Question

Consider a portfolio investment consisting of 40% invested in MTN, 60

Consider a portfolio investment consisting of 40% invested in MTN, 60% invested in Multichoice
Expected return;
MTN = -0.0020
Multichoice= 0.0033
Variance;
MTN = 0.000447561
Multichoice = 0.001247259
Standard deviation;
MTN= 0.0212
Multichoice= 0.0353
3.1 Calculate the expected return of the portfolio
3.2 Calculate the covariance of the portfolio
3.3 Calculate the variance of the portfolio and standard deviation of the portfolio
3.4 Given that the risk free rate is 0.0002. Calculate the Sharpe ratio for the portfolio
3.5 Interpret the Sharpe ratio calculated in 3.4

Answer 1

3.1 The expected return of the portfolio is the average of the return of the constituent securities weighted as per their proportion in the portfolio. So in this case the expected return is = Return of MTN*Weight of MTN + Return of Multichoice*weight of multichoice = -0.0020*0.4+0.0033*0.6 = 0.00118 Answer

3.2 Covariance is defined for a portfolio ABC as below:

innen_ (Return ABC - Average ABC) * (Return xyz - Average xyz) (Sample Size) - 1

Average return in this case is the return calculated in 3.1 and sample size is 2.

So covariance is = (-0.0020-0.00118)*(0.0033-0.00118) / (2-1) = -0.0000067 Answer

3.3 First calculate the correlation of the portfolio and that will help you calculate the variance of the portfolio

Cor(Ri,R;) = Cov(Ri,R;) 0; 0;

Correlation is = -0.0000067/(0.0212*0.0353) = -0.008953 Answer

3.4 Standard Deviation can be calculated as below

ܗܢ ܗܝܢp ܕ ' w ; « , + w ; « + 2 w/ܢ = , ܗ

=squareroot((0.4^2)*0.000447561+(.6^2)*0.001247259+2*0.4*0.6*(-0.008953)*0.0212*0.0353) =0.022747

Sharpe Ratio = Rp – Rf op where: Rp = return of portfolio Rf = risk-free rate Op = standard deviation of the portfolio's excess return

Sharpe ratio=(0.00118-0.0002)/0.022747 = 0.043083 Answer

3.5 The risk adjusted performance of the portfolio is positive and higher than the risk free rate. Hence from the sharpe ratio, we interpret that the risk is being compensated by the return. Answer