[Solution] Write One March 110
1. Winston Corporation has a beta of 1.3. The annualized market return yesterday was 12%, and the risk-free rate is currently 3%. You observe that Winston had an annualized return yesterday of 16%. Assuming that markets are efficient, could you determine whether Winston announced GOOD news or BAD news yesterday? Why?
2. An American-style call option with 6 months to maturity has a strike price of $81. The underlying stock now sells for $85. The call premium is $8.
A) What is the intrinsic value of the option?
B) What is the time value of the call?
C) If the risk-free rate is 2.5%, what should be the value of a put option on the same stock with the same strike price and expiration date?
3. Suppose you purchase one March 106 call contract at $4.55 and write one March 110 call contract at $0.45.
A) What is the maximum potential profit of your strategy? What is the maximum loss you could suffer from your strategy?
B) If, at expiration, the price of the stock is $108, what would your profit be?
C) What is the lowest stock price at which you can break even?
D) Suppose you purchase one March 110 call contract at $0.45 and one put March 95 put contract at $3.05, if at expiration, the price of the stock is $117.5, what would your profit/loss be?
E) For the straddle strategy above, what is the stock price at which you can break-even?
4. You are evaluating a stock that is currently selling for $115 per share. Over the investment period you think that the stock price might go down 20% or go up 25%. There is a call option available on the stock with an exercise price of $125. Answer the following questions about hedging your position in the stock. Assume that you will hold one share, and the risk-free rate is 3%.
A) w is the hedge ratio? How much would you borrow to purchase the stock? What is the amount of your net investment in the stock?
B) How many call options will you combine with the stock to construct the perfect hedge? Will you buy the calls or sell the calls? What must the price of one call option be?
C) What must the price of one put option with an exercise price of $125 be?
5. Use Black-Scholes to find the value of a call option and put option on the following stock:
Time to expiration 9-month
Standard deviation 18% per year
Exercise price $50
Stock price $55
Interest rate 3%
6. Suppose the current price on a stock is $30, the stock has an annual dividend of $0.90. The risk-free rate is 3%. If a futures contract on this stock is available with a 3-month maturity, what should its price be? If the future price in the market is $30.10, how can you structure an arbitrage position?
7. Determine whether the following phenomena, one by one, would be consistent with or a violation of the efficient market hypotheses? Explain briefly.
a) Nearly half of all professional managed mutual funds are able to outperform the S&P500 in a typical year.
b) Money managers that outperform the market (on a risk-adjusted basis) in one year are likely to outperform in the following year.
c) Stock returns tend to be predictably higher in January than in other months.
d) Stocks that perform well in one week perform poorly in the following week.
9. 1. What are the 3 forms of efficient market hypothesis?
2. What are efficient market anomalies?