Question

Security X has an expected return of 15% and a standard deviation of 35%, and is to be continued in a portfolio with Security Y. The correlation between both assets is 0.75. An investor plans to invest $3000 in Security X and $7000 in Security Y. (a) What will be the expected return om the portfolio? (b) If the investor has a risk tolerance of only 25% or less, will this be achieved? Show with calculations accurate to two decimal places. The pay-off matrix of Security Y is:

Economic outlook	Probability	Rate of Return
Recession	0.10	-20%
Below Average	0.15	-10%
Average	0.30	10%
Above Average	0.25	18%
Boom	0.20	50%

  

Answer 1

Expected Ret = Sum [ Prob * ret ]

Demand	Prob	Ret	Ret -Avg Ret
Recession	0.1	-0.2	-0.0200
Below Avg	0.15	-0.1	-0.0150
Avg	0.3	0.1	0.0300
Above Avg	0.25	0.18	0.0450
Boom	0.2	0.5	0.1000
Expected Ret			0.1400

SD of STock Y:

SD = sum [ Prob * (Ret - Avg Ret)^2 ]

Demand	Prob	Ret	Ret -Avg Ret	(Ret -Avg Ret)^2	Prob*(Ret -Avg Ret)^2
Recession	0.1	-0.2	-0.3400	0.1156	0.0116
Below Avg	0.15	-0.1	-0.2400	0.0576	0.0086
Avg	0.3	0.1	-0.0400	0.0016	0.0005
Above Avg	0.25	0.18	0.0400	0.0016	0.0004
Boom	0.2	0.5	0.3600	0.1296	0.0259
Sum [ Prob * [ (Ret - Abg Ret)^2] ]					0.0470

Portfolio Ret = Weighted Avg Ret of Securities in that Portfolio:

Security	Weight	Ret	Wtd Ret
Stock X	0.3	15%	4.50%
Stock Y	0.7	14%	9.80%
Portfolio ret			14.30%

Portfolio SD:

Particulars	Amount
Weight in A	0.3
Weight in B	0.7
SD of A	35%
SD of B	5%
r(1,2)	0.75

A = Stock X

B = Stock Y

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

=SQRT[((0.3*0.35)^2)+((0.7*0.047)^2)+2*(0.3*0.35)*(0.7*0.047)*0.75]

=SQRT[((0.105)^2)+((0.0329)^2)+2*(0.105)*(0.0329)*0.75]

=SQRT[0.01728916]

13.15%