Question

The following returns have been estimated for Security T and Security S:

Scenario	Security T	Security S
1	20%	10%
2	13%	-6%
3	15%	20%

Each scenario is equally likely to occur, and you plan to invest 70% in Security T and 30% in Security S. What is the standard deviation of the rate of return of the portfolio? Round your answer to the nearest tenth of a percent.

		A) 0.0%
		B) 4.5%
		C) 19.9%
		D) 59.7%

Answer 1

Weight of T, Wt = 70% = 0.7

Weight of S, Ws = 30% = 0.3

Scenario 1:

Return of T, Rt = 20%

Return of S, Rs = 10%

Hence, expected return of portfolio = (Wt * Rt) + (Ws * Rs)

expected return of portfolio = (0.7 * 0.2) + (0.3 * 0.1)

expected return of portfolio = 0.14 + 0.03

expected return of portfolio = 0.17 = 17%

Scenario 2:

Return of T, Rt = 13%

Return of S, Rs = -6%

Hence, expected return of portfolio = (Wt * Rt) + (Ws * Rs)

expected return of portfolio = (0.7 * 0.13) + (0.3 * (-0.06))

expected return of portfolio = 0.091 - 0.018

expected return of portfolio = 0.073 = 7.3%

Scenario 3:

Return of T, Rt = 15%

Return of S, Rs = 20%

Hence, expected return of portfolio = (Wt * Rt) + (Ws * Rs)

expected return of portfolio = (0.7 * 0.15) + (0.3 * 0.2)

expected return of portfolio = 0.105 + 0.06

expected return of portfolio = 0.165 = 16.5%

Hence,

returns

Scenario 1 = 17%

Scenario 2 = 7.3%

Scenario 3 = 16.5%

Variance is given by formula:

Here,

N = 3 (number of observations)

Mean = 13.6 = (17 + 7.3 + 16.5 ) / 3 = 13.6

Putting values,

= [(17 - 13.6)^2 + (7.3 - 13.6)^2 + (16.5 - 13.6)^2 ] / 3

= 59.66 / 3

= 19.886666666

Now,

Standard Deviation = Square root of variance

= sqrt ( )

= SQRT (19.88666666)

= 4.45944 = 4.5% (Option B)