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The problem is from Asset Pricing and Portfolio Theory by Back and can be found here.

The relevant info from section 2.5 can be found here. 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.

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    $\begingroup$ 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. $\endgroup$
    – jmbejara
    Commented Feb 25, 2015 at 9:10
  • $\begingroup$ Your links do not seem to be working anymore. $\endgroup$ Commented Jan 21, 2020 at 10:29

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