平均數-低偏動差模型之投資績效表現－與平均數-變異數模型之比較

The Portfolio Performance of Mean Lower Partial Moment Model-In Comparison with Mean Variance Model

陳怡伶(Yi-Ling Chen)

指導教授 ： 楊奕農

中原大學/商學院/國際貿易研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200509

摘要

摘要
傳統投資組合理論係以變異數來衡量風險，不過以此來估計風險時，無論價格上漲或下跌皆視為相同風險，但其實價格下跌才是投資人真正想規避的風險。基於上述爭議，Bawa and Lindenberg （1977）及Fishburn（1977）以低偏動差 （Lower Partial Moment）為損失風險的觀念發展出平均數-低偏動差模型。因此，本研究以低偏動差來衡量投資組合的風險，並分析其與利用變異數衡量風險時在求解最適投資組合上之差異。
近年來隨著金融商品多樣化，投資的管道也愈來愈多元，其中股票是投資人最常運用理財工具之一，因此，本研究將利用台灣股票市場八大類股-水泥業、食品類、塑化類、紡織業、機電類、造紙類、營建業及金融類為投資組合之標的。並以不同歷史資料長度、不同模擬持有期間、及不同進場時機三種角度來比較兩種投資組合的風險值（Value at Risk）、報酬率、Sharpe指標、Treynor指標及R/SV指標等績效指標的優劣。
本研究之實證結果發現，無論以不同歷史資料長度、不同模擬持有期間及不同進場時機分析投資組合績效，整體而言平均數-低偏動差模型績效表現通常會優於平均數-變異數模型。由於平均數-低偏動差模型僅將損失部分視為風險，因此，建議投資人投資在台灣股票市場時，可以利用平均數-低偏動差模型為選擇投資組合之依據。

關鍵字

平均數-低偏動差模型 ； 平均數-變異數模型 ； 風險值

並列摘要

Abstract
In the traditional portfolio theory, the investment risk is measured by the variance. But based on this method, an increase and a decrease in prices of financial asset are treated the same. However, the risk that investor really want to avoid is that the price of assets decrease. Due to the above reason, Bawa and Lindenberg (1977) and Fishburn (1977) develop a theory to evaluate the downside risk named “Mean Lower-Partial-Moment” (MLPM) which is derived from the concept of the Lower Partial Moment. (LPM)
The main subject of this paper is to find out the optimal portfolio by the comparison and analysis of the portfolio risk measured by LPM and the portfolio risk measured by variance.
In these several years, the financial markets become more diversified. One of the popular financial assets is stock market. In this paper, we will analyze the value at risk (VaR), returns, Sharpe index, Treynor index, and R/SV index of the two kinds of portfolios by simulating different historic estimation periods, different holding periods and different market timing. And the portfolios will consist of the eight sub-categories of Taiwan’s stock market index.
According to the results from this study, generally, the performance of MLPM model is better than mean-variance (MV) model, no matter what kind of different historic periods, different holding periods, or different market timing. Because MLPM only considers the lost on value of the portfolio as a risk, therefore, it is reasonable for investors to select portfolio according to the theory of MLPM if they invest in Taiwan’s stock market.

並列關鍵字

mean-lower partial moment model ； value at risk ； mean-variance model

參考文獻

Ang, J. S. and J. H. Chua (1979) “Composite Measures for The Evaluation of Investment Performance,” Journal of Financial Quantitative Analysis, 14, pp.361-384.

Bawa, V. S. (1975) “ Optimal Rules for Ordering Uncertain Prospects,” Journal of Financial Economics, 2, pp.95-121.

Bawa, V. S. and E. B. Lingenberg (1977) “ Capital Market Equilibrium in A Mean-Lower Partial Moment Framework,” Journal of Financial Economics, 5, pp.189-200.

Beder, T. S. (1995) “VAR: Seductive but Dangerous,” Financial Analysts Journal, 51, pp.12-24.

Grootveld, H. and W. Hallerbach (1999) “Variance vs. Downside Risk: Is There Really that Much Difference?” Europe Journal of Operational Research, 114, pp.304-309.