OPTIMAL INVESTMENT STRATEGIES FOR CONTROLLING DRAWDOWNS
OPTIMAL INVESTMENT STRATEGIES FOR CONTROLLING DRAWDOWNS
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DOI：
10.1111/j.1467-9965.1993.tb00044.x
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发表时间：
1993-07
影响因子：
1.6
通讯作者：
Sanford J. Grossman;Zhongquan Zhou
中科院分区：
文献类型：
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作者：
Sanford J. Grossman;Zhongquan Zhou
我们分析了投资者的最佳风险投资政策，该投资者在每个时间点都希望损失不超过其财富截至当时已实现的最大价值的固定百分比。特别是，如果“M”t是在时间“t”或之前获得的最大财富水平W，那么对他的投资组合选择施加的约束是W t α“M”t，其中α是αO和1之间的外生数。我们表明，对于恒定的相对风险厌恶效用函数，最优政策涉及在时间“t”按“盈余”“W”t - α“M”t的比例投资风险资产。最优保单可能与 Black 和 Perold (1987) 以及 Grossman 和 Vila (1989) 中分析的恒定比例投资组合保险保单类似。然而，在这些论文中，投资者将其财富保持在“非随机”下限“F”之上，而不是随机下限 α“M”t 之上。这里研究的下限的“随机”特征对财富处于历史最高水平的自然状态下的投资政策产生有趣的影响；即，当 Wt e“M”t 时。可以看出，在“W”t e“M”t 时，α“M”t 预计将以比“W”t 更快的速度增长，因此风险资产的投资预计会下降。我们还表明，当“W”t 接近α“M”t 时，风险资产的投资预计会增加。我们推测，在均衡模型中，当市场接近历史高点时，下限的随机特征会产生“阻力”水平（因为投资者在“W”t e“M”t 时不愿承担更多风险）。版权所有 1993 Blackwell 出版社。
We analyze the optimal risky investment policy for an investor who, at each point in time, wants to lose no more than a fixed percentage of the maximum value his wealth has achieved up to that time. In particular, if "M" t is the maximum level of wealth W attained on or before time "t", then the constraint imposed on his portfolio choice is that W t α"M" t , where α is an exogenous number betweenα O and 1. We show that, for constant relative risk aversion utility functions, the optimal policy involves an investment in risky assets at time "t" in proportion to the "surplus""W" t - α"M" t . the optimal policy may appear similar to the constant-proportion portfolio insurance policy analyzed in Black and Perold (1987) and Grossman and Vila (1989). However, in those papers, the investor keeps his wealth above a "nonstochastic" floor "F" instead of a stochastic floor α"M" t . the "stochastic" character of the floor studied here has interesting effects on the investment policy in states of nature when wealth is at an all-time high; i.e., when Wt e"M" t . It can be shown that at "W" t e"M" t , α"M" t is expected to grow at a faster rate than "W" t , and therefore the investment in the risky asset can be expected to fall. We also show that the investment in the risky asset can be expected to rise when "W" t is close to α"M" t . We conjecture that in an equilibrium model the stochastic character of the floor creates "resistance" levels as the market approaches an all-time high (because of the reluctance of investors to take more risk when "W" t e"M" t ). Copyright 1993 Blackwell Publishers.