1.1 What is the difference between a long forward position and a short forward position? The difference is one of buying versus selling. The party that takes the long forward position agrees to buy the underlying asset at a specified future date for a specified price. The other party that assumes the short position agrees to sell the underlying asset at the same specified date for the same price. This forms what is known as a forward contract. 1.2 Explain carefully the difference between hedging, speculation, and arbitrage. Hedgers use derivatives to reduce the risk from variation of a market variable in the future. There is no gaurantee that the outcome of hedgin will necessarily be better than not hedging. Of course, one must think of these scenarios in terms of ensembles. Hedging can be done using forward contracts and options. The former (forward contracts) is designed to reduce risk by fixing the price that the hedger will pay or recieve for the underlying asset. The latter (options) provide insurance by offering a way for the investors to protect themselves against adverse price movements in the future while allowing themselves to benefit from favorable price movements. Speculators use derivatives to bet on the future direction of a market variable. The same two financial instruments (forward and option contracts) can be used to speculate. Speculators wish to take a position in the market and are betting that either the price of the asset will go up or will go down. When a speculator uses futures, the potential loss as well as potential gain is large. When options are used, no matter how bad things get the speculator’s loss is limited to the amount paid for the options. Arbitrageurs take ofsetting position in two or more instruments to lock in a profit. They participate in futures, forward and options markets. Arbitrage involves locking in a riskless profit by simultaneously entering into transactions in two or more markets. Example: Suppose a stoc price is $140 in New York and $100 in London when the exchange rate is $1.4300 per pound. Then an arbitrageur can buy 100 shares of stock in New York and sell them in London to obtain a risk free profit of 100×[$1.43×100−$140]100×[$1.43×100−$140] or $300. These opportunities are very temporary as supply and demand would cause the dollar price to rise and the sterling price to drop. Existence of profit hungry arbitageurs makes it unlikely that a major disparity between the sterling and dollar prices exist. 1.3 What is the difference between entering into a long forward contract when the forward price is $50 and taking a long position in a call option with a strike price of $50? When you enter into a long forward contract with a forward price of $50, you are obliged to buy at the contract maturity date that is pre-specified. When you enter into a long position in a call option with a strike price of $50, you have the option but not the obligation of buying the underlying assets by a certain maturity date. Lastly, though there is no cost to entering a forward or futures contract, while there is a cost to aquiring an option. 1.4 Explain carefully the difference between selling a call option and buying a put option. The party that sells the call option is obliged to buy the stock at the strike price before the expiry date if the buyer of the call option decides to sell. Note that regardless of the buyers exercise of the option, the seller of the call option keeps the premiums. The party that buys the put option has the right, but not the obligation to sell an asset at the strike price before the expiry date. For this right, he pays a premium. An unrelated point is that for a call option, the higher the strike price, the lower the premium. For a put option, the lower the strike price, the lower the premium. 1.5 An investor enters into a short forward contract to sell 100,000 GBP for US dollars at an exchange rate of 1.4000 USD/pound. How much does the investor gain or lose at the end of the contract if the exchange rate at t.he end of the contract is (a) 1.3900 and (b) 1.4200? The investor at the end of the contract will have to sell 100,000 GBP for 140,000 USD. a. When the spot price is 1.3900 the price of 100,000 GBP is 139,000 USD. Hence, the investor gains 1000 USD for his investment. b. When the spot price is 1.4200, the price of 100,000 GBP is 142,000 USD. Hence, the investor loses 2000 USD. 1.7 Suppose that you write a put contract with a strike price of $40 and an expiration date in 3 months. The current stock price is $41 and the contract is on 100 shares. What have you commited yourself to? How much could you gain or lose? The person who writes the put contract sells the option for a premium and is obligated to buy the underlying assets before the maturity date should the buyer of the contract decide to sell. You are gauranteed to gain the premium at the writing of the contract. That is yours regardless of the outcome. Now if at anytime within the 3 months the share price goes below $40 such that it offsets the premium price, it is in the option owners interest to sell the shares. In which case, I will experience a loss of (40 - spot price) * 100 dollars. The spot price could potentially be 0, hence my maximum loss is $4000 - premiums. My maximum profit is the premiums. On the other hand, if the share price remains above ($40 - premium paid), he has no incentive to sell to me at $40 and I make the profit amounting to the premiums. Now the questions that are nagging at me are the following: * If the current stock price is $41, why would the option buyer want to sell it to me later at $40. This might be because he wants to get rid of the risk of loss from the share price going down. Actually, I hadn’t thought of this at first but he can buy the shares later at the lower price and sale it for $40. The optioner doesn’t need to preown the shares. Then, the question is why not go lower than $40? For the buyer of the option going lower might be an unacceptable risk leading to just a loss of the premium. Why not go higher than $40? The writer of the contract will have to charge higher premiums. 1.8 What is the difference between the OTC market and the exchange traded market? What are the bid and offer quotes of a market maker in the over the counter market? In an exchange-traded market, individuals are only allowed to trade standardized contracts that have been defined by the exchange. The over-the-counter market is an important alternative to exchanges. Participants are free to make any mutually attractive deal. Bid and offer prices at OTC market is a price at which they are prepared to buy and sell the asset. 1.9 You would like to speculate on a rise in the price of a certain stock. The current stock price is $29 and a 3-month call with a strike price of $30 costs $2.90. You have $5800 to invest. Identify two alternative investment stratedies, ine in the stock and the other in an option on the stock. What are the potential gains and losses from each? One approach is to buy 29 stocks at $29 dollars and if it goes up in 3 months, you can sell it for a profit. If the stock price goes down, you can potentially lose your entire capital. Another approach is to buy a call option or the right to buy stocks at the strike price during a 3 month period. In this case, he has to pay a premium of $2.90/share or $580. That is his maximum loss on his capital. Meanwhile, if the spot price goes above (30 + premium) dollars, he has the right to buy 200 shares at 30 dollars and then sell them for a profit. In this case, there is no upper bound to his profits, though it becomes more unlikely the higher the profit. A US company knows it will have to pay 3 million euros in 3 months. The current exchange rate is 1.4500 dollars/euro. Discuss how forwards and options contracts can be used by the company to hedge its exposure. The current exchange rate is 1.4500 dollars/euro. Hence, 3 million euros would need to be paid in 4.35 million USD. There are two things that could happen: (i) The exchange rate goes up and euros cost a lot more to buy then. (ii) The exchange rate goes down and euros are cheaper. We need not worry about the good scenario (ii). Rather, the question is how to hedge our exposure to the risk of the exchange rate going up? We could go into a forward contract to buy the euro at a prespecified exchange rate. So, sure the spot exchange rate at that time could be lower, but we could eliminate the risk of it being much higher. We could also buy call options and have the right without the obligation to purchase euros at a predetermined strike price. It would cost us a set premium, but it would put an acceptable bound to our losses from exchange rate fluctuation. ON other hand, we get the upside if the exchange rate fluctuates inour favor.