Risk-Free Rate Puzzle (RFRP) Definition

What Is the Risk-Free Rate Puzzle (RFRP)?

The risk-free rate puzzle (RFRP) is a market anomaly observed in the persistent difference between the lower historic real returns of government bonds compared to equities. This puzzle is the inverse of the equity premium puzzle and looks at the disparity from the perspective of the lower returning government bonds. It essentially asks: why is the risk-free rate or return so low if agents are so averse to intertemporal substitution?

Key Takeaways

• The risk-free rate puzzle refers to the gap between returns on stocks compared to government bonds. 
• Economists Edward Prescott and Rajnish Mehra in a 1985 paper that point out that the difference in returns could not be explained by then current economic models. 
• Several explanations of the puzzle have been advanced by various economists in the years since, many focusing on how to model investor preferences and a nature of risk. 

Understanding the Risk-Free Rate Puzzle (RFRP)

The risk-free rate puzzle is used to explain why bond returns are lower than equity returns by looking at investor preference. If investors tend to seek out high returns, why do they also invest so heavily in government bonds rather than in equities?

If investors did invest in more equities, then returns from equities would fall, causing the relative returns for government bonds to rise and making the equity premium smaller. Thus, we have two interrelated puzzles based on long-run empirical observation of market prices: the equity premium puzzle (why is the equity risk premium so high?) and the risk-free rate puzzle (why the risk-free rate so low?).

Academic work in the field of economics has sought for decades to resolve these puzzles, but a consensus still has not been reached on why these anomalies persist. Economists Rajnish Mehra of Columbia University and Edward Prescott of the Federal Reserve (1985) investigated U.S. market data from 1889 to 1978 and found that the average annual premium of equity returns over the risk-free rate was around 7%, which is too large to be justified by the standard economic model given a reasonable degree of risk aversion.

In other words, stocks are not sufficiently more risky than Treasury bills to explain the spread (difference) in their returns.

Mehra and Prescott additionally point out that the real interest rate observed over the same period was just 0.8%, which was too low to be explained in their model. In 1989, Harvard economist Philippe Weil argued that the low interest rate was a puzzle because it could not be justified by a representative agent model with a plausible degree of risk aversion and an arbitrary level of inter-temporal elasticity of substitution.

Solutions to the Puzzle

Several plausible solutions to the risk-free rate puzzle have been advanced by other economists. These arguments largely focus on the nature of the risks posed by equities versus Treasury securities and their relationship on people’s income and consumption over time. They variously explain the risk-free rate puzzle in terms of different assumptions about preferences (compared to Prescott and Mehra’s model), the probability of rare but disastrous events, survival bias, and incomplete or imperfect markets. Others have pointed to empirical evidence that the risk-free rate puzzle is more pronounced in the the U.S. and less so when data from world markets are considered, which might be explained by the U.S.’s historically dominant position in the global economy.

Perhaps one of the strongest lines of thinking is that the fat-tailed probability distribution of equity returns is at play. Rare but severe negative returns across equity markets are known to happen, but difficult or impossible to predict precisely. Rare events such as world wars, depressions, and pandemics can create such negative economic shocks, impacting equity returns in particular, that investors demand a higher average return on them, possibly explaining the risk-free rate puzzle. Investors build their estimates of uncertain future economic growth around an irreducibly fat-tailed distribution of negative shocks (and thus equity returns). This argument was originally developed by economist Thomas Rietz and later elaborated separately by economists Robert Barro and Martin Weitzman.