Spectral Risk Measures를 이용한 우리나라 금융자산의 최적 자산 배분
Optimal Asset Allocation of Korean Financial Assets Using Spectral Risk Measures
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대표적 coherent risk measure 인 CVaR 또는 expected shortfall(ES)은 투자자의 리스크회피 정도를 반영하지 않으며, 극단적 손실에 대해 동일한 가중치를 부여한다는 한계를 갖는다. Acerbi(2002, 2004) 해결책으로서 각 투자자의 리스크회피 정도를 반영하는 spectral risk measure(SRM)를 소개하였다. 본 논문에서는 ES 와 새로운 측정방법인 SRM 을 사용하여 국내 KOSPI, 원/달러 환율 및 국고채의 3 가지 자산으로 포트폴리오를 구성하고, 리스크회피정도에 따른 자산배분비율을 비교하였다. SRM 에서 손실분포의 꼬리부분에 동일한 가중치를 부여하는 리스크회피계수(R)를 이용하여 ES 를 SRM 에 대응시킬 수 있다. 리스크회피계수별 자산배분 결과를 살펴보면, 리스크회피정도가 클수록 고수익/고리스크에 해당하는 주식의 비중이 감소하는 반면 표준편차가 낮은 채권의 비중은 증가하였다. 또한, ES 의 효율적 투자선과 SRM 의 각 리스크회피계수별 효율적 투자선을 도출하여 다음의 두 가지 결과를 확인하였다. 첫째, 리스크회피정도에 따라 리스크 즉, SRM 값이 차이를 보인다. 둘째, 리스크회피정도가 클수록 투자자는 SRM 값이 낮은 포트폴리오를 선택한다. ES 는 SRM 의 수많은 효율적 투자선 중 하나일 뿐이며, 리스크회피정도가 클수록 ES 기준 효율적 투자선과 SRM 기준 효율적 투자선 간 차이 가 커진다는 사실도 확인하였다. 따라서 보수적으로 운영되어야 하는 포트폴리오나 리스크회피정도가 큰 투자자들의 경우, ES 를 기준으로 한 자산배분은 적절하지 않을 수 있다.
Abstract
As a coherent risk measure, CVaR or expected shortfall(ES) is limited in terms of applying equal weights to the extreme loss beyond Value-at-Risk regardless of investors' risk aversion. Acerbi(2002, 2004) introduced spectral risk measures(SRMs) that reflect investors' subjective risk aversion. In this study, portfolios are composed of three different Korean financial assets: the KOSPI index, won-dollar exchange rates, and the government bond. The asset allocations derived from ES and SRMs with various risk aversion coefficients are compared. The SRMs model converges to the ES model by imposing equal weights to the loss beyond VaR. The results show that when investors are more risk averse, the weights for high-risk stocks decrease and the weights for low-risk government bonds increase. The efficient frontiers of ES and SRMs show that the risk taken depends on the degree of risk aversion, and that investors select the lower risk portfolio when they are more risk averse. The efficient frontier of ES is one of the various efficient frontiers of SRMs, which implies that asset allocation based solely on ES is not appropriate for very risk-averse investors or conservatively managed portfolios.
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