Coefficient of Variation

CFA Level I
#1

SD/Mean right?

So how come in this question below, the workings tell me to use sample Standard Deviation? I dont see anything in the question pertaining to this.

A risk manager would like to calculate the coefficient of variation of a portfolio. The following table reports the annual returns of the portfolio and of the risk-free rate over the most recent five years:

Portfolio Return RFR 4% 2%

-1% 1.5%

7% 1

11% 1

2% 0.5

I said ans was 0.9 (SD/mean) The correct answer is 1 (Sample SD/mean)

#2

I presume that the phrase “over the most recent five years” is intended to suggest that there are more historical data than those presented; thus, the data form a sample, not a population.

It’s a frail reed. The questions on the real exam will be clearer. Trust me.

#3

Thanks.

S2000 can I ask you a question about EAR?

There was a question saying the EAR was 12%. Assuming quarterly compounding its stated annual interest rate is closest to:

a)12.55

b) 11.66

c) 11.49

I said A)

I did the following: (0.12/4 +1) ^4 which gave me 12.55

The correct answer was 11.49.

What have I done instead? I seem to remember the formula I did (I was attempting without the book)

THanks

#4

You treated the EAR as a stated annual rate. Remember, EAR already has the compounding factored in, and they are telling you this gives 12%.

Work backwards from12%.

your equation: ( i /4 +1) ^4 = 1.12

Solve for i… take the fourth root of both sides, subtract off 1 and multiply by four. Now, you have the stated annual rate.

#5

oh ok thanks tickersu

#6

If the effective annual return (i.e., the return that includes compounding) is 12%, then the effective quarterly return is:

(1 + EQR)^4 = 1.12

1 + EQR = 1.12^0.25 = 1.028737

EQR = 0.28737 = 2.8737%

Thus, the stated (i.e., nominal) annual rate is:

4 × 2.8737% = 11.4949%

I wrote an article on nominal vs. effective rates that may be of some help: Nominal vs. Effective Interest Rates | Financial Exam Help 123.

#7

Glad to help!