Question

You decide to invest in a portfolio consisting of 40 percent Stock A, 40 percent Stock B, and the remainder in Stock C. Based on the following information, what is the expected return of your portfolio?

State of Economy	Probability of State			Return if State Occurs
	of Economy			Stock A			Stock B			Stock C
Recession		.22		-	17.8	%	-	3.4	%	-	22.3	%
Normal		.47			11.2	%		8.0	%		16.6	%
Boom		.31			27.6	%		15.3	%		31.2	%

Which is the right answer?

• 10.01%

• 9.58%

• 11.32%

• 12.35%

Answer 1

Answer :

State of Economy	Probability (p)	Stock A return (r)	Expected return p * r
Recession	0.22	- 17.8	- 3.916
Normal	0.47	11.2	5.264
Boom	0.31	27.6	8.556
		E(r) =>	9.904

State of Economy	Probability (p)	Stock B return (r)	Expected return p * r
Recession	0.22	- 3.4	- 0.748
Normal	0.47	8.0	3.76
Boom	0.31	15.3	4.743
		E(r) =>	7.755

State of Economy	Probability (p)	Stock C return (r)	Expected return p * r
Recession	0.22	- 22.3	- 4.906
Normal	0.47	16.6	7.802
Boom	0.31	31.2	9.672
		E(r) =>	12.568

Now we have,

WA = 40% , WB = 40% , WC = 20%

RA = 9.904 , RB = 7.755 , RC = 12.568

Expected return on portfolio ( Rp ) = WA * RA + WB * RB + WC * RC

= ( 40% * 9.904 ) + ( 40% * 7.755 ) + ( 20% * 12.568 )

= 9.58%

Therefore, the answer is option (2) i.e., 9.58%.