Timeline for Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio Theory?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 9, 2020 at 20:01 | comment | added | John | @develarist The simple reason why I did it the way I did it is that it makes the math easier and produces the same result. The easiest way to know that is because if you take the formula for the unconstrained mean-variance weights and plug that into the formula for the Sharpe ratio you get a constant and the risk aversion parameter cancels out. In other words, it should always have the same Sharpe ratio, the maximum. This doesn't work when you add in inequality constraints though. | |
| Nov 9, 2020 at 19:36 | comment | added | develarist | i think she also means that there is a $\lambda$ in the first formula, whereas there is no $\lambda$ in the second, making them look even more unequivalent | |
| Jan 30, 2017 at 17:32 | comment | added | John | @Marie.P. If you want to maximize the Sharpe ratio, then that's generally the formula you would use. It's more difficult than standard mean variance. Under some assumptions, the optimal mean variance portfolio fully invested will equal the maximum Sharpe ratio portfolio. I just wanted to give a simple derivation of the formula the OP was asking about. I'm sure it would be useful to post other derivations here, if you want to add another. | |
| Jan 29, 2017 at 17:25 | comment | added | Marie. P. | I know it's late, but why is the tangency optimization problem $argmax\{w'\mu - \frac{ \lambda w' \Sigma w}{2} \}$ instead of $argmax \frac{w'\mu}{\sqrt{w'\Sigma w}}$? We are trying to find the portfolio on the efficient frontier that maximizes the sharpe ratio, the ratio of return to standard deviation, are we not? | |
| Aug 3, 2013 at 4:45 | comment | added | Slow Learner | Thank you so very much. I never thought it would be so simple. I think everyone is familiar with the unconstrained optimal portfolio, but for some reason I never understood how to put the constraint in. Thanks again! | |
| Aug 3, 2013 at 4:44 | vote | accept | Slow Learner | ||
| Aug 1, 2013 at 16:43 | history | answered | John | CC BY-SA 3.0 |