考虑后悔厌恶的私募股权基金投资组合优化模型
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摘要
在经典的Merton连续时间资产组合框架内引入非流动性的私募股权基金,探讨流动性约束对投资组合配置的影响.假设投资者具有终端投资组合财富的后悔厌恶型效用函数,通过求解动态承诺与投资组合优化问题,给出了投资者如何最优的向私募股权基金承诺资本,以及如何在股票和债券之间进行最优的动态再调整.通过数值模拟比较分析了后悔厌恶型投资者和CRRA型投资者的最优投资组合策略的变化情况.结果发现,由于私募股权基金非流动性的影响,后悔厌恶型投资者对私募股权基金的承诺比率低于CRRA型投资者的承诺比率,从而获得较低的投资组合财富.
This paper incorporates an illiquid private equity fund into the framework of Merton's classic theory on continous time portfolio selection, to explore the impacts of illiquidity on the restricted investor's optimal portfolio allocations. Assuming an investor derives regret aversion utility from terminal portfolio wealth, the paper solves for a dynamic commitment and portfolio strategy that shows investors how to optimally commit capital to private equity fund and how to optimally rebalance between liquid stock and bonds over time.Furthermore, the optimal portfolio strategies of regret averse investors and CRRA investors are analyzed and compared. The numerical analysis demonstrates that, as a consequence from illiquidity, regret averse investors' commitment rate to private equity funds are lower than that of CRRA investors, and thus the regret averse investors get lower terminal portfolio wealth than the CRRA investors.
This paper incorporates an illiquid private equity fund into the framework of Merton's classic theory on continous time portfolio selection, to explore the impacts of illiquidity on the restricted investor's optimal portfolio allocations. Assuming an investor derives regret aversion utility from terminal portfolio wealth, the paper solves for a dynamic commitment and portfolio strategy that shows investors how to optimally commit capital to private equity fund and how to optimally rebalance between liquid stock and bonds over time.Furthermore, the optimal portfolio strategies of regret averse investors and CRRA investors are analyzed and compared. The numerical analysis demonstrates that, as a consequence from illiquidity, regret averse investors' commitment rate to private equity funds are lower than that of CRRA investors, and thus the regret averse investors get lower terminal portfolio wealth than the CRRA investors.
引文
[1]Buchner A.Portfolio Optimization with Private Equity Funds.Passau:University of Passau,2014.
[2]Lerner J,Schoar A M.The illiquidity puzzle:Theory and evidence from private equity.Journal of Financial Economics,2004,72(1):3–40.
[3]Cumming A,Helge H,Schweizer D.Private equity benchmarks and portfolio optimization.Journal of Banking and Finance,2013,37(9):3515–3528.
[4]Longstaff F A.Portfolio claustrophobia:Asset pricing in markets with illiquid assets.American Economic Review,2009,99(4):1119–1144.
[5]Ang A,Papanikolaou D,Westerfield M.Portfolio choice with illiquid assets.Management Science,2014,60(11):2737–2761.
[6]Sorensen M,Wang N,Yang J Q.Valuing private equity.Review of Financial Studies,2014,27(7):1977–2021.
[7]Liu Y,Yang J Q.Optimal investment of private equity.Finance Research Letters,2015,14(1):76–86.
[8]Bell D E.Regret in decision making under uncertainty.Operations Research,1982,30(5):961–981.
[9]Loomes G,Sugden R.Regret theory:An alternative theory of rational choice under uncertainty.The Economic Journal,1982,92(368):805–824.
[10]梁霞,姜艳萍.考虑后悔行为的具有二元期望的随机多属性决策方法.系统工程学报,2015,30(6):719–727.Liang X,Jiang Y P.Method of stochastic multi-attribute decision making with 2-tuple aspirations considering regret behavior.Journal of System Engineering,2015,30(6):719–727.(in Chinese)
[11]Laciana C E,Weber E U.Correcting expected utility for comparisons between alternative outcomes:A unified parameterization of regret and disappointment.Journal of Risk and Uncertainty,2008,36(1):1–17.
[12]Michenaudc S,Solnik B.Applying regret theory to investment choices:Currency hedging decisions.Journal of International Money and Finance,2008,27(5):677–694.
[13]Mulaudzi M P,Petersen M A,Schoeman I M.Optimal allocation between bank loans and treasuries.Optimization Letters,2008,2(4):555–566.
[14]Egozcue M J.Gains from diversification:A regret theory approach.Economics Bulletin,2012,32(1):204–219.
[15]Merton R C.Optimum consumption and portfolio rules in a continuous-time model.Journal of Economic Theory,1971,3(4):373–413.
[16]彭涓,靳玉英,杨金强.基于过度外推的最优投资与消费策略.管理科学学报,2017,20(3):56–62.Peng J,Jin Y Y,Yang J Q.Optimal investment and consumption based on over-extrapolation.Journal of Management Sciences in China,2017,20(3):56–62.(in Chinese)
[17]王愫新,荣喜民.保险公司和再保险公司的最优投资策略.系统工程学报,2017,32(2):207–217.Wang S X,Rong X M.Optimal investment strategy for both insurer and reinsurer.Journal of Systems Engineering,2017,32(2):207–217.(in Chinese).
[18]Bordag L A,Yamshchikov I P,Zhelezov D.Optimal allocation-consumption problem for a portfolio with an illiquid asset.International Journal of Computer Mathematics,2016,93(5):1–12.
[19]Buchner A.Portfolio dynamics under illiquidit.The Journal of Risk Finance,2016,17(4):405–427.
[20]Cox J C,Huang C F.Optimal consumption and portfolio policies when asset prices follow a diffusion process.Journal of Economic Theory,1989,49(1):33–83.
[21]Kraft H,Munk C.Optimal housing,consumption,and investment decisions over the life cycle.Management Scicence,2011,57(6):1025–1041.
[22]Klimko L A,Nelson P I.On conditional least squares estimation for stochastic processes.The Annals of Statistics,1978,6(3):629–642.
[23]Kaplan S N,Schoar A.Private equity performance:Returns,persistence and capital flows.Journal of Finance,2005,60(4):1791–1823.
[24]Phalippou L,Gottschalg O.The performance of private equity funds.Review of Financial Studies,2009,22(4):1747–1776.
[25]Harris R S,Jenkinson T,Kaplan S N.Private equity performance:What do we know.Journal of Finance,2014,69(5):1851–1882.
[2]Lerner J,Schoar A M.The illiquidity puzzle:Theory and evidence from private equity.Journal of Financial Economics,2004,72(1):3–40.
[3]Cumming A,Helge H,Schweizer D.Private equity benchmarks and portfolio optimization.Journal of Banking and Finance,2013,37(9):3515–3528.
[4]Longstaff F A.Portfolio claustrophobia:Asset pricing in markets with illiquid assets.American Economic Review,2009,99(4):1119–1144.
[5]Ang A,Papanikolaou D,Westerfield M.Portfolio choice with illiquid assets.Management Science,2014,60(11):2737–2761.
[6]Sorensen M,Wang N,Yang J Q.Valuing private equity.Review of Financial Studies,2014,27(7):1977–2021.
[7]Liu Y,Yang J Q.Optimal investment of private equity.Finance Research Letters,2015,14(1):76–86.
[8]Bell D E.Regret in decision making under uncertainty.Operations Research,1982,30(5):961–981.
[9]Loomes G,Sugden R.Regret theory:An alternative theory of rational choice under uncertainty.The Economic Journal,1982,92(368):805–824.
[10]梁霞,姜艳萍.考虑后悔行为的具有二元期望的随机多属性决策方法.系统工程学报,2015,30(6):719–727.Liang X,Jiang Y P.Method of stochastic multi-attribute decision making with 2-tuple aspirations considering regret behavior.Journal of System Engineering,2015,30(6):719–727.(in Chinese)
[11]Laciana C E,Weber E U.Correcting expected utility for comparisons between alternative outcomes:A unified parameterization of regret and disappointment.Journal of Risk and Uncertainty,2008,36(1):1–17.
[12]Michenaudc S,Solnik B.Applying regret theory to investment choices:Currency hedging decisions.Journal of International Money and Finance,2008,27(5):677–694.
[13]Mulaudzi M P,Petersen M A,Schoeman I M.Optimal allocation between bank loans and treasuries.Optimization Letters,2008,2(4):555–566.
[14]Egozcue M J.Gains from diversification:A regret theory approach.Economics Bulletin,2012,32(1):204–219.
[15]Merton R C.Optimum consumption and portfolio rules in a continuous-time model.Journal of Economic Theory,1971,3(4):373–413.
[16]彭涓,靳玉英,杨金强.基于过度外推的最优投资与消费策略.管理科学学报,2017,20(3):56–62.Peng J,Jin Y Y,Yang J Q.Optimal investment and consumption based on over-extrapolation.Journal of Management Sciences in China,2017,20(3):56–62.(in Chinese)
[17]王愫新,荣喜民.保险公司和再保险公司的最优投资策略.系统工程学报,2017,32(2):207–217.Wang S X,Rong X M.Optimal investment strategy for both insurer and reinsurer.Journal of Systems Engineering,2017,32(2):207–217.(in Chinese).
[18]Bordag L A,Yamshchikov I P,Zhelezov D.Optimal allocation-consumption problem for a portfolio with an illiquid asset.International Journal of Computer Mathematics,2016,93(5):1–12.
[19]Buchner A.Portfolio dynamics under illiquidit.The Journal of Risk Finance,2016,17(4):405–427.
[20]Cox J C,Huang C F.Optimal consumption and portfolio policies when asset prices follow a diffusion process.Journal of Economic Theory,1989,49(1):33–83.
[21]Kraft H,Munk C.Optimal housing,consumption,and investment decisions over the life cycle.Management Scicence,2011,57(6):1025–1041.
[22]Klimko L A,Nelson P I.On conditional least squares estimation for stochastic processes.The Annals of Statistics,1978,6(3):629–642.
[23]Kaplan S N,Schoar A.Private equity performance:Returns,persistence and capital flows.Journal of Finance,2005,60(4):1791–1823.
[24]Phalippou L,Gottschalg O.The performance of private equity funds.Review of Financial Studies,2009,22(4):1747–1776.
[25]Harris R S,Jenkinson T,Kaplan S N.Private equity performance:What do we know.Journal of Finance,2014,69(5):1851–1882.