In: Finance
Assume the return on a market index represents the common factor
and all stocks in the economy have a beta of 1. Firm-specific
returns all have a standard deviation of 48%.
Suppose an analyst studies 20 stocks and finds that one-half have
an alpha of 3.6%, and one-half have an alpha of –3.6%. The analyst
then buys $1.6 million of an equally weighted portfolio of the
positive-alpha stocks and sells short $1.6 million of an equally
weighted portfolio of the negative-alpha stocks.
a. What is the expected return (in dollars), and what is the
standard deviation of the analyst’s profit? (Enter your answers in
dollars not in millions. Do not round intermediate calculations.
Round your answers to the nearest dollar amount.)
b-1. How does your answer for standard deviation change if the analyst examines 50 stocks instead of 20? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)
b-2. How does your answer for standard deviation change if the analyst examines 100 stocks instead of 20? (Enter your answer in dollars not in millions.)