The Fourth Swedish National Pension Fund (AP4), as well as many other large investors, has noted deficiencies the Mean-Variance framework for portfolio management of asset with non-normal characteristics. The main problem apparent in the Mean-Variance framework, when investing in alternative assets such as hedge funds, is the lacking systematic control of the balance between the measurements of risk due normal variation and tail-risk. Hedge funds constitute an asset class distinguished by non-normal characteristics such as negative skewness and heavy excess kurtosis, which suggests normality should not be assumed when optimizing a portfolio of hedge funds. Certain hedge fund strategies aim to be uncorrelated to other hedge funds and the major asset markets and are thus expected to have the capacity to hedge against extreme market events. Hedge fund performance during historically volatile market periods, including heavy losses and liquidations, has however proved this untrue. Outcomes in the tail of hedge fund distributions rather appear to occur in conjunction with increased correlation toward external indicators such as the equity stock market. With the aim to consider tail events in a portfolio of hedge funds and index futures, an optimization model intending to capture the asymmetric covariance between hedge fund assets and the equity market is developed and evaluated. The theory of copulas is applied to estimate the multivariate distribution by separating assumptions regarding univariate characteristics and dependence between assets. The estimated multivariate distribution is thereafter utilized in a scenario-based optimization model applying the Conditional Value at Risk (CVaR) measure as a risk measure, to capture events in the left tail of the portfolio distribution. The proposed GARCH-C-Vine-Mean-CVaR model is presented and evaluated against two reference models, a GARCH-C-Vine-Mean-Variance model, and a model assuming a multivariate normal distribution, EWMA-Mean-Variance. The ability to capture realized outcomes is analyzed for all three models, where the proposed GARCH-C-Vine-Mean-CVaR as well as the GARCH-C-Vine-Mean-Variance model show to capture realized outcomes to a further extent than the model assuming a multivariate normal distribution. Further, applying the risk measure CVaR has in this study shown to capture the realized outcomes to the same extent as applying variance as the risk measure. In conclusion, the proposed model manages to capture tail-events in the data analyzed in this study, to a further extent than if assuming multivariate normality. The lack of regulations and bias that denote hedge fund reporting, does however prevent a conclusion on whether the proposed model captures actual realized tail-events of hedge fund returns.

採用風險值取代標準差來衡量投資組合的下方風險，除了更符合投資人的對風險的態度，也更貼近目前金融機構多以風險值作為內部控管工具的情形。但除了風險的事後衡量，本篇論文希望能夠事前積極地控制投資組合風險值，求得最適投資組合的各資產配置權重。故本篇論文研究方法採用了Rockafellar and Uryasev.(2000)的極小條件風險值最適投資組合模型先建立Mean-CVaR效率前緣，並將此效率前緣上的投資組合風險以風險值衡量，再應用電腦上的探索方法進一步求得風險值更低的投資組合，逼近求得Mean-VaR效率前緣，最後利用Mean-VaR效率前緣採用Campbell，Huisman與Koedijk(2001)模型求得控制風險值下的最適投資組合。 在實證分析上，本篇論文採用國內三檔股票為標的，首先在實證標的資產報酬檢定為非常態分配下，使用歷史模擬法，以資產實際非常態報酬分配估計VaR，驗證了使用本篇論文研究方法極小CVaR投資組合與探索方法，可以適當逼近真實的Mean-VaR效率前緣。再者研究比較不同信賴水準、不同資產報酬分配假設與不同權重產生方式下的Mean-VaR效率前緣與Ｍean- 效率前緣效果差異，最後求得控制風險值下的最適投資組合。 / In contrast to the role of variance in the traditional Mean-Variance framework, in this thesis we introduce Value-at-Risk (VaR) as a shortfall-constraint into the portfolio selection decision. Doing so is much more in fitting with individual perception to risk and in line with the constraints which financial institutes currently face. However, mathematically VaR has some serious limitations making the portfolio selection problem difficult to attain optimal solution. In order to apply VaR to ex ante portfolio decision, we use the closely related tractable risk measure Conditional Value-at-Risk (CVaR) in this thesis as a proxy to find efficient portfolios. We utilize linear programming formulation developed by Rockafellar and Uryasev(2000) to construct a Mean-CVaR efficient frontier. Following which the VaR of resulting portfolios in the Mean-CVaR efficient frontier is reduced further by a simple heuristic procedure. After constructing an empirical Mean-VaR efficient frontier that can be proven an useful approximation to the true Mean-VaR efficient frontier, the Campbell, Huisman and Koedijk(2001) model is used to find the optimal portfolio. Three Taiwan listing stocks are used to build the Mean-VaR efficient frontier in the empirical study. And the Mean-VaR efficient frontier of different confident levels, under different asset return assumptions, and different optimal portfolio selection models are compared and results analyzed.