Final answer:
To determine the percentage of the portfolio invested in the stock with a beta of 1.08 and a portfolio beta of 0.94, the formula for the weighted average of betas is used. The calculation reveals that approximately 87.04% of the portfolio is invested in the stock.
Step-by-step explanation:
The question asks, "What percentage of the portfolio is invested in the stock?" given that the stock has a beta of 1.08, an expected return of 13.2%, a risk-free asset earning 1.2%, and the portfolio’s beta is 0.94. This can be calculated using the formula for the weighted average of betas:
(Weight of Stock × Beta of Stock) + (Weight of Risk-Free Asset × Beta of Risk-Free Asset) = Portfolio Beta
Because the risk-free asset has a beta of 0, the equation simplifies to:
Weight of Stock × Beta of Stock = Portfolio Beta
Solving for Weight of Stock, we get:
Weight of Stock = Portfolio Beta / Beta of Stock
Weight of Stock = 0.94 / 1.08
Weight of Stock ≈ 0.8704 or 87.04%
We can divide asset allocation models into three broad groups: Income Portfolio: 70% to 100% in bonds. Balanced Portfolio: 40% to 60% in stocks. Growth Portfolio: 70% to 100% in stocks.