Sharpe Ratio Question

Portfolio A earned a return of 10.23 percent and had a standard deviation of returns of 6.22 percent. If the return over the same period on Treasury bills (T-bills) was 0.52 percent and the return to Treasury bonds (T-bonds) was 4.56 percent, what is the Sharpe ratio of the portfolio? A) 0.56. B) 1.56. C) 0.91. D) 7.71.

B 10.23 - 0.52 / 6.22 = 1.56 I had trouble with this one at first when I saw it on Schweser, wanted to use T-Bonds instead of T-Bills as RF rate.

C (10.23-4.56)/6.22 = 0.91 I had a similar problem on a CFAI practice test this morning and got it wrong. I guess you use the Treasury bond rate, not the Treasury bill rate.

Your answer: C was incorrect. The correct answer was B) 1.56. Sharpe ratio = (Rp – Rf) / óp, where (Rp – Rf) is the difference between the portfolio return and the risk free rate, and óp is the standard deviation of portfolio returns. Thus, the Sharpe ratio is: (10.23 – 0.52) / 6.22 = 1.56. Note, the T-bill rate is used for the risk free rate. ============= Why do we use the T-bill rate? Both are risk free rates, I guess if the portfolio consisted of primarily short term securties, we would use Tibill, but if it had longer term securities, we should use T-bond.

I think T-bills are more appropriate for Sharpe calculation, because timeframe is relatively short. I’m going with B. If we consider long-term projects, then T-bonds would be more appropriate for RFR.

I found this Investopedia, which seems to advocate using T-Bills b/c on a long-term basis the risk premium for equities is not much when using T-Bonds as the RF rate . Even Sharpe’s own website at Stanford does not say which to use. I looked in the curriculum and in there it uses the mean U.S. T-Bill rate as the RF rate. Moto do you remember exactly the question you had on the CFAI practice test? Maybe it asked the question in such a way that you knew to use T-Bonds instead of T-Bills…

thanks Ryan!!

I’ll see if I can go back and look at it.