자산가격결정이론에 관한 연구

Abstract

This thesis consists of two essays in asset pricing theory: the equity premium puzzle and the asymmetric volatility. The first essay analyzes the equity premium puzzle. 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 to their historical averages, the equity premium is too small and the risk-free rate is too large. These phenomena are referred to as the equity premium puzzle and the risk-free rate puzzle, respectively. I found the correlation of the consumption growth and the KOSPI return is negative before the Asian currency crisis of 1997. In this paper, we re-examine these puzzles by using the sample data during the period from 1999 to 2017 because of the currency crisis and the correlation of the consumption growth and the market return. Most importantly, I extend the prior studies by adding five utility functions besides the time-additive expected utility and the non-expected utility of Epstein and Zin (1989) to explore their usefulness in resolving the two puzzles in Korea. I take three approaches to carry out the task of this study. First, following Kocherlakota (1996), I perform statistical tests directly on the Euler equation that asset returns must satisfy in equilibrium. Second, I also apply a calibration method under which closed-form solutions (or their approximations) of asset returns are compared to their historical averages. Finally, I estimate the key parameters by GMM and compare the estimated parameters to the acceptable range of those parameters. The results of the three approaches will, by and large, turn out to be consistent in each case of the seven utility functions that we consider. What I find in this study are as follows. Under the basic model that Mehra and Prescott used, the existence of the equity premium puzzle in Korea seems apparent now in the acceptable range of relative risk aversion coefficient (2-6). The risk-free puzzle gets even stronger as the risk-free interest rate has fallen significantly. The non-expected utility function of Epstein and Zin (1989) makes no difference concerning equity premium puzzle as the equity premium is determined independently of intertemporal substitution. However, it can alleviate risk-free rate puzzle substantially if the intertemporal substitution parameter ρ is small. Our estimation of this parameter using the 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 non-expected utility function with constant absolute risk aversion (CARA) has the potential to bring up the equity premium greatly. Since CARA is translated into increasing relative risk aversion, it makes a high degree of relative risk aversion acceptable. For the same reason, it brings the risk-free rate down further than the preceding utility function, other things being equal. The non-expected utility function with ambiguity aversion, the degree of which is measured by η, can also be useful in explaining both puzzles. Under certain conditions, η replaces the role played by γ in the Epstein and Zin utility function. Since ambiguity aversion means, by definition, η>γ, it acts like strengthening risk aversion with γ kept reasonably low. This leads to higher equity premium and lower risk-free rate. 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 risk-free rate puzzle. The reason is that the pricing kernel in this case boils down to the one under log utility (γ=1). If γ equals one, however, it will worsen equity premium puzzle. A multiplicative external habit model using lagged consumption weakens risk-free rate puzzle significantly, with equity premium puzzle intact. Inherently, it has the effect of magnifying the utility discount factor, and this will reduce 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 its mean as well. This will raise the equity premium and lower the risk-free rate. This model, however, has a shortcoming that the risk-free rate can easily be negative as the mean of the pricing kernel exceeds one if the consumption habit is over a certain threshold. To sum up, 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 CARA model, the ambiguity aversion model, and the additive external habit model have the potential to alleviate both puzzles simultaneously. Among the three, the non-expected utility with CARA model seems to be most successful, considering that the explanatory power of the rest is rather limited. The second essay analyzes the asymmetric volatility under the ambiguity and the asymmetric information. The asymmetric volatility, first documented by Black(1976), is the negative intertemporal relation of the risk and the return. The ambiguity can play a role in the analysis of the asymmetric volatility because the uncertainty can be decomposed into the risk and the ambiguity. In this paper, the uninformed liquidity traders face the ambiguity about the distribution of asset payoffs and change their attitudes toward ambiguity vary depending on the state of the economy. In the bad state, the uninformed traders show ambiguity-averse, while they show ambiguity-neutral(Model I) or ambiguity-seeking(Model II) in the good state. Model I cannot generate the asymmetric volatility, but the attitude toward ambiguity of the uninformed causes the asymmetric volatility in model II. An asset with lower ambiguity has higher return volatility in the bad state than that in the good state. Furthermore, the more uninformed traders, the higher possibility of the asymmetric volatility. For the empirical analysis, I construct the measure for ambiguity by the Kolmogorov-Smirnov test and show this measure has negative relation with the asymmetric volatility. The risk factor constructed by this ambiguity measure has explanatory power over the return of the 25-Fama-French portfolios in the Korean stock market by Kolmogorov-Smirnov statistic, Kullback-Leibler divergence and Benfords law.

이 논문은 주식프리미엄 의문현상과 비대칭적 변동성에 관한 두 개의 연구로 구성되어 있다. 첫 번째 연구는 한국시장의 주식프리미엄과 무위험이자율에 대한 의문현상을 재검토한다. 특히, 외환위기 이전에는 소비성장률과 주식수익률의 상관관계가 음(-)의 관계를 가진다는 것을 발견하여 외환위기 이전의 자료가 주식프리미엄 의문현상 분석에 적합하지 않다는 것을 확인하였다. 따라서 외환위기 이후의 자료를 이용하고, 기존 연구에서 사용한 시간부가적 기대효용함수와 Epstein and Zin(1989)의 비기대효용함수 외에도 다섯 종류의 효용함수, 즉 절대적 위험회피계수가 일정한 비기대효용함수, 모호성회피를 반영한 비기대효용함수, 그리고 세 가지 소비습관부 효용함수를 추가하여 분석을 시도한다. 분석방법으로는 Mehra and Prescott(1985)의 캘리브레이션 방법, Kocherlakota(1996)의 통계적 방법론, 그리고 GMM을 통해 추정한 값과 비교하는 세 가지 방법을 활용하고, 각 결과를 비교하여 그 일관성을 확인한다. 연구결과는 다음과 같다. 시간부가적 효용함수 하에서 두 의문현상은 외환위기 이전보다 뚜렷하게 나타났다. 비기대효용함수 중에서, (i) 상대적 위험회피계수가 일정한 경우, 주식프리미엄 의문현상은 개선되지 않지만 무위험이자율 의문현상은 시점간 소비대체 계수의 값에 따라 크게 완화될 가능성이 있다; (ii) 절대적 위험회피계수가 일정한 경우, 두 의문현상을 모두 큰 폭으로 해소할 수 있다; (iii) 모호성회피를 반영하면 전반적으로 도움이 되지만 주식프리미엄 의문현상에 대한 그 설명력은 제한적이다. 외부 소비습관을 반영한 효용함수 중에서는, (i) 배수형 소비습관을 일인당 현재소비와 같게 놓을 경우 두 의문현상을 동시에 해소하는 것이 불가능하다; (ii) 배수형 소비습관을 일인당 과거소비로 설정하면 무위험이자율 의문현상을 설명하는 데 상당히 효과적이나 주식프리미엄 의문현상은 더 악화시킨다; (iii) 부가형 소비습관을 일인당 과거소비와 같게 할 경우 두 의문현상을 동시에 완화할 수 있다. 두 번째 연구는 정보비대칭 하에서 Black(1976)이 제기한 비대칭적 변동성(asymmetric volatility)과 모호성의 관계를 분석한다. 이 연구에서는 Grossman and Stiglitz(1980) 모형의 유동성투자자가 경기변동에 따라 호황-불황에서 모호성에 대해 각각 중립-회피(모형 I) 또는 추구-회피(모형 II)적인 효용함수를 가진다고 가정한다. 모형 I에서는 비대칭적 변동성이 나타나지 않는 반면, 모형 II에서는 자산수익의 분포에 대한 모호성의 정도에 따라 비대칭적 변동성이 나타나는 것을 이론적으로 확인하였다. 이 모형을 통해, 주식수익률과 그 변동성이 음(-)의 관계를 가지는 비대칭적 변동성을 다음과 같이 설명할 수 있다. 유동성투자자가 불황기에 모호성을 회피하고 호황기에 모호성을 추구하는 경우(모형 II), 자산수익의 분포에 대한 모호성의 정도가 작을수록, 그리고 유동성투자자가 많을수록 불황기에 주식수익률의 변동성이 상대적으로 더 커진다. 또한 실증분석을 통해, 모호성의 정도가 작은 포트폴리오에서 비대칭적 변동성이 나타날 가능성을 확인하였고, 모호성이 포트폴리오의 수익률에 대해 체계적인 설명력을 가진다는 주장을 벤포드의 법칙 등 다양한 방법을 이용하여 확인하였다.