Asian Review of Financial Research

*Vol.33 No.1*pp.97-144*https://www.doi.org/10.37197/ARFR.2020.33.1.4*A Re-examination of the Equity Premium Puzzle and the Risk-Free Rate Puzzle in Korea

Key Words : Equity Premium Puzzle,Risk-free Rate Puzzle,Time-additive Expected Utility Function,Non-expected Utility function,Habit Formation Utility Function

**Abstract**

The puzzle posed originally by Mehra and Prescott (1985) on the asset pricing model of Lucas (1978) consists of two parts: When asset returns predicted by the model are compared with their historical averages, the equity premium is too small and the risk-free rate too large. These phenomena are referred to as the equity premium puzzle (henceforth, Puzzle I) and the risk-free rate puzzle (henceforth, Puzzle II), respectively. Dokko, Park, and Cho (2001: henceforth, DPC) examine these puzzles in the Korean market using annual data from 1975 to 1999, and conclude that while Puzzle I is very weak, Puzzle II is quite strong. In this paper, we re-examine these issues by extending their study in the following three directions: (i) We use quarterly data instead of annual data to enlarge the sample size. (ii) We use the sample data during the 1999–2017 period, considering that a paradigm shift has taken place in the Korean economy after the 1997 “currency crisis.” (iii) Most importantly, besides the time-additive expected utility and the non-expected utility of Epstein and Zin (1989) used in DPC, we adopt five additional utility functions to explore their usefulness in resolving each puzzle. We take two approaches to this study. First, following Kocherlakota (1996), we perform statistical tests directly on the Euler equation that asset returns must satisfy in equilibrium. Second, we apply a calibration method in which closed-form solutions (or their approximations) of asset returns are compared to their historical averages. The results of the two approaches are, by and large, consistent in each of the cases of the seven utility functions that we consider. We make the following observations. In Mehra and Prescott's basic model, the existence of Puzzle I in Korea is now apparent in the acceptable range of the relative risk aversion coefficient (2-6). The main reason for this may be that the equity premium has increased sharply over the last twenty years. Puzzle II is even stronger, as the risk-free interest rate has fallen significantly. These results, contrasted with those of DPC, are confirmed by several robustness check analyses. The non-expected utility function of Epstein and Zin (1989), in which relative risk aversion is constant with γ, makes no difference with respect to Puzzle I as the equity premium is determined independently of intertemporal substitution. However, it can alleviate Puzzle II substantially if the intertemporal substitution parameter ρ is small. Our estimation of ρ using Korean data shows that it is between 0.252 and 0.887. In this range, the risk-free rate predicted by the model is close to its historical average. The nonexpected utility function with constant absolute risk aversion (CARA) has the potential to substantially increase the equity premium significantly. As CARA is translated into increasing relative risk aversion, it makes a high degree of relative risk aversion acceptable. For the same reason, it decreases the risk-free rate further, compared with the preceding utility function. The non-expected utility function exhibiting ambiguity aversion can also be useful in explaining both puzzles. Under certain conditions, the ambiguity aversion parameter η replaces the role of γ in the Epstein and Zin utility function. As ambiguity aversion is, by definition, η > γ, it serves to enhance risk aversion if γ is kept reasonably low, which leads to higher equity premiums and lower risk-free rates. However, given that the empirical magnitude of η is unknown, the usefulness of this utility function is quite restrictive. Merits of the habit formation utility function vary with how habits are specified. A multiplicative external habit model using contemporaneous consumption helps explain Puzzle II, because the pricing kernel in this case becomes unity under log utility ( γ = 1). If equals one, however, it will weaken Puzzle I. A multiplicative external habit model using lagged consumption weakens Puzzle II substantially, while Puzzle I remains intact. Inherently, it has the effect of magnifying the utility discount factor, which reduces the risk-free rate. An additive external habit model using lagged consumption has a channel to resolve both puzzles simultaneously. A strong consumption habit increases the volatility of the pricing kernel, and also its mean, which raises the equity premium and lowers the risk-free rate. This model, however, has one shortcoming, in that the risk-free rate can easily be negative as the mean of the pricing kernel exceeds one if the consumption habit crosses a certain threshold. In sum, except for the time-additive expected utility, each utility function that we consider can be useful for at least a partial resolution of the two puzzles found in Korea. In particular, the non-expected utility with the CARA model, the ambiguity aversion model, and the additive external habit model have the potential to simultaneously alleviate both puzzles. Among these, the non-expected utility with the CARA model seems to be the most successful, as the explanatory power of the remaining models is rather limited.