最佳投資組合之實務效能分析

Empirical Performance Analysis of Optimal Portfolio

魏家茂(Wei, Chia Mao)

指導教授 ： 徐南蓉

國立清華大學/理學院/統計學研究所/碩士(2015年)

https://doi.org/10.6843/NTHU.2015.00313

摘要

在尋找最佳化投資組合時，Markowitz的平均數－變異數模型 (Mean-Variance Model) 是進行資產配置最常用的方法。實務上計算最佳投資組合權重時需要估計未知參數，因此傳統的做法是使用樣本平均數與樣本變異數矩陣進行估計。然而，已經有許多文獻指出估計誤差會導致投資組合的表現比理論預期的結果差，因此，許多論文進一步研究如何透過更好的統計估計減少誤差以提升投資組合的實務績效。本文使用了收縮估計 (shrinkage estimator) 與單因子模型 (single factor model) 估計來改善變異數矩陣估計的準確度，並採用Euclidean norm, Sharpe Ratio與效率前緣 (efficiency frontiers) 等評估準則比較不同估計方法所求出之投資組合的績效差異。若資產報酬率具時間相關性，則使用VAR模型估計所需參數後，再進行投資組合的計算。當樣本夠大時，考慮時間序列修正的投資組合績效會優於修正前之投資組合，此論文透過數值模擬分析，比較在各種不同程度的時間相關情況，不同估計法所得到的投資組合之績效差異，並進行台股資料之實例分析。

關鍵字

最佳投資組合 ； 平均數－變異數模型 ； VAR 模型

並列摘要

Markowitz's celebrated Mean-Variance model is the most popular method used in asset allocation for searching an optimal portfolio. Such an optimization relies on the independent and identically distributed (i.i.d.) assumption for the underlying multiple return series, as well as the known parameter values for the mean and covariance matrix. But, in practice, the mean and covariance matrix are unknown and have to be estimated from historical data. Many studies have found that the optimal portfolio based on the estimated parameters performance not well. The reason is mainly due to the estimation errors. Therefore, using more robust estimations would generally enhance the empirical performance of Markowitz's optimal portfolio. To justify the advantage of using more robust methods in determining the portfolio, this thesis compares different estimation methods in terms of several performance measures, including the efficiency frontier, Sharpe ratio, estimation error for the portfolio weights and Frobenius norm for the covariance matrix. The methods considered include the shrinkage estimates, the estimates using factor models, and the NPEB methods. Besides the i.i.d. modeling, the vector AR modeling is also considered for examining its advantage in asset allocation. Based on the simulation results, we found that shrinkage and factor model methods perform better when short position is allowed but the advantage is insignificant when short position is not allowed.

並列關鍵字

optimal portfolio ； mean-variance model ； VAR model

參考文獻

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