하방위험을 고려한 포트폴리오 성과 평가
Portfolio Performance Evaluation based on Post Modern Portfolio Theory
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초록
본 연구는 변동성(mean preserving spread)으로 정의되는 위험에 대한 정의를 세분화하여 하방위험과 상방위험으로 나눈 후 상대적 비율을 이용한 위험조정 성과지표를 제시하고 이를 국내 코스피 시장을 대상으로 실증하였다. 분석 결과는 다음과 같다. 첫째, Shapiro-Wilk 검정 결과 국내 유가증권시장에 상장된 종목의 약 80%가 정규분포를 기각하였다. 반면 고차 적률 위험을 잘 포착한다고 알려져 있는 NIG(normal-inverse Gaussian) 분포를 사용할 경우 기각율이 2% 대로 감소하였다. 둘째, 성과지표 추정치와 종목별 기초통계량과의 횡단면 상관계수를 분석한 결과 대부분의 성과지표가 평균수익률 및 왜도와 양의 상관계수를, 첨도와 음의 상관계수를 발견하였으며 이는 절대적 위험회피형(decreasing absolute risk aversion) 투자자의 위험선호성향과 일치하였다. 셋째. 독립 동일 분포 가정 하에서 성과지표별 모맨텀 효과의 존재 여부를 진단한 결과 일별수익률 기준에서 성과지표가 높을수록 평균손실률이 감소하는 현상을 발견하였으며 이를 이용한 무비용 포트폴리오가 시장지수 대비 높은 위험조정 초과성과를 발견하였다. 전술한 결과로부터 평균-분산 기준을 넘어서 보다 일반적인 성과지표를 개발할 필요가 있으며 이는 금융시장의 참여자에게 포트폴리오의 위험 대비 성과에 대해 보다 정확한 정보를 제공함으로써 금융시장의 효율성 제고에 기여할 것이다.
Abstract
This study divides risk defined as mean preserving spread into loss risk and gain risk. I present risk-adjusted performance indicators based on their ratio and compare them with traditional performance indicators. The empirical results are summarized as follows. First, about 80% of the stocks listed on KOSPI market rejected normal distribution hypothesis through Shapiro-Wilk test. On the other hand, only 2% of those stocks rejected normal-inverse Gaussian(NIG) distribution that is known to capture skewness and kurtosis risk. Second, from cross-sectional correlation analysis between performance indicators and basic statistics of each stock, most of performance indicators found positive correlation with mean, positive correlation with skewness, and negative correlation with kurtosis. This is congruent with moment preferences of DARA(decreasing absolute risk aversion) type investors. Third, it was found that there existed momentum effect in the short-term daily KOSPI market because expected loss decreased systematically according to performance index. These results imply that general risk-reward ratio beyond mean-variance criteria should be developed for portfolio optimization and market efficiency. Post modern performance indicators based on the exact distribution will improve the efficiency of investment and financial market by providing more accurate information about risk-reward ratio.
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