避險基金資產配置分析應用極值理論

1990年代因為金融市場的快速發展，產生了許多新的金融商品，雖然這些商品讓金融市場的資金更加活絡、更具流動性，但事實上這些新商品往往具有危險性且架構極其複雜，且通常會牽涉到高槓桿的投資工具像是期貨、選擇權及結構型商品，投資人常常因為其高獲利而忽略背後隱含的風險，導致更嚴重的後果，次級房貸風暴重創全球股市就是個血淋淋的例子，因此風險管理就顯得越趨重要。另外以風險值(Value-at-Risk)作為風險衡量的方式也越來越普遍，其中很重要的原因就是風險值(Value-at-Risk)不只可以應用於常態分配(Normal distribution)，也能夠應用於更能描述資產報酬的其他分配，在近年許多銀行與金融機構已經開始採用風險值(Value-at-Risk)作為風險的衡量。本研究採用Campbell, R., Huisman, R., Koedijk, K. (2001)所發展的資產配置分析架構(mean-VaR framework)進行實證研究，該分析架構的概念是在目標最大損失的限制下，極大化投資組合預期報酬，同樣也有一類似夏普指數(Sharpe ratio)的績效衡量指標。在風險的部份，我們考慮ㄧ新的風險值估計方式，也就是極值理論(Extreme Value Theory)，極值理論可以針對分配的肥尾直接配適，在使用上相較於其他風險值的估計方式有其方便性。研究樣本包含三種資產的報酬率，分別為股票及債券及避險基金，我們以S&P 500以及10年期美國政府公債來代表此兩樣傳統資產，避險基金也是近年興起的新投資工具，資料來源為Datastream及Hedge Fund Research(HFR)資料庫。研究議題可分為兩部份，第一部分在探討使用不同的風險值衡量方式會如何影響資產配置效率，第二部份主是要探討以傳統資產為原投資組合下，加入避險基金或是避險基金中不同策略的指數報酬後，能否改善資產配置效率。實證結果發現，比較常態風險值(Normal-VaR)與極值理論風險值(Extreme-VaR)後，假設資產報酬服從常態分配會導致投資策略過度積極，亦即投資於風險性資產比重偏多。在避險基金的部份，結果顯示部分的避險基金策略無法改善資產配置效率，這個結果和其他避險基金的研究文獻較為不同。

關鍵字

避險基金；風險值；極值理論；資產配置

並列摘要

In 1990s financial market grew fast and completely, and creates lots of new financial products. In fact they are complicated and dangerous, since such kind of products always involve high leveraged investment tool such as options、futures and structural products. Here is a bloody example; sub-prime crashes the financial market and there is no exception in the world. Therefore risk management became more and more important today. Besides VaR; the new measure of risk, became more popular, since it could be applied to not only normal distribution but also to other distributions which are appropriate to describe the returns of new financial products. In recent year Banks and financial institutions have adopted VaR as the measure of risk. In this paper, we adopt a mean-VaR framework developed by Campbell, Huisman and Koedijk (2001) which allocates financial assets by maximizing expected return subject to the loss constraint. Similar to the mean-variance framework, they constructed a performance index like the Sharpe ratio. Here we introduce a new method for VaR estimation, Extreme Value Theory, which incorporates the heavy tail of distribution and is convenient comparing with other methods. We use three assets in our empirical analysis; two of them are bond and stock, which are viewed as traditional assets. Another one is hedge funds which is one of new asset in financial market and is consisting of different strategies. We can divide our analysis into two parts. One is to examine how allocation efficiency changes when using different methods of VaR. The other topic is to examine whether the hedge funds improve the allocation efficiency of traditional portfolio or not. We find that when using Normal-VaR it results in too aggressive investment strategy comparing with Extreme Value Theory based VaR. And we also find that the hedge funds may not perform as well as we thought. Some strategies improve the allocation efficiency of traditional portfolio, but some do not. It is different from other researches about hedge funds.

並列關鍵字

asset allocation ； Extreme Value Theory ； VaR ； hedge funds

參考文獻

Agarwal, V. and N. Naik., (2000), “On Taking the “Alternative” Route: Risks, Rewards, Style and Performance Persistence of Hedge Funds.” Journal of Alternative Investments, 6-23.

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Campbell, R.A., Huisman, R., Koedijk, C.G., (2001). Optimal portfolio selection in a

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避險基金資產配置分析應用極值理論

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