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題名 伴隨估計風險時的動態資產配置
Dynamic asset allocation with estimation risk作者 湯美玲
Tang, Mei Ling貢獻者 陳松男<br>江彌修
Chen, Son Nan<br>Chiang, Mi Hsiu
湯美玲
Tang, Mei Ling關鍵詞 資產配置
估計風險
對數常態資本市場
不確定性通膨
多重群組架構
貝氏估計
Asset allocation
Estimation risk
Lognormal-securities market
Uncertain inflation
Multi-group framework
Bayesian estimation日期 2012 上傳時間 2-Jan-2013 13:22:02 (UTC+8) 摘要 本文包含關於估計風險與動態資產配置的兩篇研究。第一篇研究主要就當須估計的投資組合其投入參數具有高維度特質的觀點下，探究因忽略不確定性通膨而對資產配置過程中帶來的估計風險。此研究基於多重群組架構下所發展出的新投資決策法則，能夠確實地評價不確定性通膨對資產報酬的影響性，並在應用於建構大規模投資組合時，能有效減少進行最適化投資決策過程中所需的演算時間與成本。而將此模型應用於建構全球ETFs投資組合的實證結果則進一步顯示，若在均值變異數架構下，因建構大型投資組合時須估計高維度投入參數而伴隨有大量估計風險時，參數估計方式建議結合採用貝氏估計方法來估算資產報酬的一階與二階動差，其所對應得到的投資組合樣本外績效會比直接採用歷史樣本動差來得佳。此實證結果亦隱含：在均值變異數架構下，穩定的參數估計值比起最新且即時的參數估計資訊對於投資組合的績效來得有益。同時，若當投入參數的樣本估計值波動很大時，增加放空限制亦能有利投組樣本外績效。 第二篇文章則主要處理當處於對數常態證券市場下時，投資組合報酬率不具有有限動差並導致無法在均值變異數架構下發展出最適化封閉解時的難題。本研究示範此時可透過漸近方法的應用，有效發展出在具有放空限制下，考量了估計風險後的簡單投資組合配置法則，並且展示如何將其應用至實務上的資產配置過程以建構全球投資組合。本文的數值範例與實證模擬結果皆顯示，估計風險的存在對於最適投資組合的選擇有實質的影響，無估計風險下得出的最適投資組合，不必然是存有估計風險下的最適投資組合。此外，實證模擬結果亦證明，當存有估計風險時，本文所發展的簡單法則，能使建構出的投資組合具有較佳的樣本外績效表現。
This dissertation consists of two essays on dynamic asset allocation with regard to dealing with estimation risk as being in different uncertainties in the mean-variance framework. The first essay concerns estimation errors from disregarding uncertain inflation in terms of the need in estimating high-dimensional input parameters for portfolio optimization. This study presents simplified and valid criteria referred to as the EGP-IMG model based on the multi-group framework to be capable of pricing inflation risk in a world of uncertainty. Empirical studies shows the proposed model indeed provides a smart way in picking worldwide ETFs that serves well to reduce the amount of costs and time in constructing a global portfolio when facing a large number of investment products. The effect of Bayesian estimation on improving estimation risk as the decision maker is subject to history sample moments for input parameters estimations is meanwhile examined. The results indicate portfolios implementing the Stein estimation and shrinkage estimators offer better performance compared with those applying the history sample estimators. It implicitly demonstrates that yielding stable estimates for means and covariances is more critical in the MV framework than getting the newest up-to-date parameters estimates for improving portfolio performance. Though short-sales constraints intuitively should hurt, they do practically contribute to uplift portfolio performance as being subject to volatile estimates of returns moments. The second essay undertakes the difficulty that the probability distribution of a portfolio`s returns may not have finite moments in a lognormal-securities market, and thus leads to the arduous problem in solving the closed-form solutions for the optimal portfolio under the mean-variance framework. As being in a lognormal-securities market, this study systematically delivers a simple rule in optimization with regard to the presence of estimation risk. The simple rule is derived accordingly by means of asymptotic properties when short sales are not allowed. The consequently numerical example specifies the detailed procedures and shows that the optimal portfolio with estimation risk is not equivalent to that ignoring the existence of estimation risk. In addition, the portfolio performance based on the proposed simple rule is examined to present a better out-of-sample portfolio performance relative to the benchmarks.參考文獻 Alexander, G. J., and B. G. Resnick, 1985,"More on estimation risk and simple rules for optimal portfolio selection," Journal of Finance 40, 125-133. Alexander, G. J., A. M. Baptista, and S. Yan, 2009, "Reducing estimation risk in optimal portfolio selection when short sales are allowed," Managerial and Decision Economics 30, 281-305. Badrinath, S. G., and S. Chatterjee, 1988, "On measuring skewness and elongation in common stock return distributions: the case of the market index," Journal of Business 61, 451-472. Badrinath, S. G., and S. Chatterjee, 1991, "A data-analytic look at skewness and elongation in common-stock-return distributions," Journal of Business and Economic Statistics 9, 223-233. Bakshi, G. S., and Z. Chen, 1996, "Inflation, asset returns, and the term structure of interest rates in monetary economies," Review of Financial Studies 9, 241-275. Barberis, N., 2000, "Investing for the long run when returns are predictable," Journal of Finance 55, 225-264 Barnes, M., J. H. Boyd, and B. D. Smith, 1999, "Inflation and asset returns," European Economic Reviews 43, 737-754. Barry, C. B., 1974, "Portfolio analysis under uncertain mean, variances, and covariances," Journal of Finance 29, 515-522. Bawa, V. S., S. J. Brown, and R. W. Klein, 1979, Estimation risk and optimal portfolio choice, North-Holland Publishing Company, New York. 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Seagle, 1971, "Portfolio selection: The effects of uncertain means, variances, and covariances," Journal of Financial and Quantitative Analysis 6, 1251-1262. Frost, P. A., and J. E. Savarino, 1986, "An empirical Bayes approach to efficient portfolio selection," Journal of Financial and Quantitative Analysis 21, 293-305. Frost, P. A., and J. E. Savarino, 1988, "For better performance: Constrain portfolio weights," Journal of Portfolio Management 15, 29-34. Garlappi, L., R. Uppal, and T. Wang, "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," Review of Financial Studies 20, 41-81. Grauer, R. R., and N. H. Hakansson, 1995, "Stein and CAPM estimators of the means in asset allocation," International Review of Financial Analysis 4, 35-66. Green, R. C., and B. Hollifield, 1992, "When will mean-variance efficient portfolios be well diversified?" Journal of Finance 47, 1785-1809. Gultekin, N. B., 1983, "Stock market returns and inflation: Evidence from other countries," Journal of Finance 38, 49-65. Jagannathan, R., and T. Ma, 2003, "Risk reduction in large portfolios: Why imposing the wrong constraints helps," Journal of Finance 58, 1651-1683. James, W., and C. Stein, 1961, "Estimation with quadratic loss," Proceedings of the Fourth Berkeley Symposium on Mathematical and Statistical Probability, Vol. 1, 361-380, University of California Press, Berkeley and Los Angeles. Jorion, P., 1985, "International portfolio diversification with estimation risk," Journal of Business 58, 259-278. Jorion, P., 1986, "Bayes-Stein estimation for portfolio analysis," Journal of Financial and Quantitative Analysis 21, 279-292. Joyce, J. M., and R. C. Vogel, 1970, "The uncertainty in risk: Is variance unambiguous?" Journal of Finance 25, 127-134. Kallberg, J. G., and W. T. Ziemba, 1984, "Mis-specification in portfolio selection problems," in G. Bamberg and K. Spremann, eds, Risk and Capital: Lecture Notes in Economics and Mathematical Systems, Springer-Verlag Publishing Company, New York. Kandel, S., and R. F. Stambaugh, 1996, "On the predictability of stock returns: An asset-allocation perspective," Journal of Finance 51, 385-424. Kan, R., and G. Zhou, 2007, "Optimal portfolio choice with parameter uncertainty," Journal of Financial and Quantitative Analysis 42, 621-656. Kaul, G., 1987, "Stock returns and inflation: the role of the monetary sector," Journal of Financial Economics 18, 253-276. Klein, R. W., and V. S. Bawa, 1976, "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics 3, 215-231. Kuhn, D., P. Parpas, B. Rustem, and R. Fonseca, 2009, "Dynamic mean-variance portfolio analysis under model risk," Journal of Computational Finance 12, 91-115. Lee, W. Y., and R. K. S. Rao, 1988, "Mean lower partial moment valuation and lognormally distributed returns," Management Science 34, 446-453. Ledoit, O., and M. Wolf, 2003, "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance 10, 603-621. Ledoit, O., and M. Wolf, 2004a, "Honey, I shrunk the sample conariance matirx," Journal of Portfolio Management 30, 110-119. Ledoit, O., and M. Wolf, 2004b, "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis 88, 365-411. Ledoit, O., and M. Wolf, 2008, "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance 15, 850-859. Lintner, J., 1975, "Inflation and security returns," Journal of Finance 30, 259-280. Liu, J., 2007, "Portfolio selection in stochastic environments," Review of Financial Studies 20, 1-39. Markowitz, H., 1952, "Portfolio selection," Journal of Finance 7, 77-91. Marshall, D. A., 1992, "Inflation and asset returns in a monetary economy," Journal of Finance 47, 1315-1342. Merton, R. C., 1971, "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory 3, 373-413. Merton, R. C., 1980, "On estimating the expected returns on the market: an exploratory investigation," Journal of Financial Economics 8, 323-361. Michaud, R. O., 1989, "The Markowitz optimization enigma: Is "optimized` optimal?" Financial Analysts Journal 45, 31-42. Mishkin, F. S., 1992, "Is the Fisher effect real? A reexamination of the relationship between inflation and interest rates," Journal of Monetary Economics 30, 195-215. Muirhead, R. J., 1987, "Developments in eigenvalue estimation," in A. K. Gupta, ed., Advances in Multivariate Statistical Analysis, 277-288, Springer, Boston, Moore, A. B., 1964, "Some characteristics of changes in common stock prices," in E. Paul H. Cootner, ed., The Random Character of Stock Market Prices, MIT Press, Cambridge, Mass. Munk, C., C. Søensen, and T. N. 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Peiró A., 1994, "The distribution of stock returns: International evidence," Applied Financial Economics 4, 431 - 439. Samuelson, P. A., 1970, "The fundamental approximation theorem of portfolio analysis in terms of means, variances, and higher moments," Review of Economic Studies 37, 537-542. Stambaugh, R. F., 1997, "Analyzing investments whose histories differ in length," Journal of Financial Economics 45, 285-331. Stein, C., 1956, "Inadmissibility of the usual estimator for the mean of a multivariate normal distribution," in Neyman, J. ed., Proceedings of the Third Berkeley Symposium on Mathematical and Statistical Probability, Vol. 1, 197-206, University of California Press, Berkeley and Los Angeles. Tu, J., and G. Zhou, 2010, "Incorporating economic objectives into Bayesian priors: Portfolio choice under parameter uncertainty," Journal of Financial and Quantitative Analysis 45, 959-986. Wachter, J. A., 2002, "Portfolio and consumption decisions under mean-reverting returns: An exact solution for complete markets," Journal of Financial and Quantitative Analysis 37, 63-91. Wismer, D. A., and R. Chattergy, 1978, Introduction to nonlinear optimization: A problem solving approach, North-Holland Publishing Company, New York. Xia, Y., 2001, "Learning about predictability: The effects of parameter uncertainty on dynamic asset allocation," Journal of Finance 56, 205-246. 描述 博士
國立政治大學
金融研究所
94352507
101資料來源 http://thesis.lib.nccu.edu.tw/record/#G0094352507 資料類型 thesis dc.contributor.advisor 陳松男<br>江彌修 zh_TW dc.contributor.advisor Chen, Son Nan<br>Chiang, Mi Hsiu en_US dc.contributor.author (Authors) 湯美玲 zh_TW dc.contributor.author (Authors) Tang, Mei Ling en_US dc.creator (作者) 湯美玲 zh_TW dc.creator (作者) Tang, Mei Ling en_US dc.date (日期) 2012 en_US dc.date.accessioned 2-Jan-2013 13:22:02 (UTC+8) - dc.date.available 2-Jan-2013 13:22:02 (UTC+8) - dc.date.issued (上傳時間) 2-Jan-2013 13:22:02 (UTC+8) - dc.identifier (Other Identifiers) G0094352507 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/56503 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融研究所 zh_TW dc.description (描述) 94352507 zh_TW dc.description (描述) 101 zh_TW dc.description.abstract (摘要) 本文包含關於估計風險與動態資產配置的兩篇研究。第一篇研究主要就當須估計的投資組合其投入參數具有高維度特質的觀點下，探究因忽略不確定性通膨而對資產配置過程中帶來的估計風險。此研究基於多重群組架構下所發展出的新投資決策法則，能夠確實地評價不確定性通膨對資產報酬的影響性，並在應用於建構大規模投資組合時，能有效減少進行最適化投資決策過程中所需的演算時間與成本。而將此模型應用於建構全球ETFs投資組合的實證結果則進一步顯示，若在均值變異數架構下，因建構大型投資組合時須估計高維度投入參數而伴隨有大量估計風險時，參數估計方式建議結合採用貝氏估計方法來估算資產報酬的一階與二階動差，其所對應得到的投資組合樣本外績效會比直接採用歷史樣本動差來得佳。此實證結果亦隱含：在均值變異數架構下，穩定的參數估計值比起最新且即時的參數估計資訊對於投資組合的績效來得有益。同時，若當投入參數的樣本估計值波動很大時，增加放空限制亦能有利投組樣本外績效。 第二篇文章則主要處理當處於對數常態證券市場下時，投資組合報酬率不具有有限動差並導致無法在均值變異數架構下發展出最適化封閉解時的難題。本研究示範此時可透過漸近方法的應用，有效發展出在具有放空限制下，考量了估計風險後的簡單投資組合配置法則，並且展示如何將其應用至實務上的資產配置過程以建構全球投資組合。本文的數值範例與實證模擬結果皆顯示，估計風險的存在對於最適投資組合的選擇有實質的影響，無估計風險下得出的最適投資組合，不必然是存有估計風險下的最適投資組合。此外，實證模擬結果亦證明，當存有估計風險時，本文所發展的簡單法則，能使建構出的投資組合具有較佳的樣本外績效表現。 zh_TW dc.description.abstract (摘要) This dissertation consists of two essays on dynamic asset allocation with regard to dealing with estimation risk as being in different uncertainties in the mean-variance framework. The first essay concerns estimation errors from disregarding uncertain inflation in terms of the need in estimating high-dimensional input parameters for portfolio optimization. This study presents simplified and valid criteria referred to as the EGP-IMG model based on the multi-group framework to be capable of pricing inflation risk in a world of uncertainty. Empirical studies shows the proposed model indeed provides a smart way in picking worldwide ETFs that serves well to reduce the amount of costs and time in constructing a global portfolio when facing a large number of investment products. The effect of Bayesian estimation on improving estimation risk as the decision maker is subject to history sample moments for input parameters estimations is meanwhile examined. The results indicate portfolios implementing the Stein estimation and shrinkage estimators offer better performance compared with those applying the history sample estimators. It implicitly demonstrates that yielding stable estimates for means and covariances is more critical in the MV framework than getting the newest up-to-date parameters estimates for improving portfolio performance. Though short-sales constraints intuitively should hurt, they do practically contribute to uplift portfolio performance as being subject to volatile estimates of returns moments. The second essay undertakes the difficulty that the probability distribution of a portfolio`s returns may not have finite moments in a lognormal-securities market, and thus leads to the arduous problem in solving the closed-form solutions for the optimal portfolio under the mean-variance framework. As being in a lognormal-securities market, this study systematically delivers a simple rule in optimization with regard to the presence of estimation risk. The simple rule is derived accordingly by means of asymptotic properties when short sales are not allowed. The consequently numerical example specifies the detailed procedures and shows that the optimal portfolio with estimation risk is not equivalent to that ignoring the existence of estimation risk. In addition, the portfolio performance based on the proposed simple rule is examined to present a better out-of-sample portfolio performance relative to the benchmarks. en_US dc.description.tableofcontents Abstract i Acknowledgement iii Contents v Lists of Table vii Lists of Figures viii 1 Introduction 1 2 Optimal Asset Allocation under Uncertain Inflation and Estimation Risk: The Multi-Group Case 2 2.1 Introduction 2 2.2 Uncertain Inflation in the Multi-Group Case 5 2.2.1 Case with Short-Sales Allowed 6 2.2.2 Case of Long-Only Permitted 8 2.3 Consider Inflation or Not: A Numerical Example 9 2.4 Estimation Risk Calibration in the Multi-Group Case 12 2.4.1 Estimate the First-Order Moment of Securities Returns 12 2.4.2 Estimate the Second-Order Moment of Group Indices 15 2.5 Practical Application 18 2.5.1 Performance Evaluation and Data Sources 18 2.5.2 Portfolio Performance regarding Risk of Uncertain Inflation 20 2.5.3 Portfolio Performance regarding Estimation Risk 23 2.6 Summary 26 3 Portfolio Optimization with Estimation Risk on Return Distribution:The Case of The Lognormal-Securities Market 28 3.1 Introduction 28 3.2 Estimation Risk in a Lognormal Market 30 3.3 Portfolio Construction with and without Estimation Risk 33 3.4 Numerical Example 38 3.5 Practical Applications 42 3.5.1 Performance Evaluation and Data Sources 42 3.5.2 Results from Simulated Data 43 3.6 Summary 48 4 Conclusion and Future Research in Prospect 51 A. Appendix for Chapter 2 54 A.1 Proofs for Equations (4) to (6) 54 A.2 Proofs for Equations (9) to (12) 56 A.3 Optimal Portfolio Weights for the EGP-MG Model 57 B. Appendix for Chapter 3 59 B.1 Proof for Equation (7) 59 B.2 Proofs for Equations (10) to (14) 60 B.3 Security Path Generating Process 61 B.4 Figures for Robustness Test 63 Bibliography 65 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0094352507 en_US dc.subject (關鍵詞) 資產配置 zh_TW dc.subject (關鍵詞) 估計風險 zh_TW dc.subject (關鍵詞) 對數常態資本市場 zh_TW dc.subject (關鍵詞) 不確定性通膨 zh_TW dc.subject (關鍵詞) 多重群組架構 zh_TW dc.subject (關鍵詞) 貝氏估計 zh_TW dc.subject (關鍵詞) Asset allocation en_US dc.subject (關鍵詞) Estimation risk en_US dc.subject (關鍵詞) Lognormal-securities market en_US dc.subject (關鍵詞) Uncertain inflation en_US dc.subject (關鍵詞) Multi-group framework en_US dc.subject (關鍵詞) Bayesian estimation en_US dc.title (題名) 伴隨估計風險時的動態資產配置 zh_TW dc.title (題名) Dynamic asset allocation with estimation risk en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) Alexander, G. J., and B. G. Resnick, 1985,"More on estimation risk and simple rules for optimal portfolio selection," Journal of Finance 40, 125-133. Alexander, G. J., A. M. Baptista, and S. Yan, 2009, "Reducing estimation risk in optimal portfolio selection when short sales are allowed," Managerial and Decision Economics 30, 281-305. Badrinath, S. G., and S. Chatterjee, 1988, "On measuring skewness and elongation in common stock return distributions: the case of the market index," Journal of Business 61, 451-472. Badrinath, S. G., and S. Chatterjee, 1991, "A data-analytic look at skewness and elongation in common-stock-return distributions," Journal of Business and Economic Statistics 9, 223-233. Bakshi, G. S., and Z. Chen, 1996, "Inflation, asset returns, and the term structure of interest rates in monetary economies," Review of Financial Studies 9, 241-275. Barberis, N., 2000, "Investing for the long run when returns are predictable," Journal of Finance 55, 225-264 Barnes, M., J. H. Boyd, and B. D. 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