Standrd deviation of annual returns

CFA Level I
#1

In a 5 years period, the annual returns on an investment are 5%,-3%,-4%,2% and 6%. The standrd deviation of annual returns on this investment is closest to: A.4% b.4.5% c.20.7%

#2
  1. Calculate the average return: (5-3-4+2+6)/5=1.2 2. Calcuate the population variance: (5-1.2)^2+(-3-1.2)^2+(-4-1.2)^2+(2-1.2)^2+(6-1.2)^2/(5) = 20.68 3. Calculate the population standard deviation: 20.68^0.5 = 4.54

So the answer is B.

Alternatively use the STAT function of your Calculator and look for Sx.

Regards,

Oscar

#3

Is this a sample of returns, or a population of returns?

#4

As these are the returns of one investment, and the SD of the investment itself should be analyzed I would assume this is a population. Therefore I divided by n (=5).

#5

I used 5 too, but I’m not getting the same calculation

You have:

(5-1.2)^2+(-3-1.2)^2+(-4-1.2)^2+(2-1.2)^2+(6-1.2)^2/(5) = 20.68

I get:

(5-1.2)^2+(-3-1.2)^2+(-4-1.2)^2+(2-1.2)^2+(6-1.2)^2/(5) = 16.56

Since I used 5 assuming a population, I got A which is ~4%

#6

Correct, your answer is correct. I took wrongly sample insteat of population.

#7

I think you took _ rightly _ sample instead of population: it’s not very likely that this 5-year period is the entire life of the investment; it’s more likely that it’s a sample from a much longer period.

#8

s2000 thanks for the clarification…yes it must be treated as a SAMPLE. And the right ans is B.

#9

My pleasure.

#10

If you are using a BA II Plus an easy way to calculate this as mentioned above is to use the stat function.

  1. Enter 2nd > Data

  2. Input returns as a whole number into X1, X2, X3 and use the down key to navigate. (Remember to hit the enter key next to the arrows to input the number).

  3. Once finished 2nd > Stat > Mode should be LIN if not hit [2nd] [Enter] and to have the Stdev of the Sample scroll down till you see Sx.

Note if you looing for the population Stdev scroll down once more till you see sigma x.