Question

Question Three

1. Explain the effects of inadequate working capital to a firm
2. An investor has an investment capital of Sh.2,000,000. He wishes to invest in two securities, A and B in the following proportion; Sh.400,000 in security A and Sh.1, 600,000 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
Boom	0.4	18%	24%
Normal	0.5	14%	22%
Recession	0.1	12%	21%

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

=400000+1600000

=2000000

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

= 400000/2000000

=0.2

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

= 1600000/2000000

=0.8

i

Sec A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.4	18	7.2	2.6	0.0002704
Normal	0.5	14	7	-1.4	9.8E-05
Recession	0.1	12	1.2	-3.4	0.0001156
	Expected return %=	sum of weighted return =	15.4	Sum=Variance Sec A=	0.00048
			Standard deviation of Sec A%	=(Variance)^(1/2)	2.2
Sec B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.4	24	9.6	1.3	6.76E-05
Normal	0.5	22	11	-0.7	2.45E-05
Recession	0.1	21	2.1	-1.7	2.89E-05
	Expected return %=	sum of weighted return =	22.7	Sum=Variance Sec B=	0.00012
			Standard deviation of Sec B%	=(Variance)^(1/2)	1.1

i

Expected return%=	Wt Sec A*Return Sec A+Wt Sec B*Return Sec B
Expected return%=	0.2*15.4+0.8*22.7
Expected return%=	21.24

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
Boom	0.4	2.6	1.3	0.0001352
Normal	0.5	-1.4	-0.7	4.9E-05
Recession	0.1	-3.4	-1.7	5.78E-05
			Covariance=sum=	0.000242
		Correlation A&B=	Covariance/(std devA*std devB)=	1

iii

Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.2^2*0.022^2+0.8^2*0.011^2+2*0.2*0.8*0.022*0.011*1
Variance	0.000170
Standard deviation=	(variance)^0.5
Standard deviation=	1.30%