You have the following information:Year X Returns Y Returns MarketReturns2010 15% 12% 15%2011 18% 7% 10%2012 -17% -5% -12%2013 4% 2% 3%2014 20% 12% 15%The risk-free rate is 8% and the market risk premium is 4%.a. Calculate: Coefficients βX and βYb. Using the results of question 1, calculate the required rate of return for stock X andstock Y. The expected rate of return of X:13%, Y:14%. Discuss about the value of thesestock.c. Using the results of questions 1 and 2, calculate the required rate of return for aportfolio with a composition of 30% X shares and 70% Y shares.
Question
You have the following information:Year X Returns Y Returns MarketReturns2010 15% 12% 15%2011 18% 7% 10%2012 -17% -5% -12%2013 4% 2% 3%2014 20% 12% 15%The risk-free rate is 8% and the market risk premium is 4%.a. Calculate: Coefficients βX and βYb. Using the results of question 1, calculate the required rate of return for stock X andstock Y. The expected rate of return of X:13%, Y:14%. Discuss about the value of thesestock.c. Using the results of questions 1 and 2, calculate the required rate of return for aportfolio with a composition of 30% X shares and 70% Y shares.
Solution
To answer this question, we need to follow several steps:
a. Calculate the coefficients βX and βY
The beta coefficient is a measure of a stock's volatility in relation to the overall market. It can be calculated using the formula:
β = Covariance(Return of asset, Return of market) / Variance(Return of market)
First, we need to calculate the returns relative to the market for each year for both X and Y. Then, we calculate the covariance of these returns with the market returns, and divide by the variance of the market returns.
b. Calculate the required rate of return for stock X and stock Y
The required rate of return can be calculated using the Capital Asset Pricing Model (CAPM), which is:
Required return = Risk-free rate + β(Market return - Risk-free rate)
We already have the risk-free rate (8%) and the market risk premium (4%), so we just need to plug in our calculated beta values for X and Y.
c. Calculate the required rate of return for a portfolio with a composition of 30% X shares and 70% Y shares
The required return for a portfolio is simply the weighted average of the required returns of the individual assets, so:
Required return of portfolio = 0.3 * Required return of X + 0.7 * Required return of Y
Please note that the actual calculations require the specific numbers which are not provided in the question.
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