Question

		Rate of return if state occurs
State of economy	Probability of state of economy	Stock A	Stock B	Stock C
Boom	0.3	0.35	0.45	0.38
Good	0.3	0.15	0.20	0.12
Poor	0.3	0.05	–0.10	–0.05
Bust	0.1	0.00	–0.30	–0.10

5.         Consider the following information on three stocks in four possible future states of the economy:                       

1. Your portfolio is invested 30% in A, 50% in B, and 20% in C. What is the expected return of your portfolio?
2. What is the variance of this portfolio?                 
3. What is the standard deviation of this portfolio?   (1 mark)

            Just For Fun (JFF):

            See if you can find the optimal portfolio using the Solver function in MS Excel. To optimize the portfolio, you would want to find the optimal portfolio weights that will minimize the portfolio risk (standard deviation) while achieving a required rate of return (say, 15%). No marks are assigned for this problem, as it is JFF.

Answer 1

Expected return of stock A:

Expected return = R1*P1+R2*P2+R3*P3+R4*P4

Where R = return

P = Probability

Expected return of Stock A = 0.3*0.35+0.3*0.15+0.3*0.05+0.1*0

= 0.165

Expected return of stock B= 0.3*0.45+0.3*0.20+0.3*(-0.1)+0.1*(-0.3)

= 0.135

Expected return of Stock C= 0.3*0.38+0.3*0.12+0.3*(-0.05)+0.1*(-0.1)

= 0.125

a) Calculation of Expected return of portfolio:

Probability (1)	Return (2)	Expected return (3) (1*2)
0.3	0.165	0.0495
0.5	0.135	0.0675
0.2	0.125	0.025
	Expected return	0.142

b) Calculation of Variance of portfolio:

Probability (1)	Return (2)	Return-Expected return (3)	Square of Return-Expected return (4)	Variance (5) (1*4)
0.3	0.165	0.165-0.142=0.023	(0.023)^2=0.000529	0.0001587
0.5	0.135	0.135-0.142=-0.007	(-0.007)^2=0.000049	0.0000245
0.2	0.125	0.125-0.142=-0.017	(-0.017)^2=0.000289	0.0000578
			Variance	0.000241

c) Calculation of standard deviation of portfolio:

Standard deviation = Square root of Variance

= Square root of 0.000241

= 0.0155 or 1.55%