Question

Suppose the risk-free return is 3.2% and the market portfolio has an expected return of 8.3% and a voatility of 14.3%. Merck \& Co. (Ticker: MRK) stock has a 20.1% volatility and a correlation with the market of 0.041 .

a. What is Merck's beta with respect to the market?
b. Under the CAPM assumptions, what is its expected return?

Answer 1

Merck & Co.'s beta with respect to the market is 0.058, indicating low volatility in relation to the market. Under the CAPM assumptions, Merck & Co.'s expected return is calculated to be 3.496%.

Step-by-step explanation:

The question is related to the calculation of the beta coefficient for Merck & Co. (MRK) and its expected return under the Capital Asset Pricing Model (CAPM). Beta is a measure of the stock's volatility in relation to the market. It can be calculated using the stock's volatility, the market's volatility, and the correlation between the two.

To calculate Merck's beta:

Beta = (Correlation between Merck & market) x (Volatility of Merck / Volatility of market)
Beta = (0.041) x (20.1% / 14.3%)
Beta = 0.058

Under the CAPM, the expected return of a stock is calculated as:

Expected Return = Risk-free rate + Beta x (Market return - Risk-free rate)
Expected Return = 3.2% + 0.058 x (8.3% - 3.2%)
Expected Return = 3.2% + 0.058 x 5.1%
Expected Return = 3.2% + 0.296%
Expected Return = 3.496%

Therefore, under the CAPM assumptions, the expected return for Merck & Co. is 3.496%.