| On Portfolio Optimization: Forecasting Covariances and Short-Sale Restriction |
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Sang Whan Kim |
| 공분산행렬 추정방법과 공매도제한 제약의 자산배분성과에 대한 영향분석 |
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김상환 |
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| Abstract |
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This article tackles how to forecast the covariance matrix of returns. We compare the performance of different methods of forecasting covariances, with an eye to judging which models improve the ability to optimize portfolio risk. We tested the forecasting performance of the sample covariance matrix, the constance correlation model (CCOR), the constant covariance model (CCOV) and the estimation method using random matrix theory (RMT). We find that the forecast performance did not show significant difference among the estimation methods. But they had different performances in the context of optimized portfolios. We conduct two types of experiments, the global minimum variance portfolio under each model and minimizing tracking error portfolio. We find that minimum variance portfolios based on CCOR and RMT method have annualized standard deviations 19.15% and 17.87%, respectively, which are lower than 22.97% when using the sample covariance matrix. The better risk-minimization performance using CCOV and RMT method holds again in the experiment of minimizing tracking error volatility. In addition, we tested the effect of short-sale constraint on the portfolio performance. The short-sale constraint typically shrinks the larger elements of the covariance matrix towards zero, which leads to a more precise estimate. But the constraint introduces specification error. The net effect depends on the trade-off between sampling and specification errors. We demonstrate that with the constraint in place, minimum variance portfolios constructed using the sample covariance matrix perform as well as those constructed using covariance matrices estimated using CCOV and RMT methods. |
| Key Words:
공매도제한,공분산행렬,임의행렬이론,추적오차 최소화,포트폴리오 최적화,Covariance Matrix,Minimum Tracking Error,Portfolio Optimization,Random Matrix Theory,Short-Sale Constraint |
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