Leptokurtic Distribution and Optimal Hedge Ratio

[[abstract]]當使用期貨契約以規避風險性資產價格波動風險時，主要議題就在於如何找出一最適避險比率(OHR)。但moving average, GARCH以及EWMA等方法係依據樣本的變異數及共變數估計式以估計OHR，樣本變異數估計式及共變數估計式雖為母體變異數及共變數的一致估計式，不過卻忽略了資料的分配型態，以致樣本變異數及共變數估計式並不具效率性。尤其當資料分配具有高狹峰的情況時，以上述方法估計OHR將可能賦予極端值過多的權重。有證據顯示，短期金融資產報酬率並非常態分配，而是具有高狹峰的特性。 本研究將採用Guermat and Harris (2002)所推導出的Power EWMA估計式〈本文稱為健全估計式〉以估計OHR，並與標準估計式所估計出避險效果進行比較。Power EWMA估計式不但可解決變異數叢聚問題，且能捕捉到資料分配具高狹峰特性。以SGX-DT摩根台股期貨與TAIFEX台股期貨為研究對象，實證發現在報酬率分配具高狹峰特性較為明顯的時期(即SGX-DT市場子期間一)，健全估計式相較於標準估計式，避險組合的變異數及OHR的變異數均有較大的降幅，此也大大的減低因OHR變動所引發從新調整OHR的成本。[[abstract]]When we use futures to hedge a portfolio of risky assets, the most important objective is to estimate the optimal hedge ratio (OHR). When the futures price follows a martingale and investors have mean-variance utility, the OHR is equal to the minimum variance hedge ratio. Owing to time-varying volatility in financial asset returns, moving average, GARCH, or EWMA models are commonly employed to estimate OHR. All of the approaches to estimating the OHR described above are based on the sample variance and covariance estimators of returns. These are consistent estimators of the population variance and covariance, irrespective of the underlying distribution of data, but they are not in general efficient. In particular, when the distribution of the data is leptokurtic, these estimators will attach too much weight to extreme observations. This paper uses the Power EWMA estimator of Guermat and Harris (2002) to estimate OHR. The Power EWMA estimator (that is, the robust estimator) can capture the leptokurtic distribution of the data. We also compare the results of the robust estimator to those based on the standard estimators. Our empirical analysis is restricted to the SGX-DT and the TAIFEX Taiwan stock index futures. The empirical results show that use of the robust estimator generates reductions in the variance of the hedged portfolio and the volatility of the OHR for the SGX-DT futures market, and for subperiod 1 of high kurtosis. It also reduce the transaction costs of rebalancing that are associated with changes in the OHR