1. Assume that you are an equity portfolio manager with a well-diversified portfolio valued at $2.5 million with a beta of 1.1, but you have a positive outlook on the short-term prospects of the stock market and want to increase your market risk using index futures by increasing your beta to 1.6. Assume that the S&P500 is trading at a price of 2655, the futures multiplier is $250, and the futures price is currently 2670. 

a. How many contracts would you need to go long or short to adjust the portfolio to the desired beta? 


b. Assume that the risk-free interest rate is 2% and the continuous market dividend yield is 2%. Furthermore, assume that 6-months later the index is trading at 2785 and the futures price is 2795. What is the value of the total position (equity portfolio plus gains or losses from the futures contract)? 


c. What are some reasons that a futures contract cannot provide a perfect hedge to an equity portfolio in a situation like this?

2. (10 points) Consider a European call option with a strike price of $82 and 8 months remaining to maturity on a non-dividend-paying stock that currently trades at a price of $80. At expiration, the stock will be priced at either $84 or $72. The risk-free interest rate is 3%.

a. Is the call option currently in-the-money or out-of-the-money? 


b. What are the intrinsic and time values of the option? 


c. When constructing a replicating portfolio, should you buy or sell the underlying 
stock? How many shares should you buy or sell? 


d. What is the current price of the option in an arbitrage-free market? 


3. (10 points) A stock is currently trading at a price of $30 with a continuous dividend rate of 1% when the risk-free interest rate is 5%. In 3 months, the stock will be trading at either $38 or $24.

a. What is the current price of a European put option with a strike price of $29 and three month until expiration? 


b. If the put option in Part A is trading at a market price of $3.25, what three transactions can an arbitrageur enter into today to guarantee a risk-free profit? And how much money will be earned (in present value terms)? 


4. (10 points) Use a two-period Cox-Ross-Rubinstein binomial tree to price a European call option with the following terms: strike price is $20; expiration is in 8 months; the current price of the stock is $19; the stock’s volatility is 10%; continuous dividend rate is 2%; risk-free interest rate is 6%. 


5. (15 points) Use a two-period Jarrow-Rudd binomial tree to price an American put option with the following terms: spot price is $50; strike price is $52; expiration is in one year; the stock’s volatility is 25%; risk-free interest rate is 6%; dividend rate is 2%. 


a. Why does the price of this option differ from a European put with the same terms?

Answer rating: 100% (QA)

1 15 points Assume that you are an equity portfolio manager with a welldiversified portfolio valued at 25 million with a beta of 11 but you have a positive outlook on the shortterm prospects of the st... View the full answer