Final answer:
According to CAPM, the expected return on the market portfolio is 6%, and for a zero-beta stock, it's 4%. For a stock with β = -0.5, the fair rate of return is 3%, and the calculated expected return is 14.55%, indicating the stock is underpriced.
Step-by-step explanation:
According to the Capital Asset Pricing Model (CAPM), the expected return on the market portfolio can be inferred since we have a risk-free rate of 4% and an expected return for a portfolio with a beta (β) of 1 being 6%. The market risk premium is the expected return of the market above the risk-free rate, which is 6% - 4% = 2%. Given that a portfolio with a β of 1 would reflect the market, the expected return on the market portfolio is also 6%.
The expected return on a zero-beta stock, according to CAPM, would equal the risk-free rate as it carries no systemic risk – therefore, it is 4%.
For a stock with a β of -0.5, using the CAPM formula, the fair rate of return can be calculated as follows: the risk-free rate plus beta times the market risk premium. Here, we have 4% + (-0.5)(2%) = 3%. This is the fair rate of return for a stock with β = -0.5.
The expected rate of return using the expected price and dividend is calculated by the dividend yield plus the capital gain rate: ($6 + ($57 - $55)) / $55 = 14.55%.
To determine if the stock is overpriced or underpriced, the fair rate of return and the expected rate of return must be compared. Since the expected rate of return (14.55%) is significantly higher than the fair rate of return (3%), the stock is underpriced.