Question

1. a. If you know the variance of a portfolio es 0.01. What is the standard deviation? If the expected return of the portfolio is 5%, what is a possible interval where the return can be?

b. If the weights on your portfolio composed of three assets are 20%, 30% and 50% and the expected return on the same assets are 4%, 6%, and 7.5%, respectively. What is the expected return on the portfolio?

c. If you invest 20% in asset A and 80% in asset B, and the variances are 0.1 and 0.08, respectively What is the standard deviation of this portfolio is the covariance between A and B is zero?

Answer 1

Answer (a):

Standard Deviation of Portfolio = √Variance

Variance of portfolio = 0.01

Therefore Standard Deviation of Portfolio = √0.01

= 0.1

If the expected return of the portfolio is 5 % , then possible interval of return is :

Upper limit = 5% + (5% * 0.1)

= 5 % + 0.5 % = 5.5 %

Lower Limit = 5 % - (5% * 0.1)

= 5% - 0.5% = 4.5 %

Therefore possible interval = 4.5 % to 5.5%

Answer (b):

Calculation of Expected Return of the portfolio:

Expected Portfolio Return = W_1*E(R₁₎+W_2*E(R₂)+W_3*E(R₃₎

W₁ = Weight of security 1 = 20 % = 0.20

W₂ = Weight of security 2 = 30 % = 0.30

W₃= Weight of security 3 = 50 % = 0.50

E(R₁₎ = Expected Return of Security 1 = 4%

E(R₂₎ = Expected Return of Security 2 = 6%

E(R₃₎ = Expected Return of Security 3 = 7.5%

Therefore Expected Portfolio Return = (0.20*4%)+(0.30*6%)+(0.50*7.5%)

= 0.8%+1.8%+3.75%

= 6.35%

Answer(c):

Calculation of Standard Deviation of the portfolio:

Expected Standard Deviation of the portfolio = √(w_a² * σ_a² + w_b² * σ_b² + 2 * w_a * w_b * covariance of a,b)

W_a = Weight of asset A = 20 % = 0.20

W_b = Weight of asset B = 80% = 0.80

σ_a²= variance of asset A = 0.1

σ_b²= variance of asset B = 0.08

covarince between a,b = 0

Therefore Standard Deviation of the portfolio = √( 0.20² * 0.1 + 0.80² * 0.08 + 2 * 0.20 * 0.80 * 0 )

=√( 0.004+0.0512+0)

=√(0.0552)

Therefore Standard Deviation of the portfolio = 0.2349