Coefficient of Variation

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rexthedog

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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)
 
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.
 
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
 
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.
 
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: http://financialexamhelp123.com/nominal-vs-effective-interest-rates/.
 
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