Question

The probability distribution of returns for Stocks A and B are given in the table below. If you invest $1,200,000 in Stock A and $800,000 in Stock B, calculate the expected return of your portfolio.

State of Economy	Probability of state	Stock A's Return	Stock B's Return
Boom	0.20	40%	28%
Normal	0.40	25%	12%
Slow Down	0.30	0%	7%
Recession	0.10	-20%	0%

a.16.00%

b.15.2%

c.12.8%

d.14.6%

Group of answer choices

Answer 1

The expected return is computed as shown below:

= Return of Stock A x Weight of Stock A + Return of Stock B x Weight of Stock B

Return of Stock A is computed as follows:

= Prob. of Boom Economy x return of Stock A in Boom Economy + Prob. of Normal Economy x return of Stock A in Normal Economy + Prob. of Slow Down Economy x return of Stock A in Slow Down Economy + Prob. of Recession Economy x return of Stock A in Recession Economy

= 0.20 x 0.40 + 0.40 x 0.25 + 0.30 x 0.00 + 0.10 x - 0.20

= 0.08 + 0.10 + 0 - 0.02

= 16% or 0.16

Return of Stock B is computed as follows:

= Prob. of Boom Economy x return of Stock B in Boom Economy + Prob. of Normal Economy x return of Stock B in Normal Economy + Prob. of Slow Down Economy x return of Stock B in Slow Down Economy + Prob. of Recession Economy x return of Stock B in Recession Economy

= 0.20 x 0.28 + 0.40 x 0.12 + 0.30 x 0.07 + 0.10 x 0.00

= 0.056 + 0.048 + 0.021 + 0

= 12.5% or 0.125

So, the expected return is computed as follows:

= 0.16 x [ $ 1,200,000 / ($ 1,200,000 + $ 800,000) ] + 0.125 x [ $ 800,000 / ($ 1,200,000 + $ 800,000) ]

= 0.16 x [$ 1,200,000 / $ 2,000,000] + 0.125 x [$ 800,000 / $ 2,000,000]

= 0.096 + 0.05

= 14.6%

So, the correct answer is option d.

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