Question

b) You are considering the two securities listed below.

Stock	Stock A	Stock B
Initial Investment	RM25,000	RM35,000

Economy Outcomes	Probability	Stock A Returns	Stock B Returns
Pessimistic	20%	5%	13%
Normal	50%	10%	8%
Optimistic	30%	15%	-15%

i) Calculate the expected return for portfolio.

ii) Calculate the standard deviation of returns for portfolio.

iii) Justify why diversification work best for these stocks.

Answer 1

i) Expected Return = P₁E₁ + P₂E₂ +...........

where P₁, P₂ ...... are Probabilities and E₁, E₂ ..... are Returns

Stock A Expected Return = 0.20*5% + 0.50*10% + 0.30*15% = 10.5%

Stock B Expected Return = 0.20*13% + 0.50*8% - 0.30*15% = 2.10%

ii)

where X is the return,  μ is the mean of return and P(x) is the probability

Stock A

μ = (5% + 10% + 15%)/3 = 10%

σ² = 0.20(5%-10%)² + 0.50(10%-10%)² + 0.30(15%-10%)²

σ² = 0.125

σ = sqrt (0.125) = 0.3535

Stock B

μ = (13% + 8% - 15%)/3 = 2%

σ² = 0.20(13%-2%)² + 0.50(8%-2%)² + 0.30(-15%-2%)²​​​​​​​

σ² = 1.289

σ = sqrt (1.289) = 1.1353

iii) Diversification reduces the standard deviation of the two stocks, which reduces the variance in the stocks and hence reduces the variability of stocks. As shown in Stock A the variation in the returns is from 5% to 15% , while by diversification the variability is reduced to (10%-0.3535*3) to (10+3*0.3535) i.e 8.93% to 11.06%.