Question

Your portfolio is comprised of $20,000 in Cyclone Inc. and $30,000 in Blooper Corp. State of Economy Probability of State of Economy Returns if State Occurs Cyclone Blooper Boom 15% 18% 12% Normal 85% 7% 6% 1. What is the expected return and standard deviation of return for Cyclone? 2. What is the expected return for the portfolio in a Boom? 3. What is the expected return and standard deviation of return for the portfolio? (Hint: Find the portfolio return in each state first, then use the probabilities in the same manner as for a single stock. You don’t need the correlation coefficient when using this method.) 4. Your portfolio is comprised of 30 percent of stock AA, 50 percent of stock BB, and 20 percent of stock CC. Stock AA has a beta of 0.64, stock BB has a beta of 1.48 and stock CC has a beta of 1.04. What is the beta of your portfolio? 5. Which one of the following stocks is correctly priced if the risk-free rate of return is 2.5 percent and the market risk premium is 8 percent?

Answer 1

Calculation of Expected Return of Cyclon:

State	Return %	Probability	Expected Ret.(Ret.*Prob.)
Boom	18	0.15	2.7
Normal	7	0.85	5.95
Expected return of Cyclon			8.65

Calculation of Standard Deviation of Cyclon:

State	Return %	Expected Ret.	Deviation(Ret.-Exp Ret.)	Deviation2
Boom	18	2.7	15.3	234.09
Normal	7	5.95	1.05	1.1025
Total of Deviation2				235.1925
S.D.(=√Total of Deviation2)				15.335987

Calculation of Portfolio Return in Boom:

Boom (Prob 15%)
Company	Return %	Weight	Weighted Return
Cyclone	18	0.4	7.2
Blooper	12	0.6	7.2
Portfolio Return			14.4

Calculation of Portfolio Return in Normal:

Normal(Prob 85%)
Company	Return %	Weight	Weighted Return
Cyclone	7	0.4	2.8
Blooper	6	0.6	3.6
Portfolio Return			6.4

Calculation of Expected return of Portfolio:

State	Portfolio Return %	Probability	Expected Ret.(Ret.*Prob.)
Boom	14.4	0.15	2.16
Normal	6.4	0.85	5.44
Expected Portfolio return			7.6

Calculation of Standard Deviation of returns of Portfolio:

State	Portfolio Return %	Expected Ret.	Deviation(Ret.-Exp Ret.)	Deviation2
Boom	14.4	7.6	6.8	46.24
Normal	6.4	7.6	-1.2	1.44
Total of Deviation2				47.68
S.D.(=√Total of Deviation2)				6.9050706

Calculatin of Portfolio Beta:

Stock	Beta	Weight	Product(Beta*Weight)
AA	0.64	0.3	0.192
BB	1.48	0.5	0.74
CC	1.04	0.2	0.208
Portfolio Beta			1.14

Calculation of Expected return Rj (CAPM Return).:

Rj=Risk Free ret(Rf) + Beta(Risk Premium)

Rj(AA)=2.5+.64(8)

=2.5+5.12

=7.62

Rj(BB)=2.5+1.48(8)

=2.5+11.84

=14.34

Rj(CC)=2.5+1.04(8)

=2.5+8.32

=10.82