The Trouble with Discount Rates

Let's start with my claim that the risk-free rate is hard to estimate. What is a risk-free asset? In the narrow sense of what asset you could buy right now that removes any uncertainty as to the real return you're going to obtain over a defined period, it is the zero-coupon inflation-protected bond issued by the U.S. government. But this raises a logical contradiction: If this asset is truly risk-free, in the sense that its intrinsic value should have no risk premium embedded in its discount rate, then it is always trading at fair value. There is no such thing as it being over- or under-valued. It is perfectly priced, as if handed down by the Almighty.

This is clearly not true. Bond prices don't spring from the mind of God; they're the result of many investors betting against each other based on their private forecasts of future interest rates. If the short-term rate permanently rose 10%, the present value of the long-duration, zero-coupon, inflation-protected bond--"risk-free" in a narrow sense--would take a permanent hit, as the unfortunate bearer of such a bond has forever lost the opportunity to earn a higher return on his capital because he has locked in a low interest rate. Opportunity cost may not feel tangible, but it's no less real than any other form of loss. This insight is the basis for the theory of comparative advantage. Treating opportunity cost differently is fallacious mental accounting.

The true theoretical risk-free rate is unknowable, as it's determined by the future path of short-term interest rates. Using Treasury yields as the risk-free rate implicitly assumes that the market provides the best estimate of the future path of interest rates. This is a reasonable assumption most of the time. I'm not so sure it's reasonable today.

Things don't get any easier when we're talking about risk premiums. Recall that a risk premium is the expected return the market demands above the risk-free rate as compensation for the riskiness of an asset's cash flows. One influential paradigm assumes that the market randomly generates a return around a central tendency and that this central tendency can be estimated by looking at the past. This may be true in a loose sense, but it's problematic. Consider the equity risk premium, or ERP, which can refer to two closely related ideas: 1) the return equities earned over bonds or 2) the return equities are expected to earn over bonds. One is a historical fact, the other is a forecast. Many investors have long used the historical ERP as a forecast of the future ERP. This approach would have told you the Japanese ERP was higher in 1989 than ever before, whereas a glance at any fundamental valuation measure would have told you the opposite.

Strangely enough, bond investors understand that past returns are largely irrelevant. They look at present yields to estimate future returns--that is, they look at the prices they're paying today for cash flows tomorrow. Only a rank amateur would look at past bond returns to project future returns, yet this is what many equity investors do when they plug the historical ERP into their discounted cash flow models. This confused thinking originates from early efficient-market models that predicted a constant ERP, which we now know is false.

There are good reasons to believe the historical ERP is optimistic. History has been kind to the United States, which grew into a superpower despite a depression, a pandemic, two world wars, stagflation, racial unrest, and a cold war. Many other countries facing similar tribulations ended up weaker. According to economists Elroy Dimson, Paul Marsh, and Michael Staunton, foreign equities earned a 2.9% annualized premium to long-term bonds from 1900 to 2013; the U.S. market earned a 4.5% annualized premium, among the highest of all countries in their sample. In addition, markets have become more liquid and transparent, and the rule of law has strengthened, so equities are fundamentally less risky than they were 50 or 100 years ago, warranting a lower ERP.

Compounding the error of assuming constant risk premiums is the application of the flawed capital asset-pricing model. The CAPM predicts that an asset's expected return is proportional to its beta, a measure of how an asset's returns move in concert with the market's. If the ERP is, say, 5%, and a stock's beta is 1, then the stock's expected excess return is 5%. If the stock's beta is 1.5, then its expected excess return is 7.5% (1.5*5%). This model simply does not work. Many studies have shown high-beta stocks have not offered higher returns than low-beta stocks in the U.S. and abroad.

One way to use discount rates generated by the historical ERP-plus-CAPM approach is to treat them like consistent but biased measuring sticks. After all, if your 12-inch ruler really is 15 inches, you can still determine the relative lengths of anything you measure. The problem is that you might end up really thinking a foot is 15 inches.

My preferred approach is to ignore discount rates and look at normalized cash flow yields, which is why you never see me assign a target price to a fund. This approach is robust to the problems I raised.

Summary

• Estimating intrinsic value requires forecasting future cash flows and discounting them to the present.
• The appropriate discount rate is a combination of a risk-free rate and a risk premium.
• The risk-free rate is commonly assumed to be the Treasury yield. This approach implicitly assumes the Treasury yield curve is the best forecast of the future path of interest rates--a dangerous assumption in today's ultralow-rate environment.
• Many investors use the historical excess returns stocks earned over bonds as their equity risk premium forecast. This approach is flawed because the historical U.S. ERP is likely biased upward due to the U.S.' past success and ignores present valuations.
• Investors compound the above error by using the capital asset pricing model, which doesn't work.
• A more robust approach is to ignore discount rates and look directly at an asset's expected cash flow yield.