[心得] 效用函數-2-應用:資產配置

Blog post:
https://daze68.blogspot.com/2021/03/2-utility-function-2-asset-allocation.html

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在上一篇，我們已估計了自己的相對風險趨避係數η
我們可以嘗試一個應用: 決定資產配置

先考慮較簡單的狀況:
沒有現金流，在兩種資產間配置
一種為無風險資產，姑且稱為債券
一種為風險資產，姑且稱為股票
假設預期股票溢酬(stock premium)為x，標準差s，滿足對數常態分布

最大化utility的風險資產比例 = (1/η)*x/(s^2) (Merton's Solution)

舉例來說:
η=3, x=0.05, s=0.16 => (1/η)*x/(s^2)=0.65。理想配置是 65%股票， 35%債券
η=1, x=0.05, s=0.16 => (1/η)*x/(s^2)=1.95。理想配置是 195%股票，-95%債券(註)

值得一提的是
這方法並不需要無風險資產的回報率
而是使用股票溢酬

如果覺得算出來的配置很合理，當然不錯
如果直覺就覺得怪怪的，有幾個可能性:
1.不了解自己。對η的估計有較大差距
2.不了解市場。對預期股票溢酬與標準差的估計有較大差距
3.模型不適用。實際utility function與Isoelastic utility有較大差距

如果有多種資產或不滿足常態分佈的資產
不一定可以求解析解
但可以用數值方法求近似解

如果有未來收入呢?有一些可能的處理方式。
1.維持相同資產配比。傳統作法
2.將未來收入視為債券，從債券部位扣除。<<Lifecycle investing>>建議這種作法

本篇主要concept來自boglehead論壇的使用者Uncorrelated
Uncorrelated還提供了求近似解的程式碼

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註: Merton's Solution假設可以用無風險利率借貸。如果借款利率高於無風險利率，可參見 https://daze68.blogspot.com/2021/03/higher-than-risk-free-rate.html

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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.

--

抱歉，打錯。已更正。