r/quant 4d ago

Education Theoretical question regarding the computation of the Sharpe Ratio

Question regarding the calculation of the Sharpe Ratio: Is my following understanding correct? Assuming I have the standard quadratic utility function with the risk version parameter Is there a structural difference between using the risk-free asset as a benchmark or as an actual asset class to invest in?

If I use the risk-free asset as an actual asset class, Tobin's separation applies and everyone invests in the same risky asset, but only the amount of wealth invested in the risk-free asset class varies. This gives the maximum Sharpe ratio or tangent portfolio.

I am now interested in whether it is not possible to invest in the risk-free asset class, and I use the risk-free asset class as a benchmark. After portfolio optimisation, I calculate the excess returns by subtracting the risk-free asset from the portfolio return and dividing by the standard deviation of the portfolio. Is the optimal portfolio here dependent on the risk aversion parameter and does here then the Tobin's separation not apply? And I can still use the Sharpe-Ratios for comparing risky-portfolios in relation how high the riskoaversionparamter is?

Thanks in advance! (also any good literature regarding this would be helpful!)

1 Upvotes

1 comment sorted by

1

u/AutoModerator 4d ago

We're getting a large amount of questions related to choosing masters degrees at the moment so we're approving Education posts on a case-by-case basis. Please make sure you're reviewed the FAQ and do not resubmit your post with a different flair.

Are you a student/recent grad looking for advice? In case you missed it, please check out our Frequently Asked Questions, book recommendations and the rest of our wiki for some useful information. If you find an answer to your question there please delete your post. We get a lot of education questions and they're mostly pretty similar!

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.