Question

There are three assets A, B and C. The returns for shares A, B and C over the next year have expected values 10%, 5%, 3% respectively. The standard deviations for A, B and C are 30%, 25% and 20% respectively. The covariance between these A and B is 0.0375, the covariance between A and C is -0.018, the covariance between B and C is -0.03. Ben currently has invested equal amounts of his portfolio in shares A, B and C.

a) Calculate the expected return on Ben’s portfolio. [1 marks]

b) Calculate the correlations

c) Calculate the variance and standard deviation of the return on Ben’s portfolio. [4 marks]

d) Alice also wants to invest in shares A, B and C, but her risk appetite is lower than Ben. Suggest a weight allocation such that Alice’s portfolio will have a lower risk than Ben’s portfolio, and explain why. You are NOT required to provide calculations.

Answer 1

Assets	A	B	C
Return	10%	5%	3%
Standard Deviation (SD)	30%	25%	20%
Weights in porfolio(W)	1/3	1/3	1/3
Covariance of A & B	0.0375
Covariance of B & C		-0.03
Covariance of A & C	-0.018
a) Expected return on Ben's Portfolio:
Assets	Return	Proportion in Portfolio	Weighted Return
A	10%	1/3	3.33%
B	5%	1/3	1.67%
C	3%	1/3	1.00%
Return of Portfolio	6.00%
b) Correlation computations:
Correlation fomula = Covariance between A&B /(SD(a)*SD(b))
Correlation between A&B:
=	0.0375/(0.3*0.25)
=	0.5
Correlation Between B&C:
=	-0.03/(0.25*0.2)
=	-0.6
Correlation Between A&C:
=	-0.018/(0.3*0.2)
=	-0.3
c) Variance and standard deviation of Ben's Portfolio:
Standard deviation of portfolio contains A,B&C securities:
=√(W(a)*SD(a))^2+(W(b)*SD(b))^2+(W©*SD©)^2+2W(a)*W(b)*Cov.(a,b)+ 2W(b)*W(c)*Cov.(b,c)+
2W(a)*W(c)*Cov.(a,c)
=√(1/3*0.3)^2+(1/3*0.25)^2+(1/3*0.2)^2+2*1/3*1/3*0.5+2*1/3*1/3*(-0.6)+2*1/3*1/3*(-0.3)
=√(0.01+0.00694+0.0044+0.1111-0.1333-0.0667)
=√(-0.0675)