Question

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 33%.
Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3.1%, and one-half have an alpha of –3.1%. The analyst then buys $1.3 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1.3 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?

Answer 1

Answer:

The Expected return is $80,600

The standard deviation of the analyst’s profit is $191854.63.

Explanation:

the expected return

= $1,3 million*[0.031 + 1.0*Rm] - 1,3 million*[-0.031 + 1.0*Rm]

= $403,000 + $1,300,000Rm + $403,000 - $1,300,000Rm

= $80,600

Therefore, The Expected return is $80,600

the varience = 20*[(130,000*0.33)^2]

                     = $36808200000

Therefore, The standard deviation of the analyst’s profit is $191854.63.