The Equity Premium Puzzle and Stephen J. Fisher's Explanation

The 'equity premium puzzle' is a term coined by the economists Rajnish Mehra and Edward Prescott regarding the observation of anomalously higher historical returns of stocks over government backed, risk-free bonds, or T-bills. It is supposed to reflect the relative risk of stocks compared to government bonds, but the puzzle arises because this unexpectedly large value implies a high level of risk aversion among investors, which is questionable. General utility based models of asset prices have trouble empirically fitting and explaining why the T-bills rates are so low and the risky equity rates so high. In the United States from 1889 – 1978, the mean return on a T-bill was around .8% and the mean return on equity was 6.98%. Thus, the observed equity premium, defined as equity returns less bond returns, is around 6.18%, which is far higher than standard models predict. There has been extensive research conducted and a variety of useful theoretical ideas and plausible explanations have been presented, but a generally accepted solution does not yet exist.

Many research papers have been presented to mitigate the low equity premium found through modeling. Hansen and Jagganathan put criteria on the preference structure as a possible solution to the puzzle. Campbell and Cochrane used a habit persistence model in which one analyzes a household’s consumption in the past and/or analyzes household consumption with respect to the aggregate per capita consumption (the “keeping up with the Jones’” approach). They allow the degree of relative risk aversion to be time varying and countercyclical and come up with some encouraging results and possible explanations. Many other explanations have come about in recent years, however, I have not had chance to study these yet.

I recently studied a model and possible explanation by Stephen J. Fisher (1994) that attempts to explain the historical size of the U.S. equity premium by analyzing gross and net returns accruing to agents. He augments Mehra and Prescott’s standard model with a bid-ask spread, then calibrates and simulates the results using real world data. This is a Lucas model which basically converts an infinite horizon problem into a two-period recursive expression and maximizes utility for agents in the economy who need to allocate their consumption, stock holdings, and bond holdings (I have left out the math calculations here). Fisher acquires and equity premium in the range of 3 – 4 % using plausible data inputs and parameters. Fisher basically argues that since agents incur an expense to trade, they need to be compensated with higher expected gross returns. Shorter holding periods for securities imply higher turnover rates. Thus, higher transaction costs are a direct result of increased turnover and actively managing one’s portfolio. This implies rational agents require higher expected returns. Thus, the equity premium should consist of a trading cost compensation component in addition to the risk component.

This paper illustrates some convincing evidence for why equilibrium asset pricing models should consider the bid-ask spread in calculating the equity premium and distinguish between gross and net returns. A 4% equity premium using plausible data inputs can be found in comparison to Mehra and Prescott’s .38%. Thus, the equity premium calculated through this paper is far closer to the historical 6.18%. The GMM (General Method of Moments) procedure by Hansen that Fisher also uses provides supporting results for his claims. The bid-ask spread estimates appear to dominate risk related parameters as determinants of the equity premium.

One has to wonder why a bid-ask spread or transaction costs have not been implemented into the standard models in some way or another. These variables are clearly a factor in one’s investment decisions. Furthermore, one would think that it is likely people invest more in modern times in comparison to the past since there is more liquidity, far better technology, and thus lower transaction costs. However, the equity premium puzzle utilizes data accumulated over the last century. Therefore, it may be a good idea to at least explore the relation between trading volume, transaction costs, and expected returns in more detail over time. The results of this paper are encouraging in finding a generally accepted solution to the equity premium puzzle, and individuals researching this elusive concept should take note of Fisher’s results.