The problem states that we have four stocks, a, b, c, and d, with betas of 0.6, 0.8, 1.5, and 0.7 respectively. We are asked to find the beta of the portfolio if the stocks are equally weighted.

1. Problem Description

The problem states that we have four stocks, a, b, c, and d, with betas of 0.6, 0.8, 1.5, and 0.7 respectively. We are asked to find the beta of the portfolio if the stocks are equally weighted.

2. Solution Steps

Since the stocks are equally weighted, each stock has a weight of $\frac{1}{4} = 0.25$. The portfolio beta is the weighted average of the individual stock betas.

The formula for portfolio beta is:

$Portfolio\ Beta = \sum_{i=1}^{n} (Weight_i \times Beta_i)$

In this case, n = 4, and $Weight_i = 0.25$ for all i.

$Portfolio\ Beta = (0.25 \times 0.6) + (0.25 \times 0.8) + (0.25 \times 1.5) + (0.25 \times 0.7)$

$Portfolio\ Beta = 0.25 \times (0.6 + 0.8 + 1.5 + 0.7)$

$Portfolio\ Beta = 0.25 \times (3.6)$

$Portfolio\ Beta = 0.9$

3. Final Answer

0.9