Blog post: https://daze68.blogspot.com/2021/03/2-utility-function-2-asset-allocation.html ====== 在上一篇，我们已估计了自己的相对风险趋避系数η 我们可以尝试一个应用: 决定资产配置 先考虑较简单的状况: 没有现金流，在两种资产间配置 一种为无风险资产，姑且称为债券 一种为风险资产，姑且称为股票 假设预期股票溢酬(stock premium)为x，标准差s，满足对数常态分布 最大化utility的风险资产比例 = (1/η)*x/(s^2) (Merton's Solution) 举例来说: η=3, x=0.05, s=0.16 => (1/η)*x/(s^2)=0.65。理想配置是 65%股票， 35%债券 η=1, x=0.05, s=0.16 => (1/η)*x/(s^2)=1.95。理想配置是 195%股票，-95%债券(注) 值得一提的是 这方法并不需要无风险资产的回报率 而是使用股票溢酬 如果觉得算出来的配置很合理，当然不错 如果直觉就觉得怪怪的，有几个可能性: 1.不了解自己。对η的估计有较大差距 2.不了解市场。对预期股票溢酬与标准差的估计有较大差距 3.模型不适用。实际utility function与Isoelastic utility有较大差距 如果有多种资产或不满足常态分布的资产 不一定可以求解析解 但可以用数值方法求近似解 如果有未来收入呢?有一些可能的处理方式。 1.维持相同资产配比。传统作法 2.将未来收入视为债券，从债券部位扣除。<<Lifecycle investing>>建议这种作法 本篇主要concept来自boglehead论坛的使用者Uncorrelated Uncorrelated还提供了求近似解的程式码 ====== 注: Merton's Solution假设可以用无风险利率借贷。如果借款利率高於无风险利率，可 参见 https://daze68.blogspot.com/2021/03/higher-than-risk-free-rate.html ====== Reference: Uncorrelated (2020, March 05). Risk tolerance and asset allocation with mathematics. Retrieved 2021, March 01, from https://www.bogleheads.org/forum/viewtopic.php?t=305919 Uncorrelated (2020, August 09). A mean variance framework for portfolio optimization. Retrieved 2021, March 01, from https://www.bogleheads.org/forum/viewtopic.php?t=322366 -- You got to know when to hold 'em, know when to fold 'em, Know when to walk away and know when to run. You never count your money when you're sittin' at the table. There'll be time enough for countin' when the dealin's done. 'Cause ev'ry hand's a winner and ev'ry hand's a loser, And the best that you can hope for is to die in your sleep." now Ev'ry gambler knows that the secret to survivin' Is knowin' what to throw away and knowing what to keep. --

※ 发信站: 批踢踢实业坊(ptt.cc), 来自: 36.237.73.127 (台湾) ※ 文章网址: https://webptt.com/cn.aspx?n=bbs/CFP/M.1614605334.A.6CD.html ※ 编辑: daze (36.237.73.127 台湾), 03/01/2021 23:17:23 抱歉，打错。已更正。 ※ 编辑: daze (36.237.73.127 台湾), 03/02/2021 01:39:07 ※ 编辑: daze (114.39.50.205 台湾), 03/04/2021 01:45:59