Question

1. You hold a portfolio of securities which have had the following annual returns: {4%, 18%, -22%, 0%, 26%, 10%}. What is the arithmetic mean of the returns?

a. 4% b. 8% c. 6% d. 7%

2. You hold a portfolio of securities which have had the following annual returns: {4%, 18%, -22%, 0%, 26%, 10%}. What is the sample variance of the returns?

a. 248.3 b. 195.2 c. 276.8 d. 325.6

3.  You hold a portfolio of securities which have had the following annual returns: {4%, 18%, -22%, 0%, 26%, 10%}. What is the sample standard deviation of the returns?

a. 16.64% b. 17.36% c. 19.54% d. 12.87%

Answer 1

1). Arithmetic Mean = [(Ri)] / n

= [4% + 18% - 22% + 0% + 26% + 10%] / 6

= 36% / 6 = 6%

Hence, Option "c" is correct.

2). Sample Variance = [{E(Ri) - Ri}²] / (n - 1)

= [(6% - 4%)² + (6% - 18%)² + (6% + 22%)² + (6% - 0%)² + (6% - 26%)² + (6% - 10%)²] / (6 - 1)

= [4%² + 144%² + 784%² + 36%² + 400%² + 16%²] / 5

= 1384%² / 5 = 276.8%²

Hence, Option "c" is correct.

3). Sample Standard Deviation = [Sample Variance]^1/2

= [276.8%²]^1/2 = 16.64%

Hence, Option "a" is correct.