Question

1. Lily plans to construct a portfolio consisting of only two equity investments in TTT and SSS ordinary shares. From her research, she finds out that these two investments have a correlation coefficient of -0.389

She plans to invest 80% in share SSS and the remaining in share TTT. The following are additional information collected in respect of these two investments:

	Share TTT	Share SSS
Standard deviation:	13.39%	8.16%
Mean return:	9.10%	5.96%

Based on the portfolio investment information given above, you are required to compute the

1. portfolio returns                                                                               

2. portfolio risk                                                                                     

Answer 1

i) Weight of share of SSS in portfolio = W1 = 80% Weight of share of TTT in portfolio = W2 = 1 - W1 = 1 - 80% = 20%

Mean return of SSS = R1 = 9.10% and Mean return of TTT = 5.96%

Portfolio return = Weighted average of return of stocks = W1 x R1 + W2 x R2 = 80% x 9.10% + 20% x 5.96% = 7.28% + 1.192% = 8.472% = 8.47% (rounded to two decimal places)

Portfolio return = 8.47%

ii) Standard deviation of SSS = S1 = 13.39% and Standard deviation of TTT = S2 = 8.16%

Correlation between SSS & TTT = Corr = -0.389

Portfolio variance = (W1 x S1)² + (W2 x S2)² + 2 x W1 x W2 x S1 x S2 x Corr

Portfolio variance = (80% x 13.39%)² + (20% x 8.16%)² + 2 x 80% x 20% x 13.39% x 8.16% x -0.389 =

Portfolio variance = 0.0114746 + 0.0002663 - 0.0013601 = 0.0103808

Standard deviation of portfolio return = 0.1018862 = 10.18862%

Portfolio risk = Standard deviation of portfolio return = 10.18862% = 10.19% (rounded to two decimal places)