ECN 134 Exam 2- What are the perfect market

ECN 134 Exam 2- What are the perfect market

Subject: Economics    / General Economics
Question
Practice Questions for Exam 2 – Economics 134
I. Short answer:
1. What are the perfect market assumptions?
2. Explain whether the following statements are true or false. In each case,
provide justification for your answer:
• In a perfect capital market, expected returns on all bonds must be
equal to the risk-free (T-bill) rate.
• In a perfect capital market with risk-neutral investors, expected returns on all bonds must equal the risk-free rate.
3. Write down the CAPM formula. What are the economy-wide inputs and
what are the firm-specific inputs?
II. The table below describes the return rates for a stock X and a market index
fund, call it M. Find the (true, as opposed to estimated) beta of stock X. Assume
the probability of the “good” state is 1/3 (“bad” has probability 2/3). M
Asset X Good
10%
4% Bad
6%
10% III. Suppose Intel’s stock has an expected return of 10% and a volatility (standard
deviation) of 5%, while Coca-Cola’s has an expected return of 5% and volatility
of 2%. Assume these two stocks have correlation coefficient ?1.
1. Calculate the portfolio weights that remove all risk.
2. If there are no arbitrage opportunities, what is the risk-free rate of interest
in this economy?
IV. A biotech company has a drug in development that will allow you to sell your
firm for $10 billion next year. Assume your boss wants you to use the CAPM.
Your firm has a beta of 4, the risk-free rate is 5% per year, and the equity premium is 2% per year. What do you think the firm is worth today?
V. Your borrowing rate is 15% per year. Your lending rate is 5% per year. The
project costs $1,000 and has a rate of return of 10%.
1. Assume you have $500 of your own money to invest. Should you invest in
this project?
1 2. Find the maximal amount the investor would be willing to borrow in order
to invest in the project?1
VI. Option pricing:
1. Consider a European call option on a single share of stock in company
X. The strike price is $25 and the maturity date is 1 year. Call this a “25call” for simplicity (and, generally, a “K”-call, where K is the strike price).
Draw the payoff diagram in the two cases where (i) an investor goes long
on a single 25-call, and (ii) an investor shorts both a 25-call and a 20-call.
2. Consider (European) call and put options on a single share of stock in
company X. Each has a strike price of $25 and matures in 1 year. Assume
the (per share) stock price at the time the options are written is $22 and
that the cost of the put is $2. Also assume that the risk-free rate is 10%.
Find the price of the call. 1 An equivalent way to phrase this turns out to be: Find the threshold wealth level such that
the investor would select the project whenever his(her) wealth is at or above this level. 2