I have gathered stock prices from 15 companies over a year. I calculated the averages, yearly volatilizes, and the correlation matrix.

I was asked to find the optimum weight for each stock with a required 10% return and I had to minimize variance. I solved this question.

However, I was then asked to find appropriate weights to optimize the risk-return of the portfolio.

As a student, I did not realize the difference in the questions. Thank you for your help.

  • 1
    $\begingroup$ Hi: You need to create what is referred to in the literature as the efficient frontier. That means, choose some return and then minimize the variance subject to the return being equal to that constant. Then, choose a different constant, and do the same thing. Then, choose another constant and do the same thing. Rinse and repeat until you have enough returns to make a curve. The weights for each constant optimize the risk-return profile of the portfolio. You can use similar machinery that you used for the first question but now you loop over different returns. I hope it helps. $\endgroup$
    – mark leeds
    Mar 24 '20 at 14:32
  • $\begingroup$ Okay I see what you mean! Thank you $\endgroup$
    – Mike Harb
    Mar 24 '20 at 14:38

Your lecturer was almost certainly asking for the "max-Sharpe" portfolio.

See below for the formula. Essentially it equalises the marginal-contribution-to-return/marginal-contribution-to-vol, such that adding or subtracting from any weights won't change the expected-return/expected-vol of the portfolio.

Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio Theory?

hope this helps, W

  • $\begingroup$ To me, optimizing the risk-return makes me think "efficient frontier" but you might be correct. To the OP: You can take your efficient frontier points and then calculate the max sharpe from all of them ( return/variance ) in case that is what is being asked for.. $\endgroup$
    – mark leeds
    Mar 25 '20 at 0:57
  • $\begingroup$ Don;t disagree with any of this, or see any inconsistency here! The efficient frontier is the max-return for any given level of vol; or the min-vol for any given level of return. As such, it optimises one of the variables given the other. I read the question to be where on the efficient frontier gives you the best combination of risk and return, which is the max-Sharpe point (which will lie on the EF by definition). $\endgroup$
    – demully
    Mar 25 '20 at 14:43

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