1. I am buying a firm with an expected perpetual cash flow of $630 but am unsure of its risk. If I think the beta of the firm is zero, when the beta is really 1, how much more will I offer for the firm than it is truly worth? Assume the risk-free rate is 6% and the expected rate of return on the market is 18%. (Input the amount as a positive value.)

Present value difference $

2.Assume both portfolios A and B are well diversified, that E(r_A) = 15.2% and E(r_B) = 17.6%. If the economy has only one factor, and _A = 1 while _B = 1.3,What must be the risk-free rate? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

Risk-free rate %

3.

Assume 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 36%.

Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3.2%, and one-half have an alpha of 3.2%. 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 analysts profit? (Enter your answers in dollars not in millions. Do not round intermediate calculations. Round your answers to the nearest dollar amount.)

Expected return	$
Standard deviation	$

b-1. How does your answer 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.)

Standard deviation $

b-2. How does your answer change if the analyst examines 100 stocks instead of 20? (Enter your answer in dollars not in millions.)

Standard deviation $

4.

Suppose there are two independent economic factors, M₁ and M₂. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 50%. Portfolios A and B are both well diversified.

Portfolio	Beta on M1	Beta on M2	Expected Return (%)
A	1.6	2.5	40
B	2.4	-0.7	10

What is the expected returnbeta relationship in this economy? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected returnbeta relationship E(r_P) = % + _P1 + _P2

5.

Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:

Market Return	Aggressive Stock	Defensive Stock
7%	2.7%	4.5%
14	29	10

a. What are the betas of the two stocks? (Round your answers to 2 decimal places.)

Beta A
Beta D

b. What is the expected rate of return on each stock if the market return is equally likely to be 7% or 14%? (Round your answers to 2 decimal places.)

Rate of return on A	%
Rate of return on D	%

c. If the T-bill rate is 8%, and the market return is equally likely to be 7% or 14%, what are the alphas of the two stocks? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Alpha A	%
Alpha D	%