the formula the P/E multiple for the S&P 500 would be 14.6x. If CPI Inflation went to 8%, then the P/E multiple would be 11.2.

Given today’s CPI inflation data of 0.6%, the exponential regression model indicates a P/E multiple of 21.4x. The S&P 500 is currently trading at 3271.12 and has earned $131.03 giving it a P/E multiple of 25.0x. This would indicate that the stock market is approximately 14% overvalued.

Joseph S. Kalinowski, CFA

Consumer Price Index (CPI) Databases. (n.d.). Retrieved August 03, 2020, from https://www.bls.gov/cpi/data.htm