Question

Question 1

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	-18	-10
Above Average	0.2	-4	2
Average	0.4	12	8
Below Average	0.2	24	12
Boom	0.1	30	18

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 $48,000 in stock A and $32,000 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 -0.52.

Answer 1

Expected Ret = SUm [ Prob * ret ]

Stock A:

State	Prob	Ret	Prob * Ret
Recession	0.1000	-0.1800	-0.0180
Above Avg	0.2000	-0.0400	-0.0080
Avg	0.4000	0.1200	0.0480
Below Avg	0.2000	0.2400	0.0480
Boom	0.1000	0.3000	0.0300
Expected Ret	0.1

Stock B:

State	Prob	Ret	Prob * Ret
Recession	0.1000	-0.1000	-0.0100
Above Avg	0.2000	0.0200	0.0040
Avg	0.4000	0.0800	0.0320
Below Avg	0.2000	0.1200	0.0240
Boom	0.1000	0.1800	0.0180
Expected Ret	0.068

Part B:

SD = SQRT [ Prob * ( X- AvgX)^2 ]

Stock A:

State	Prob	X	X-Avg X	(X-Avg X)^2	Prob * (X-AvgX)^2
Recession	0.1000	-0.1800	-0.2800	0.0784	0.0078
Above Avg	0.2000	-0.0400	-0.1400	0.0196	0.0039
Avg	0.4000	0.1200	0.0200	0.0004	0.0002
Below Avg	0.2000	0.2400	0.1400	0.0196	0.0039
Boom	0.1000	0.3000	0.2000	0.04	0.0040
Variance = Sum [ Prob * (X -Avg X)^2 ]	0.0198
SD = SQRT [ Variance ]	0.1409

Stock B:

State	Prob	X	X-Avg X	(X-Avg X)^2	Prob * (X-AvgX)^2
Recession	0.1000	-0.1000	-0.1680	0.028224	0.0028
Above Avg	0.2000	0.0200	-0.0480	0.002304	0.0005
Avg	0.4000	0.0800	0.0120	0.000144	0.0001
Below Avg	0.2000	0.1200	0.0520	0.002704	0.0005
Boom	0.1000	0.1800	0.1120	0.012544	0.0013
Variance = Sum [ Prob * (X -Avg X)^2 ]	0.0051
SD = SQRT [ Variance ]	0.0717

Part C:

Portfolio Ret = Weighted Avg ret of securities in portfolio

Stock	Investment	Weight	Ret	Wtd Ret
A	48000	60%	10%	6.00%
B	32000	40%	6.80%	2.72%
Portfolio Ret	8.72%

Part D:

Portfolio SD:

Particulars	Amount
Weight in A	0.6000
Weight in B	0.4000
SD of A	14.09%
SD of B	7.17%
r(1,2)	-0.52

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(1,2)]

=SQRT[((0.6*0.1409)^2)+((0.4*0.0717)^2)+2*(0.6*0.1409)*(0.4*0.0717)*-0.52]

=SQRT[((0.08454)^2)+((0.02868)^2)+2*(0.08454)*(0.02868)*-0.52]

=SQRT[0.0054]

7.38%