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Chapter 13, Problem 16P

a.

Summary Introduction

To determine: The alpha that informed traders make.

Introduction: Stock alpha is the overabundance risk of the required return; it implies that it is controlled by subtracting the required return of the stock as per SML (security market line) from the expected return of the stock.

b.

Summary Introduction

To determine: The alpha that passive traders make.

c.

Summary Introduction

To determine: The expected return of fad followers.

d.

Summary Introduction

To determine: The alpha that fad followers make.

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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 40%.Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 2.3%, and one-half have an alpha of –2.3%. The analyst then buys $1.2 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1.2 million of an equally weighted portfolio of the negative-alpha stocks.  Required: a. What is the expected profit (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.)
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 40%. Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 2.3%, and one-half have an alpha of –2.3%. The analyst then buys $1.2 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1.2 million of an equally weighted portfolio of the negative-alpha stocks. 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.)
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.)

Chapter 13 Solutions

Corporate Finance Plus MyLab Finance with Pearson eText -- Access Card Package (4th Edition) (Berk, DeMarzo & Harford, The Corporate Finance Series)

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