Most of the asset-pricing literature implicitly assumes a one-month investment horizon, and one-month bills are therefore considered as the risk-free asset. But this assumption seems clearly unrealistic, and it is therefore worth examining the potential distortions it may cause in financial modeling.
In a new research paper,1 we investigate this question by searching for the actual risk-free rate implied by investors’ behavior in equity markets. For that, we start by looking at what the theoretical implications would be if the CAPM is tested assuming that one-month Treasury bills are the risk-free asset, while the true risk-free asset is in fact an ‘N-year’ bond.
The CAPM states that E(R)= Rf + β x (E(Rm)-Rf),2 and a simple derivation from this formula shows that if the incorrect risk-free asset is assumed, it should show up in stocks with low equity betas (β) co-moving with bond returns. Specifically, if N-year bonds are the risk-free asset, low-beta stocks should exhibit a positive exposure to N-year bond returns.
In other words, if an investor’s horizon is indeed much longer than one month, low-beta stocks should exhibit a positive correlation with multi-year bond prices, not short-term bills, and thus benefit from falling interest rates. Meanwhile, high-beta stocks should exhibit a negative correlation with multi-year bond prices, and thus benefit from rising rates.
Our empirical tests strongly confirm this hypothesis. We find that low-beta stocks are indeed very bond-like, while the opposite is true for high-risk stocks. What’s more, we find that the negative relation between the equity beta and the bond beta of a stock is almost perfectly linear.
This means, for example, that a stock with an equity beta of 0.7 will show a bond beta of 0.3, while a stock with beta of 1.5 has a bond beta of -0.5. The combined stock and bond betas always neatly add up to 1. These results are valid for the US stock market but also for other markets. Also, they are robust over different sample sub-periods.
Finally, by relating stock returns to the returns of bonds with different maturities, we believe it is possible to pinpoint that bonds with a maturity of about 5 years provide the best fit. Hence, the risk-free asset which financial models ought to consider is bonds with a maturity of about 5 years, and definitely not one month.
Implications for risk-adverse investors
Besides their repercussions for the asset pricing literature, our findings also have important implications for investors trying to reduce risk in portfolios. While the classic way to cut equity beta is to increase allocation to bonds – say, for example, 70% to equities and 30% to bonds – investors should be mindful that this type of mix may not lead to the best outcome.
Allocating to low-risk, bond-like stocks, such as those we hold in our Conservative Equities portfolios, instead of to bonds, we believe allows investors to benefit from the alpha that low-risk stocks are known to offer. The bond-like properties of low-risk stocks also makes them attractive to investors who need to hedge liabilities.
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