Question

An investor has an investment capital of KES. 9,000,000. He wishes to invest in a portfolio of two securities, A and B in the following proportion; KES. 4,950,000 in security A and KES. 4,050,000 in security B.

The returns on these two securities depend on the state of the economy as shown below:

State of Economy	Probability	Return on Security A	Return on security B
Expansion	0.4	25%	5%
Boom	0.3	20%	10%
Recession	0.2	12%	20%
Depression	0.1	-20%	35%

Required:

1. Compute the expected portfolio return.
2. Determine the correlation coefficient between security A and Security B and interpret it.
3. Calculate the portfolio risk as measured by standard deviation.

Answer 1

Total Portfolio value = Value of Sec A + Value of Sec B

=4950000+4050000

=9000000

Weight of Sec A = Value of Sec A/Total Portfolio Value

= 4950000/9000000

=0.55

Weight of Sec B = Value of Sec B/Total Portfolio Value

= 4050000/9000000

=0.45

i

Sec A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Expansion	0.4	25	10	8.6	0.0029584
Boom	0.3	20	6	3.6	0.0003888
Recession	0.2	12	2.4	-4.4	0.0003872
Depression	0.1	-20	-2	-36.4	0.0132496
	Expected return %=	sum of weighted return =	16.4	Sum=Variance Sec A=	0.01698
			Standard deviation of Sec A%	=(Variance)^(1/2)	13.03
Sec B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Expansion	0.4	5	2	-7.5	0.00225
Boom	0.3	10	3	-2.5	0.0001875
Recession	0.2	20	4	7.5	0.001125
Depression	0.1	35	3.5	22.5	0.0050625
	Expected return %=	sum of weighted return =	12.5	Sum=Variance Sec B=	0.00863
			Standard deviation of Sec B%	=(Variance)^(1/2)	9.29

Expected return%=	Wt Sec A*Return Sec A+Wt Sec B*Return Sec B
Expected return%=	0.55*16.4+0.45*12.5
Expected return%=	14.65

ii

Covariance Sec A Sec B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Expansion	0.4	8.6	-7.5	-0.00258
Boom	0.3	3.6	-2.5	-0.00027
Recession	0.2	-4.4	7.5	-0.00066
Depression	0.1	-36.4	22.5	-0.00819
			Covariance=sum=	-0.0117
		Correlation A&B=	Covariance/(std devA*std devB)=	-0.97

iii

Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.55^2*0.13032^2+0.45^2*0.09287^2+2*0.55*0.45*0.13032*0.09287*-0.96669
Variance	0.00109
Standard deviation=	(variance)^0.5
Standard deviation=	3.30%