Question

1.preston inc. stock has a 20%chance of producing a 45% return, a 50% chance of producing a 9% return, and a 30% chance of producing a -28% return. what is the firm's standard deviation of return

2. microsoft annual stock returns for the last five years are: 20.79%, 40.75%. 15.07%, 22.69% and 27.58% what is microsoft coefficient of variation for this time period

Answer 1

1). Mean = [Pi x Ri]

= [0.2 x 45%] + [0.5 x 9%] + [0.3 x -28%] = 9% + 4.5% - 8.4% = 5.1%

S.D. = [Pi x (E(r) - Ri)²]^1/2

= [{0.2 x (5.1% - 45%)²} + {0.5 x (5.1% - 9%)²} + {0.3 x (5.1% + 28%)²}]^1/2

= [318.402%² + 7.605%² + 328.683%²]^1/2 = [654.69]^1/2 = 25.59%

2). Mean = [Pi ] / n

= [20.79% + 40.75% + 15.07% + 22.69% + 27.58%] / 5 = 126.88% / 5 = 25.38%

S.D. = [{(E(r) - Ri)²} / (n - 1)]^1/2

= [{(25.38% - 20.79%)² + (25.38% - 40.75%)² + (25.38% - 15.07%)² + (25.38% - 22.69%)² +

(25.38% - 27.58%)²} / (5 - 1)]^1/2

= [21.03%² + 236.36%² + 106.21%² + 7.21%² + 4.86%²} / 4]^1/2

= [375.68%² / 4]^1/2 = [93.92%² / 4]^1/2 = 9.69%

C.V. = S.D. / Mean = 9.69% / 25.38% = 0.38, or 38%