Suppose that there are 3 stocks, A, B, and C, each of which has a current price

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Question:

Suppose that there are 3 stocks, A, B, and C, each of which has a current price per share of $100:

• A is a non-dividend-paying stock

• B pays a known, discrete $10 dividend in 2 months

• C pays dividends at a continuously compounded dividend yield of 3%

• The continuously compounded risk-free rate is ???? = 5% at all maturities.

Question:

a) Consider forward contracts that expire in 6 months. What is the no-arbitrage forward price for stock A? For stock B? For stock C?

b) Suppose that your local commercial bank quotes a $100.5 forward price for stock A. Is there an arbitrage opportunity? If so, explain the transactions you could undertake today (i.e., at time t=0) to guarantee a positive payoff in 6 months and zero payoff at all other times. (Be sure to show that your positions achieve zero payoff at all intermediate dates and a positive payoff in 6 months.)

c) Do the same for stocks B and C, assuming that the bank also quotes $100.5 forward prices for both of them. (Again, be sure to show that your positions achieve zero payoff at all intermediate dates and a positive payoff in 6 months.)

Question:

You manage a portfolio with a value of $250,000, which is currently fully invested in Stock A. You wish to engage in a futures overlay strategy to temporarily convert your position from stock A to risk-free bonds over the next six months. Suppose that the bank is now quoting the correct no-arbitrage forward prices that you calculated in Part (a) of Question 1 and disregard the differences between forward and futures contracts. (e.g, suppose there is no intermediate marking to market, no margin account, etc.) Further, suppose that the contract size for Stock A futures is 10.

a) How many shares of stock A do you currently hold?

b) To engage in a futures overlay that fully converts your position to risk-free bonds,will you long or short Stock A futures? How many futures contracts must you long or short?

c) Report the payoffs to your portfolio after implementing the strategy and show that they successfully convert your portfolio from a position in Stock A to a position in risk-free bonds.