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Consider shares in two companies, JAY and KAY, as follows:
a) Calculate the covariance between Share JAY and KAY returns.
b) What is the expected return and standard deviation of returns on a portfolio comprising 35% in Share JAY and 65% in Share KAY?
c) If you wanted to create a portfolio consisting only of these two shares, how much would you need to invest (weights) in each share so that your portfolio return would be equal to 15.6%? Note: do not round.
d) Using the weights calculated in part c); calculate the variance and standard deviation of your portfolio.
Covariance between Share JAY and KAY returns: - To calculate the Covariance between Share JAY and KAY returns following formula is used:-
= Standard Deviation of JAY * Standard Deviation of KAY *(Correlation Coefficient)
= 18 *32 *(0.3)
Hence, Covariance between Share JAY and KAY returns is 172.6
(i) Expected Return: - Expected return means that the return the investor can expect in the future. It is not the accurate return but only expected return.
Expected Return = Weight of JAY *(Expected Return) + Weight of KAY * (Expected Return)
Expected Return = 0.35*(12) + 0.65 * (24)
Expected Return = 19.8%
Hence, the Expected Return is 19.8%
(ii) Standard Deviation
√(WA2σa2 )+ (WB2σB2 )+2 (σA*WA*Σb *WB)* Correlation Coefficient
σ = 19.84
If a portfolio is to create consisting only of these two shares, and to make the portfolio return equal to 15.6% then the investment is to be made of :-
Let assume the weight of JAY is W, then the Weight of KAY WILL BE 1-W
Desired Portfolio Return = 15.6%
15.6% = W*12%+ (1-W)* 24%
0.156 = 0.12W +0.24- 0.14 W
0.156 -0.24 =-0.12W
0.084 = 0.12W
0.084 / 0.12 = W
Expected weight which is earned is 15.6%
Then weight of JAY (W) will be 70%
Weight of KAY (1-W) will be 30%.
(i) Basis on the above calculation revised Standard Deviation is:-
σ = √ (0.70 * 0.70 *18 *18) + (0.30 * 0.30 * 32 * 32) + 2 (0.70 *18*0.30 *32 *- 0.3)
σ = √158.76 + 92.16 -36.288
σ = 14.65
(ii) Variance is the square of standard deviation
Variance = (σ) 2
= (14.65) 2
Variance = 214.62.
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