Question

Consider a portfolio investment consisting of 40% which is 0,4 invested in MTN, 60% which is 0,6 invested in Multichoice

Expected return calculated as MTN =-0,002 Multichoice= 0,0033
Expected Portfolio Return =0.00118

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

Given information

Portfolio is consisting two securities

MTN = 40%= 0.4, Multichoice= 60%=0.6

Expetcted Returns of MTN [(MTN)]=0.002,

Expected Returns of Multichoice [(Multichoice)]=0.0033,

Portfolio return(p)=0.00118

Anser 3.2 Calculation of covariance of portfolio

Note: Calculation of Reurns of the stock:

Expected Returns ()= Ri * Pri

where Ri= Returns of the stock i

Pri= Probability assiciated with its reutrns

Hence by rewriting the equation we get,

Ri= /Pri

Returns of (MTN) = 0.002/0.4= 0.005

Returns of (Multichoice) = 0.0033/0.6 = 0.0055

Covariance of Portfoli(Cov p) = /n

= [0.005-0.002] [0.0055-0.0033] / 2

=(0.003)(0.0022)/2

Covariance of the portfolio =0.0000033

Anser 3.3 Calculation of variance of the portfolio and standard deviation of the portfolio

Standard deviation of returns (σ)=

where R= Expected returns of stock

=Returns of the portfolio

Pri= Probability Associated with its return

by substitution

σp= Square root of { [ R (MTN) - R (p) ] * 0.4 } + { [ R (Multichoice) - R ( p) ] ] *  0.6 }

=Square root of [(0.002-0.00118)*0.4] + [ ( 0.0033- 0.00118) * 0.6]

=Square root of [0.000328 + 0.001272 ]

=Square root of (0.0016)

σp=0.04

Variance of the portfolio= Square of the Standard deviation

=(0.04)^2

σ^2p =0.0016

Answer 3.4 Calculation of Sharpe Ratio

Given: Risk Free rate of return =Rf- 0.0002

Computation of Sharpe ratio=  p - Rf

σp

Where p= Expected returns of the portfolio

RF= Risk free rate of return

σp= Standard deviation of the portfolio

Hence by substitution

Sharpe ratio = 0.00118-0.0002/0.04

Sharpe Ratio =0.0245

Note: σp= 0.04 is calculated in answer 3.3

Anser 3.5  Interpretation of Sharpe ratio:

It is a measure for calculating risk adjusted return. It is the ratio of excess expected returns over the risk free rate of return per unit of standard deviation. Greater is the ratio, better is the performance of the portfolio. Usually Sharpe ration greater than 1 is considered acceptable by the investor. A ratio less than 1 is considered sub optimal. As in the anser Sharpe ratio for the given portfolio is 0.0245 which is less than 1 is considered as sub aptimal. There is a scope for portfolio revision to increase expected returns which can be achieved by change in stock or change in its weights. A ratio higher than 2 is considered very good and a ratio higher than 3 is considered excellent.