臺灣博碩士論文加值系統

在做資產配置時，市場風險的量測必然是財務投資者要注重的，量測的方法很多，如資產報酬率的標準差、VaR、CVaR，這些風險指標各有其優劣，而本文選擇的是Aumann 和 Serrano在2008年提出的Riskiness，因為Riskiness滿足一階及二階隨機優越單調性，對選擇資產有幫助，這是以往指標通常沒有的特性；此外，計算上若假設資產報酬率為常態分配，也能簡化計算，有實務上的參考價值。在常態假設下，本文用Riskiness作為風險指標來衡量投資組合，找出投資組合機會的效率前緣之後，再依投資者可接受的風險高低提供配置資產之投資組合建議。

For asset allocation, the measure of financial risk is definitely important. There are plenty of ways of measuring, such as the standard deviation, VaR, and CVaR, with their own advantages and disadvantages. In this paper, the index focused on is Riskiness introduced by Aumann and Serrano (2008). Because of its first- (second-) order monotonicity, it helps selecting assets, and this property is not usually owned by the previous indices. In addition, when assuming the rate of return to follow normal distribution, the computation of Riskiness is simplified and thus with practical use. Under the assumption of normal distribution, this paper will present Riskiness as an index of risk to evaluate portfolios, find efficient frontier of portfolio opportunities, and make it provide some suggestions of asset allocation with regard to risk levels accepted by investors.

口試委員會審定書 i
誌謝 ii
中文摘要 iii
Abstract iv
目錄 v
圖目錄 vii
表目錄 ix
第一章 文獻回顧 1
1.1 Riskiness文獻回顧及簡介 1
1.1.1 Aumann和Serrano的Riskiness，以及Foster和Hart的Riskiness 1
1.1.2 一些引用2008年Aumann和Serrano的Riskiness的文章 2
1.1.3 Riskiness的主要優缺點及特性 3
1.1.4 常態分配下的Riskiness 5
1.1.5 小結 5
1.2 資產配置與風險指標的文獻回顧 6
第二章 Riskiness於資產配置之應用 8
2.1 Riskiness於資產配置之應用－兩個資產 8
2.1.1 風險指標為標準差之曲線方程式及漸近線方程式 9
2.1.2 風險指標為Riskiness之曲線方程式及漸近線方程式 11
2.1.3 舉例說明－風險指標為標準差、Riskiness 12
2.1.4 兩個資產下的效率前緣及資產配置建議 17
2.1.5 小結 20
2.2 Riskiness於資產配置之應用－三個資產 21
2.2.1 三個資產下的Riskiness－期望值座標圖 21
2.2.2 三個資產下的效率前緣及資產配置建議 23
2.2.3 小結 30
2.3 Riskiness於資產配置之應用－多個真實資產 31
2.3.1 多個真實資產下的Riskiness－期望值座標圖、效率前緣與資產配置比重 31
2.3.2 小結 43
第三章 結論 44
參考文獻 46
附錄 48
附錄一 2009-2010兩年台灣上市股票，低風險投資組合舉例 48
附錄二 2009-2010兩年台灣上市股票，中風險投資組合舉例 54
附錄三 2009-2010兩年台灣上市股票，高風險投資組合舉例 60
附錄四 2009-2010兩年台灣上市股票指數，低風險投資組合舉例 66
附錄五 2009-2010兩年台灣上市股票指數，中風險投資組合舉例 67
附錄六 2009-2010兩年台灣上市股票指數，高風險投資組合舉例 68

[1] Robert J. Aumann and Roberto Serrano. 2008. “An Economic Index of Riskiness”, Journal of Political Economy, Vol. 116, no. 5, pp. 810-836.
[2] Dean P. Foster and Sergiu Hart. 2009. “An Operational Measure of Riskiness”, Journal of Political Economy, vol. 117, no. 5, pp. 785-814.
[3] D. B. Brown and M. Sim. 2009. “Satisficing Measures for Analysis of Risky Positions”, Management Science, vol. 55, pp. 71-84.
[4] S. Drapeau and M. Kupper. 2009. “Risk Preferences and their Robust Representation”, Preprint.
[5] K. Schulze. 2010. “Existence and Computation of the Aumann-Serrano Index of Riskiness ”, McMaster University and Fields Institute, Hamilton, ON, Canada
[6] A. Chamorro and J. M. Usategui. 2011. “Riskiness and Preferences in Gambles with Uniform Distributions”, University of the Basque Country, the Basque Country, Spain
[7] U. Homm and C. Pigorsch. 2011. “Beyond the Sharpe Ratio: Performance Measurement with an Economic Index of Riskiness”, Working Paper, University of Bonn. Available at http://www.eea-esem.com/files/papers/EEA-ESEM/2011/1166/EPM_ESEM.pdf
[8] U. Homm and C. Pigorsch. 2012. “An operational interpretation and existence of the Aumann-Serrano index of riskiness”, Economics Letters, vol. 114, issue 3, pp. 265-267.
[9] M. Rothschild and J. E. Stiglitz. 1970. “Increasing risk: I. A Definition”, Journal of Economic Theory, vol. 2, no. 3, pp. 225-243.
[10] H. Markowitz, 1952. “Portfolio Selection”, The Journal of Finance, vol. 7, no. 1, pp. 77-91.
[11] Kolman, Joe; Onak, Michael; Jorion, Philippe; Taleb, Nassim; Derman, Emanuel; Putnam, Blu; Sandor, Richard; Jonas, Stan et al. 1998. “Roundtable: The Limits of VaR”. Derivatives Strategy
[12] R. T. Rockafellar and S. Uryasev. 2000. “Optimization of conditional value-at-risk”, Journal of Risk, vol. 2, no. 3, pp. 21-41.
[13] G. Pflug. 2000. “Some Remarks on the Value at Risk and the Conditional Value at Risk”, In, Uryasev, S. (Editor). Probabilistic Constrained Optimization: Methodology and Applications. Kluwer Academic Publishers. Available at http://www.univie.ac.at/sor/aurora6/Papers/Kluwer.pdf