uppose that Ms Neemaeli can invest all her savings in shares of Sophi Ltd, or al

Question

uppose that Ms Neemaeli can invest all her savings in shares of Sophi Ltd, or all her Savings i Nelly Ltd. Alternatively she could diversify her investment between these Ther are two possible states of the economy, growth or recession, and the returns on Sophi Ltd and Nelly Ltd depend on which state will occur. te of theProbability of the state of Sophi return Nelly return econony Growth Recession the economy occurring 0.7 0.3 30 10 15 20 Required: (a) Calculate the expected return, variance and standard deviation for each share (6 Marks) (b) Calculate the expected return, variance and standard deviation for the following diversifying allocations of Ms Neemaeli's savings: (i) 50% in Sophi, 50% in Nelly (ii) 1 1% in Sophi, 89% in Nelly Explain the relationship between risk reduction and the correlation between individual financial security returns. (6 Marks) (6 Marks) (c) (2 Marks)

Explanation / Answer

SOPHI

Standard deviation = (Variance)^1/2 = (336)^1/2 = 18.33 %

NELLY RETURN

Standard deviation = (5.25 )^1/2 = 2.29%

B) (i)

50% in sophi and 50% in nelly =

Expected return = 18 * 0.5 + 16.5 * 0.5 = 17.25 %

Co-variance = 0.7 * (30-18)*(15-16.5) + 0.3 * (-10-18)*(20-16.5) = -42

Variance = 336 * 0.52 + 5.25* 0.52 + (2*.5 * .5 * -42)

= 64.3125

Standard deviation = (64.3125)^1/2 = 8.02 %

(ii)

11% in sophi and 89% in nelly =

Expected return = 18 * 0.11 + 16.5 * 0.89 = 16.665 %

Co-variance = 0.7 * (30-18)*(15-16.5) + 0.3 * (-10-18)*(20-16.5) = -42

Variance = 336 * 0.112 + 5.25* 0.892 + (2*0.11 * 0.89 * -42)

= 0

Standard deviation = (0)^1/2 = 0 %

Economy Probability Sophi return (%) Expected return Growth 0.7 30 21 Recession 0.3 -10 -3 Expected Return (X) 18

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