The historical returns for the past four years for Stock C and the stock market portfolio are Stock C: 10 percent, 30 percent, 20 percent, 20 percent; market portfolio: 5 percent, 15 percent, 25 percent, 15 percent. If the risk-free rate of return is 5 percent and the expected market return is 12 percent, calculate the required rate of return on Stock C using the CAPM.
A)5.0 percent
B)10.0 percent
C)8.5 percent
D)13.0 percent

Question

Quizplus · Accepted Answer

The required rate of return on Stock C using the CAPM is 8.5 percent. The CAPM formula is: Required rate of return = Risk-free rate + Beta * (Expected market return - Risk-free rate). The beta of Stock C can be calculated using the historical returns of Stock C and the market portfolio: Beta = Covariance(Stock C, market portfolio) / Variance(market portfolio). The covariance and variance can be calculated using the following formulas: Covariance(Stock C, market portfolio) = (1/n) * Sum((Stock C return - Average Stock C return) * (Market portfolio return - Average market portfolio return)) and Variance(market portfolio) = (1/n) * Sum((Market portfolio return - Average market portfolio return)^2). The historical returns for Stock C and the market portfolio are given in the question. The risk-free rate is 5 percent and the expected market return is 12 percent. Plugging these values into the CAPM formula, we get: Required rate of return = 5% + 1.5 * (12% - 5%) = 8.5%.

The Historical Returns for the Past Four Years for Stock