Question

Question
1. A bank is offering 12% compounded quarterly. If you put $100 in an account, how much will you have
at the end of one year? What is the effective annual rate? How much will you have at the end of two
years?
2. The Constant Company has just paid a dividend of $0.30 per share. The divided grows at a steady rate
of 8% per years. What will the dividend be in 5 years? (2marks)
3. We have invested in the portfolio below with 50% in Share A, 25% in share B and 25% in Share C. What
is portfolio return when the economy is boom? What is the expected return of the portfolio? What is the
standard deviation of the portfolio?
Returns
Share A Share B Share C Economy Probability
10% 15% 20% Boom 0.4
8% 4% 0% Bust 0.6

Answer 1

1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

Effective Annual Rate = ((1+12/4*100)^4-1)*100

Effective Annual Rate% = 12.55

Price in 1 year

Future value = present value*(1+ rate)^time

Future value = 100*(1+0.125509)^1

Future value = 112.55

Price in 2 years

Future value = present value*(1+ rate)^time

Future value = 100*(1+0.125509)^2

Future value = 126.68

2

Future value = present value*(1+ rate)^time

Future value = 0.3*(1+0.08)^5

Future value = 0.44

3

Portfolio return in economic boom:

Expected return%=	Wt Share A *Return Share A +Wt Share B*Return Share B+Wt Share C*Return Share C
Expected return%=	0.5*10+0.25*15+0.25*20
Expected return%=	13.75

For other parts:

Share A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%
Boom	0.4	10	4	1.2
Bust	0.6	8	4.8	-0.8
	Expected return %=	sum of weighted return =	8.8	Sum=Variance Share A =
			Standard deviation of Share A %	=(Variance)^(1/2)
Share B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%
Boom	0.4	15	6	6.6
Bust	0.6	4	2.4	-4.4
	Expected return %=	sum of weighted return =	8.4	Sum=Variance Share B=
			Standard deviation of Share B%	=(Variance)^(1/2)
Share C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%
Boom	0.4	20	8	12
Bust	0.6	0	0	-8
	Expected return %=	sum of weighted return =	8	Sum=Variance Share C=
			Standard deviation of Share C%	=(Variance)^(1/2)
Covariance Share A Share B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Boom	0.4	1.2000	6.6	0.0003168
Bust	0.6	-0.8	-4.4	0.0002112
			Covariance=sum=	0.000528
		Correlation A&B=	Covariance/(std devA*std devB)=	1
Covariance Share A Share C:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
Boom	0.4	1.2	12	0.000576
Bust	0.6	-0.8	-8	0.000384
			Covariance=sum=	0.00096
		Correlation A&C=	Covariance/(std devA*std devC)=	1
Covariance Share B Share C:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
Boom	0.4	6.6	12	0.003168
Bust	0.6	-4.4	-8	0.002112
			Covariance=sum=	0.00528
		Correlation B&C=	Covariance/(std devB*std devC)=	1
	Expected return%=	Wt Share A *Return Share A +Wt Share B*Return Share B+Wt Share C*Return Share C
	Expected return%=	0.5*8.8+0.25*8.4+0.25*8
	Expected return%=	8.5
	Variance	=w2A*σ2(RA) + w2B*σ2(RB) + w2C*σ2(RC)+ 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB) + 2*(wA)*(wC)*Cor(RA, RC)*σ(RA)*σ(RC) + 2*(wC)*(wB)*Cor(RC, RB)*σ(RC)*σ(RB)
	Variance	=0.5^2*0.0098^2+0.25^2*0.05389^2+0.25^2*0.09798^2+2*(0.5*0.25*0.0098*0.05389*1+0.25*0.25*0.05389*0.09798*1+0.5*0.25*1*0.0098*0.09798)
	Variance	0.001838
	Standard deviation=	(variance)^0.5
	Standard deviation=	4.29%