考量放空及交易成本之不同風險測度模型於不同類投資標的之比較

本研究提出四種不同風險衡量的再調整模型如平均數-變異數模型 (MV)、平均絕對偏差模型 (MAD)、下行風險模型 (DSR)、條件風險值模型 (CVaR) 來做為測試的基礎。針對實際市場的交易情況加入了放空、交易成本這兩個因素，從多種資產類別間的相關性及不同投資標的所購成的投資組合這兩個層面來探討考量不允許放空與允許放空的情況下，並且結合移動視窗法來模擬實際多時期不同期間的交易狀況，探討資產間的相關性以及最佳的投資組合績效，並找出有那一種風險測度模基適合那一類的投資標。本研究以美國指數股票型基金、能源商品基金、貴重金屬基金、房地產基金以及固定收益(美國國庫債券到期日為30年及1年) 為研究對象，以四種績效指標及來衡量，即夏普指數、市場價值、投資權重、相似度指標，並觀察不同投資期間的結果。實驗結果發現，CVaR模型較適合多個投資標的下所組成的投資組合；DSR模型適合在投資標的波動與市場上呈反向變動所組成的投資組合，並在牛熊市交替時投資明顯別於其他模型的現象；MAD模型及MV模型投資的相似度較相近；Buy & Hold (B&H)在各種情況下除了加入固定收益的實驗外，並沒有較好的表現。此外，在不同時期方面，本研究以10天、20天、40天、60天為再調整期間測試，發現再調整期間相對越長，並沒有發揮較佳的績效，再調整期間亦不宜太短，結果顯示再調整期間為20天較佳。

關鍵字

均異模型；平均絕對偏差模型；下行風險模型；條件風險值模型；交易成本；放空

並列摘要

With different risk measurements, the rebalancing portfolio selection models including the Mean Variance model, the Mean Absolute Deviation model, the Downside Risk model, and the Conditional Value at Risk model with short selling and trading cost have been studied. Using the rolling window technique, multi-period trading simulation is performed while short selling and transaction cost are also taken into consideration to these four models. Four kinds of performance assessments, which are sharpe ratio, market value, portfolio weight and similarity index are used to compare performances among these four models. The simulating result from using the historical data which is consisted of different asset types including the Exchange Traded Funds, S&P 500 Volatility Index, Commodity, Energy, Precious Metal, Real Estate Investment Trust and Fixed Income. Then we try to find out which risk measure is suitable for which asset type. Therefore, according to this study, we can infer that Conditional Value at Risk is suitable for the asset types which are the combination of many different asset types. Downside risk measure is suitable for the portfolio which consists of assets with negative correlation to the market. The similarity proportion with Mean Absolute Deviation and Mean Variance are more similar than other two models. On the other hand, Buy and Hold strategy in each situation can not have a great benefit without fixed income. In different rebalancing period, the longer and shorter rebalancing period cannot have a good performance in our test with holding period 10 days, 20days, 40days and 60days. The best rebalancing period is 20days for portfolio selection according to our results.