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학술자료 검색

한국시장에서의 주식프리미엄과 무위험이자율 의문현상 : 외환위기 이후의 자료를 이용한 재검토

  • 김민직 서울대학교 경영대학 박사과정
  • 조재호 서울대학교 경영대학 교수
이 논문은 한국시장에서 주식프리미엄 및 무위험이자율에 대한 의문현상 (이하, 의문현상Ⅰ 및 Ⅱ)을 검토한 독고윤, 박종원, 조재호(2001)의 연구를 1997년 외환위기 이후의 자료를 이용하여 재검토한다. 특히, 전에 사용한 시간 부가적 기대효용함수와 Epstein and Zin(1989)의 비기대효용함수 외에도 다섯 종류의 효용함수를 추가하여 새로이 분석을 시도한다. 연구결과는 다음과 같다. 시간 부가적 효용함수 하에서 두 의문현상은 과거보다 뚜렷하게 나타나고, 강건성 점검을 통해서도 이를 확인할 수 있었다. 비기대효용함수 하에서, (ⅰ) 상대적 위험회피계수가 일정한 경우 의문현상Ⅰ은 여전히 남지만 의문현상Ⅱ는 시점간 소비대체 계수의 값에 따라 크게 축소될 여지가 있다; (ⅱ) 절대적 위험회피 계수가 일정한 경우 의문현상Ⅱ뿐 아니라 의문현상Ⅰ도 큰 폭으로 해소될 수 있다; (ⅲ) 모호성회피를 반영하면 전반적으로 도움이 되지만 의문현상Ⅰ에 관한 한 그 유용성은 제한적이다. 외부 소비습관을 반영한 효용함수 하에서는, (ⅰ) 배수형 소비습관을 일인당 현재소비와 같게 놓을 경우 두 의문현상을 동시에 해소하기란 불가능하다; (ⅱ) 일인당 과거소비를 배수형 소비습관으로 설정하면 의문현상Ⅱ를 설명하는 데 상당히 효과적이다; (ⅲ) 부가형 소비습관을 일인당 과거소비와 같게 할 경우 두 의문현상을 동시에 완화할 수 있다.
주식프리미엄 의문현상; 무위험이자율 의문현상; 시간부가적 기대 효용함수; 비기대효용 함수; 소비습관부 효용함수 ;Equity Premium Puzzle; Risk-free Rate Puzzle; Time-additive Expected Utility Function; Non-expected Utility function; Habit Formation Utility Function

A Re-examination of the Equity Premium Puzzle and the Risk-Free Rate Puzzle in Korea

  • Min-Jik Kim
  • Jaeho Cho
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.