Answer:
1.15
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
