<p>The problem is from Asset Pricing and Portfolio Theory by Back and can be found <a href="https://i.sstatic.net/KPQY9.jpg" rel="nofollow noreferrer">here</a>. </p>

<p>The relevant info from section 2.5 can be found <a href="https://i.sstatic.net/mMvy7.png" rel="nofollow noreferrer">here</a>. Given that we have the Expected value and the variance of end of period wealth, I tried substituting them into the equation, differentiating and setting to 0. </p>

<p>I'm not sure this is the right method, or if I'm even taking the derivative correctly. Any help would be appreciated.</p>

CC BY-SA 3.0
2015-02-25T09:10:56.760Z
Remember that if someone has quadratic utility, then he/she only cares about the mean and variance of the investment. So, the investor will, by the two-fund theorem, just choose a linear combination of the risk-free asset and the tangency portfolio. $\xi$ will tell you where this combination is on the mean-variance efficient frontier.
jmbejara
CC BY-SA 4.0
2020-01-21T10:29:27.483Z
Your links do not seem to be working anymore.
Richard Hardy
<asset-pricing><optimization><risk-aversion><portfolio-theory>
Calculating the optimal portfolio for an investor with quadratic utility
user2034
# Calculating the optimal portfolio for an investor with quadratic utility

(Asked by: username_0 on 2015-02-24)

The problem is from Asset Pricing and Portfolio Theory by Back and can be found [here](https://i.sstatic.net/KPQY9.jpg).

The relevant info from section 2.5 can be found [here](https://i.sstatic.net/mMvy7.png). Given that we have the Expected value and the variance of end of period wealth, I tried substituting them into the equation, differentiating and setting to 0.

I'm not sure this is the right method, or if I'm even taking the derivative correctly. Any help would be appreciated.

**Tags:** asset-pricing, optimization, risk-aversion, portfolio-theory

> **Comments:**
> **username_1**: Remember that if someone has quadratic utility, then he/she only cares about the mean and variance of the investment. So, the investor will, by the two-fund theorem, just choose a linear combination of the risk-free asset and the tangency portfolio. $\xi$ will tell you where this combination is on the mean-variance efficient frontier.  
> **username_2**: Your links do not seem to be working anymore.  

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## 0 answers

