Assume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 1.6 on the market index. Firm-specific returns all have a standard deviation of 25%. Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +2.5%, and the other half have an alpha of −2.5%. Suppose the analyst invests $1.0 million in an equally weighted portfolio of the positive alpha stocks, and shorts $1 million of an equally weighted portfolio of the negative alpha stocks. a. What is the expected profit (in dollars) and standard deviation of the analyst’s profit? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.) b. How does your answer change if the analyst examines 50 stocks instead of 20 stocks? 100 stocks? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)
Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
Assume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 1.6 on the market index. Firm-specific returns all have a standard deviation of 25%.
Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +2.5%, and the other half have an alpha of −2.5%. Suppose the analyst invests $1.0 million in an equally weighted portfolio of the positive alpha stocks, and shorts $1 million of an equally weighted portfolio of the negative alpha stocks.
a. What is the expected profit (in dollars) and standard deviation of the analyst’s profit? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)
b. How does your answer change if the analyst examines 50 stocks instead of 20 stocks? 100 stocks? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
