Q1. Alex has a short forward contract on 100 shares of a company, named ACE, with a strike price $200. Q1-1. Suppose the spot price of the share at the maturity of the forward contract is $190. How can Alex trade ACE shares to make a profit? How much can he gain? Q1-2. Suppose the spot price at maturity is $220 instead. How much does Alex lose from the forward contract?
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Q1-1: Suppose the spot price of the share at the maturity of the forward contract is $190. How can Alex trade ACE shares to make a profit? How much can he gain? ** Show more…
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Akash M.
A stock is expected to pay a dividend of $$\$ 1$$ per share in two months and in five months. The stock price is $$\$ 50$$, and the risk-free rate of interest is $8 \%$ per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock. a. What are the forward price and the initial value of the forward contract? b. Three months later, the price of the stock is $$\$ 48$$ and the risk-free rate of interest is still $8 \%$ per annum. What are the forward price and the value of the short position in the forward contract? (a) The present value, $I$, of the income from the security is given by: $$ I=1 \times e^{-0.08 \times 2 / 12}+1 \times e^{-0.08 \times 5 / 12}=1.9540 $$ From equation (5.2) the forward price, $F_0$, is given by: $$ F_0=(50-1.9540) e^{0.08 \times 0.5}=50.01 $$ or $$\$ 50.01$$. The initial value of the forward contract is (by design) zero. The fact that the forward price is very close to the spot price should come as no surprise. When the compounding frequency is ignored the dividend yield on the stock equals the risk-free rate of interest. (b) In three months: $$ I=e^{-0.08 \times 2 / 12}=0.9868 $$ The delivery price, $K$, is 50.01. From equation (5.6) the value of the short forward contract, $f$, is given by $$ f=-\left(48-0.9868-50.01 e^{-0.08 \times 3 / 12}\right)=2.01 $$ and the forward price is $$ (48-0.9868) e^{0.08 \times 3 / 12}=47.96 $$
Question 3 (Futures and Forward Prices - 20 marks) An investor has just taken a short position in a six-month forward contract on a dividend-paying stock. The stock price is ÂŁ132.00, and the risk-free rate of interest is 6% per annum with continuous compounding for all maturities. The stock is expected to pay a dividend of ÂŁ2 per share in two months and in five months. Required (a) What are the forward price and the initial value of the forward contract? (2 marks) (b) Three months later, the price of the stock is ÂŁ48 and the risk-free rate of interest is still 6% per annum. What are the forward price and the value of the short position in the forward contract? (3 marks) The risk-free rate of interest is 6% per annum with continuous compounding, and the dividend yield on a stock index is 3.0% per annum. The current value of the index is 500. Required (c) What is the six-month futures price? (2 marks) (d) Assume that the futures price for a contract deliverable in six months is 510. What arbitrage opportunities does this create? (3 marks) (e) The futures price of gold can be calculated from its spot price and other observable variables whereas the futures price of copper cannot. Discuss why this is the case.
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