4Q- 26 An analyst gathered the following information about a common stock portfolio: Arithmetic mean return 14.30% Geometric mean return 12.70% Variance of returns 380 Portfolio beta 1.35 If the risk-free rate of return is 4.25%, then the coefficient of variation and the Sharpe ratio, respectively, for the portfolio are closest to: Coefficient of Sharpe ratio variation A. 1.36 0.52 B. 1.36 7.44 C. 1.53 0.52 D. 1.53 7.44 -------------------------------------------------- my answer :C ó=(380)^0.5=19.49 CV=19.49/12.7=1.53 sharpe ratio=(12.7-4.25)/19.49=0.43. the answer 0.52 is calculated with arithmetic mean return 14.3. I disagree on that. But C is only closest answer.
In that case, then it is A. But I also think that you should use the geometric mean. Others?
I also agree. CFA text clearly says geometric is best for evaluating historic returns. Only thing I can think is that you are looking at the return over 1 period, in which case you’d go with arithmetic.
If you are looking at the return over 1 period, then geometric and arithmetic are the same.
Dreary Wrote: ------------------------------------------------------- > If you are looking at the return over 1 period, > then geometric and arithmetic are the same. ---------------------------------------- should be
So why are they using the arithmetic in this question?
So you don’t have to memorize the geometric. Or at least that is one thing I am just not going to memorize.
Nothing really to memorize with geometric averages. I think that geometric average calculations is one of the most important, frequently used calcs across the test with all the return concepts.
It should use arithmetic mean (see Q13 of Reading 7, CFA Program Curriculum Vol. 1) it seem arithmetic mean should be used for sharpe ratio and CV. and answer is A
Really? That’s good to know.
ANSWER IS CLEARLY A CV = sigma/X = 1.36 Sh = Rp - Rp/( sigma of portfolio) sigma = sq root of 380 = 19.49% Sh = .52 THEY TRY TO TRICK YOU WITH THE BETA, WHICH GOES IN THE DENOM OF THE TREYNOR RATIO, which is a variation of the Sharpe and looks very much like it. Nice.