Fortune favors the bold, and so does misfortune

The figure below illustrates a truth that most investors know, but tend to forget. Taking high levels of risk in the financial markets increases the tail probabilities, which are associated with massive gains and massive losses. The lure of high-risk decisions and related investment instruments often acts as a sort of tax on the statistically illiterate.

But investors can reduce the chances that they will end up at the left tail end of the probability distribution. When it comes to stock investing, paying attention to two events can help. The first is the percentage difference between 10-year and 3-month U.S. Treasury yields falling below zero, because a U.S. recession tends to occur within the next 18 months.

The second is the stock market, measured by an index such as the S&P 500, reaching a double-top within that that period of 18 months after the percentage difference between 10-year and 3-month U.S. Treasury yields falls below zero. This combination is extremely bearish. And this is where we are about now. The video linked below discusses this in a bit more detail.

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.