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 so low if agents are so averse to intertemporal substitution?

Explaining 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, returns from equities would fall, causing the 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 6%, 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 riskier 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.

More recent research has sought to explain this puzzle by using a consumption-based asset pricing model with three ingredients:

  1. the life cycle
  2. a borrowing constraint
  3. a majority decision rule on capital structure