The nonlinear relationship between the PE and PEG ratios

Summary

- The price/earnings (PE) and the price/earnings to growth (PEG) ratios are widely used measures of company valuation.

- Generally speaking, a PE of 12 is considered indicative of fair value, and so is a PEG of 1.

- These are gross simplifications that would apply only to a company whose annual earnings growth rate is about 10 percent.

- For example, a company whose earnings are growing at an annual 75 percent rate would be fairly valued with a PE of 260.47 and a PEG of 3.47.

The PE ratio

One can easily obtain the price/earnings (PE) ratio for any publicly traded company from Yahoo Finance (). The PE ratio is one of the most widely used measures of company valuation (). It is calculated by dividing a company's share price by its earnings per share. Essentially, the PE ratio reflects a company’s value, as seen by the stock market, divided by its net profits.

Earnings growth and the PEG ratio

The price/earnings to growth (PEG) ratio can also be easily obtained from Yahoo Finance. It is calculated as the PE ratio divided by the expected annual earnings growth rate (). At the time of this writing, the PEG value shown on Yahoo Finance (noted as “PEG Ratio (5 yr expected)”) reflects the expected annual earnings growth rate for the next 5 years. With both the PE and PEG ratios, one can obtain the expected annual earnings growth by dividing the PE by the PEG.

The nonlinear relationship between the PE and PEG ratios

Let us assume that a good investment today would give you the same return in 10 years as a very low-cost fund tracking the S&P 500 would have given in the past 10 years. Such an investment would turn US$ 10,000 into US$ 32,272 in a period of 10 years. For the rationale behind these assumptions, see a previous post where I introduce a simulation-based approach for company valuation ().

The table below shows the simulation-based fair value PE and PEG ratios associated with various annual earnings growth rates. The lowest growth rate shown is minus 50 percent, which would refer to a company whose net profits are going down by 50 percent every year. The highest growth rate shown is 100 percent, for a company whose net profits are doubling every year.

Generally speaking, a PE of 12 is considered indicative of fair value, and so is a PEG of 1. As you can see, these are gross simplifications that would apply only to a company whose annual earnings growth rate is about 10 percent. By contrast, a company whose earnings are contracting at a 2 percent annual rate would be fairly valued with a PE of 6.51 and a PEG of -3.25. At the other end of the growth rate scale, a company whose earnings are growing at an annual 75 percent rate would be fairly valued with a PE of 260.47 and a PEG of 3.47.

The bottom line: the relationship between the PE and PEG ratios is nonlinear. This is why valuations sometimes look odd to those thinking in terms of a PE of 12 and a PEG of 1. High growth companies, often in cutting-edge technology areas, may be fairly valued at PEs that look astronomical and PEGs that are significantly greater than 1.

A simulation-based valuation of the S&P 500: October 2023

The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.

The numbers on the left consider a more benign scenario: S&P 500 earnings in 2023 are up by 3.20% from the previous year, and the 10-year U.S. Treasury yield is at 4.91%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 1.10%, and the 10-year U.S. Treasury yield is at 5.47%.

The second scenario takes us to a fair price for the S&P 500 of 2,015.07, which is 58.18% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.

A simulation-based valuation of the S&P 500: September 2023

The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.

The numbers on the left consider a more benign scenario: S&P 500 earnings in 2023 are up by 3.20% from the previous year, and the 10-year U.S. Treasury yield is at 4.62%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 1.20%, and the 10-year U.S. Treasury yield is at 5.48%.

The second scenario takes us to a fair price for the S&P 500 of 2,012.28, which is 58.24% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.

How many times until a coincidence becomes a pattern? The case of yield curve inversions preceding recessions and the magical number 7

Let us say that a coincidence involving two events, where one seems to predict the other, happens a number of times. How many times until it can be considered not only a coincidence, but a statistically significant pattern? We propose a framework to answer this question. Using the framework, we find that the number of times required is 7. We illustrate the practical application of our framework in the context of a very important phenomenon: When the percentage difference between 10-year and 3-month U.S. Treasury yields falls below zero, a U.S. recession appears to occur within the next 18 months.

All of this is laid out in much more detail in the article linked below. In this article, we have established the minimum number of times required for the inversion-recession phenomenon to be deemed more than a coincidence, and rather a statistically significant pattern. That number is 7. Therefore, given that since 1970 we have observed 8 instances of the inversion-recession phenomenon, we can conclude that this not a coincidence, and that it is in fact a statistically significant pattern.

https://www.tandfonline.com/doi/full/10.1080/03610926.2023.2232908

The video below complements this post, by briefly addressing some of the issues discussed in the post.

The big difference between today and the 1980s: Valuations

The figure below shows two main graphs. The graph at the top shows the Fed funds rate from 1978 to 1987, approximately the period in which Paul Volcker served as Chair of the Federal Reserve. Rate hikes preceded the 1980 recession. Rates were raised again around 1981, then reduced, and then raised again; leading to the 1981-1982 recession.

The graph at the bottom shows the U.S. 10 Year Treasury yield, the CPI inflation rate (left scale), and the value of the S&P 500 index (right scale). Note that the U.S. 10 Year Treasury yield generally followed the Fed funds rate in the period, and that both were high while CPI inflation was still within approximately two-thirds of its previous peak. Interestingly, the S&P 500 was mostly flat during this period of major turmoil.

Could one conclude that the Fed’s current hiking cycle to combat inflation may have a similar outcome – i.e., a period where the S&P 500 is mostly range-bound? While it is possible that the answer to this question is “yes”, there is a big difference between today and the 1980s, namely valuations. The figures below show the valuations in the 1980s and now.

As you can see, valuations in the 1980s during the two recessions were largely below 10, whether we look at the S&P 500 PE ratio or the corresponding inflation-adjusted Shiller PE10 ratio. Today they are slightly above 20 (PE ratio) and 27 (PE10 ratio). The video linked below discusses these and related issues, as well as some recent developments.

A simulation-based valuation of the S&P 500: February 2023

The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.

The numbers on the left consider a more benign scenario: S&P 500 earnings in 2023 are up by 4.70% from the previous year, and the 10-year U.S. Treasury yield is at 3.73%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 4.70%, and the 10-year U.S. Treasury yield is at 4.30%.

The second scenario takes us to a fair price for the S&P 500 of 2,537.50, which is 47.34% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.

A simulation-based valuation of the S&P 500: January 2023

The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.

The numbers on the left consider a rather benign scenario: S&P 500 earnings in 2023 are up by 4.70% from the previous year, and the 10-year U.S. Treasury yield is at 3.49%. The numbers on the right refer to a more likely scenario: S&P 500 earnings are up by 4.70%, and the 10-year U.S. Treasury yield is at 4.22%.

The second scenario takes us to a fair price for the S&P 500 of 2,667.12, which is 44.65% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other options.