Page 110 Vol. 5 (Alternatives) Ques 12

CFA Level III
#1

Hi guys. I need a little help

Page 110 Vol. 5 (Alternatives)

Compute the annualized downside deviations for the hedge fund and the index, and contrast them to the standard deviation. The annualized standard deviations for the hedge fund and the index are, respectively, 8.64 percent and 9.19 percent.

Compute the Sortino ratio and, based on this statistic, evaluate the performance of the hedge fund against the performance of the index portfolio.

Answer

A hurdle rate of 5% per year equates to a monthly hurdle rate of 5%/12 = 0.4167%.

The downside deviation for the hedge fund = sq root of 28.78 (12 − 1) × sq root of 12 = 5.60%.

The downside deviation for the index = sq root of 65.04 (12 − 1) × sq root of 12 =

8.42%.

The downside deviation is lower than the standard deviation because downside deviation takes into account only the deviations on the downside. The downside deviation of the hedge fund is lower than that of the index in this case.

What am I missing?

Where did they pick up the 5% hurdle rate?

Not seeing where the 28.78 and 65.04 come from?

#2

5% hurdle rate is specified in footnote 1 at bottom of page in very tiny fine print.

1 This table shows monthly returns for a hedge fund and an index portfolio. For the purpose of computa- tion, the hurdle rate is the U.S. T-bill rate, assumed to be 5 percent per year.

Take the 5 returns -2, -2, -1, -1, -3.2 and take the deviation

2.4167^2+2.4167^2+1.4167^2 + 1.4167^2 + 3.6167^2 = 28.77547

#3

Thanks cpk123 how did you arrive at the 2.4167 ?

#4

-2 - 0.4167

since you are squaring it … the sign does not matter.

#5

2.4167% = difference between actual return (-2%) and hurdle rate (0.4167%/month = 5%/year.)

std dev of any sample = square root of (sum of (R - E)^2) / (n-1)) where R = actual return (-2%, -2%, -1% and so on), E = expected return or in this case, hurdle rate, n = sample size.

#6

Got it! Thanks guys!