Estimating the time decay of inverse leveraged funds

The figure below shows the performance of two funds: the iShares Russell 2000 ETF (IWM), and the Direxion Daily Small Cap Bear 3X Shares (TZA). The TZA is expected to return 3 times the inverse of the IWM within very short time frames. As you can see, over 6 months the IWM drops -15.41% and the TZA gains 30.63%.

Three times the inverse of -15.41% is 46.23%. Since the TZA gained only 30.63%, the difference of 15.60% (46.23% minus 30.63% = 15.60%) is the decay associated with the 6-month period.

You can do similar estimations for other inverse leveraged funds. The video linked below discusses this and a few other options.

Is a PE ratio of 12 attractive? A simulation-based view of company valuation

Summary

- The price/earnings (PE) ratio is one of the most widely used measures of company valuation.

- Through a simulation, we show that if growth is expected to slow down, then PE ratios are likely to go down, possibly in a dramatic fashion.

- For example, if earnings are expected to grow only 2% per year, then an attractive PE ratio would be 7.95. This is much lower than the PE ratio of 12, which is generally seen as attractive.

- For a PE ratio of 12 to be attractive, the expected earnings growth has to be at least 10.18% per year.

The PE ratio

The price/earnings (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.

What is an attractive PE ratio?

From early 2009 to early 2019 the SPY exchange-traded fund (ETF) has gone up in value approximately 222.72%. The SPY is an index fund, which tracks the S&P 500 index (, ). It had a relatively low net expense ratio of 0.09% at the time of this writing. The SPY has also paid dividends during this period. In early 2019 the dividend was a little less than 2%.

If you bought US$ 10,000 in shares of a company, and had a return comparable to buying and holding the SPY in the 2009-2019 period above, the shares would be valued at approximately US$ 32,272 after 10 years. The spreadsheet section in the figure below shows a simulation where earnings are assumed to grow 2% per year over a period of 20 years. As you can see, the value of US$ 32,272 is reached at year 10. The EP percentages go up because they assume that the share prices remain constant; in reality those prices would go up, keeping the PE ratio somewhat constant. The first EP percentage is the reverse of the PE ratio.

At the top left you see the PE ratio associated with this return. It is a fairly low 7.95. This is much lower than the PE of 12, which is often seen as attractive by investors. That is, if you want to purchase shares of a company whose earnings are expected to grow only 2% per year, and obtain a return for the next 10 years that is comparable to the S&P 500 in the 2009-2019 period, then you should buy shares in a company with a PE ratio of 7.95.

The same simulation-based approach can be used to find out what growth rate would be needed for a PE ratio of 12 to be attractive. This is summarized in the spreadsheet section in the figure below. For a PE ratio of 12 to be attractive, the expected earnings growth has to be at least 10.18% per year.

The PEG ratio

Note that the PEG ratio () in the first spreadsheet section, also shown at the top left, is 3.97. The PEG ratio is the PE ratio divided by the expected annual earnings growth. This PEG ratio is much higher than 1, which is generally perceived as an attractive PEG ratio. And still, the return on the investment in 10 years will no doubt be attractive (the S&P 500 had a remarkable run in the 2009-2019 period), as long as the PE ratio is a low 7.95.

In the second spreadsheet section, the PEG ratio is 1.179, which is much closer to 1. This highlights one interesting property of the relationship between the PEG and the PE ratios - it is a nonlinear relationship. The closer the earnings growth gets to zero, the more warped it becomes, pushing the PEG ratio higher and away from 1 (assuming that the PE ratio is positive).

When growth slows down, the stock market may collapse, even without a recession

The above discussion highlights the fact that, if growth is expected to slow down, then PE ratios are also likely to go down. PE ratios may go down dramatically, leading to a severe stock market correction, even without a recession ().

In fact, as we can see from the discussion above, a severe correction may happen even without earnings going down! In other words, earnings may still keep growing, but at such a slow pace that the market is compelled to adjust PE ratios downward to match the lowered return expectations.

Where is the yield curve un-inversion?

The figures below show the graphs of the 10y-3m Treasury yields and 10y-2y Treasury yields. The inversion in the 10y-3m graph is the best indication of an impending recession, and that graph typically un-inverts immediately prior to a recession.

While the first graph does not show an un-inversion, the second (i.e., 10y-2y) does. And the second tends to predict the first, because the 2y yields tend to predict the 3m yields. That is where the yield curve un-inversion is, at the moment. The video linked below discusses this in a bit more detail.

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.

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.