Question

You own a portfolio equally invested in a Rf asset and two stocks. If one of the stocks has a beta of 1.85 and the total portfolio is equally as risky as the market, what must be the beta for the other stock in your portfolio?

Answer 1

1.15

Step-by-step explanation:

If investment is made in equal proportions, it means that;

weight in risk free ; wRF = 33.33% or 0.3333

Let the stocks be A and B

weight in stock A ; wA = 33.33% or 0.3333

weight in stock B; wB = 33.33% or 0.3333

Beta of A; bA = 1.85

Let the beta of the other stock be represented by "bB"

Beta of risk free; bRF = 0

Beta of portfolio = 1 since it is mentioned that "the total portfolio is equally as risky as the market "

The weight of portfolio is equal to the sum of the weighted average beta of the three assets. The formula is as follows;

wP = wAbA + wBbB + wRF bRF

1 = (0.3333 * 1.85) + (0.3333*bB) + (0.3333 *0)

1 = 0.6166 +0.3333bB + 0

1 - 0.6166 = 0.3333bB

0.3834 = 0.3333bB

Next, divide both sides by 0.3333 to solve for bB;

bB = 0.3834/0.3333

w=bB = 1.15

Therefore, the beta for the other stock would be 1.15