Question

Consider the two assets A and B for which returns (%) under different conditions of economy are given as below.

		Returns (%)
State of the Economy	Probability	Stock A	Stock B
Recession	0.1	-16	-12
Above Average	0.2	-3	4
Average	0.4	14	10
Below Average	0.2	28	15
Boom	0.1	35	20

1. Find the expected return of each asset
2. Find the risk (as measured by standard deviation of return) of each asset
3. If an investor decides to invest $8,000 in stock A and $12,000 in stock B, calculate the expected returns of the investor’s portfolio of stocks A and B.
4. Using the information, calculate the portfolio’s standard deviation if the correlation of the returns between stocks A and B returns is -0.25.

Please show work and how you get the numbers

Answer 1

Weight of stock A = 8000/(12000+8000)

= 0.40

Weight of stock B = 1- weight of stock A

= 1-0.40

= 0.60

Expected return on portfolio= (Return on Stock A * Weight of stock A) + (Return on Stock B* Weight of Stock B)

= 12.5*0.40 + 8.6*0.60

= 5 + 5.16

= 10.16%

is standard deviation of portfolio

w_A and w_B are weights of stock A and B

and are variances of stock A and B

is the correlation coefficient

= 6.80%