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What is the variance of the returns on a portfolio comprised of $4,200 of Stock G...

What is the variance of the returns on a portfolio comprised of $4,200 of Stock G and $5,300 of Stock H?

State of Economy Probability of State of Economy

Rate of Return If State Occurs

Stock G, Stock H
Boom 0.18 0.18, 0.08
Normal 0.82 0.14, 0.11

Multiple Choice .000248 .001324 .000209 .000000 .000168

Solutions

Expert Solution

Here we first need to compute weight of each stock in the portfolio:
Weight = amount invested in stock / total amount
Weight of G = 4200 / (4200+5300)
0.442105
Weight of H = 5300 / (4200+5300)
0.557895
Portfolio return = sum of weight x return
Portfolio return (boom) = 0.18 x 0.442105 + 0.08 x 0.557895
0.1242105
Portfolio Return (Normal) =0.14 x 0.442105 + 0.11 x 0.557895
                                                     = 0.086 0.12326315
State P Rp P x Rp Rp - ER (Rp-0.12343) P x (Rp - ER)^2
Boom 0.18 0.1242105 0.02236 0.00078 0.00000010862
Normal 0.82 0.1232632 0.10108 -0.0002 0.00000002384
ER 0.12343 0.00000013247
Variance = sum of P x (Rp - ER)^2
Variance =    0.00000013247
Answer is B)

ekkarill92 answered 1 year ago
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