Futures and Options

Finance 436 – Futures and Options Review Notes for Midterm Exam Chapter 1 1. Derivative securities: concepts 2. Futures and forward contracts: definitions and comparison Exchange trading; contract size, delivery; default risk; marking to market 3. Options: concepts 4. Players in options and futures markets Hedgers: reduce price risk (uncertainty) Speculators: bet on price movement Arbitrageurs: look for risk-free profit 5. Applications 6. Examples discussed in class and assignments Chapter 2 1. Specification of futures contracts Opening vs. closing a futures position Long vs. short a futures position Underlying asset Contract size (will be given if needed) Delivery month; Daily price limit; Position limit Settlement price: concepts Open interest: concepts and calculations 2. Convergence of futures price to spot price: concepts and proof 3. Margins: concepts and calculations Initial margin; Maintenance margin; Margin call; Variation margin 4. Marking to market process: concepts and calculations 5. Orders and applications Market order; Limit order; Stop (stop-loss) order Stop-limit order; Day order; Open order 6. Cash settlement: concepts 7. Forward contracts: profit/loss diagrams 8. Examples discussed in class and assignments Chapter 3 1. Hedging: concepts Long hedging vs. short hedging 2. Basis risk: definitions and applications 3. Cross hedging Hedge ratio: definition, estimation, and implication Minimum variance hedge ratio: minimize the variance Optional number of contracts 4. Hedging with stock index futures: concepts and calculations 5. Examples discussed in class and assignments 1 Chapter 4 1. 2. 3. 4. 5. 6. Types of interest rates Measuring interest rates: concepts and calculations Zero rates: concepts Forward rates: concepts and calculations Term structure theories Examples discussed in class and assignments Chapter 5 1. Investment assets vs. consumption assets 2. Continuous compounding (erT) and discounting (e-rT ) 3. Forward price for an asset with no income: F = S*erT --- (5.1) 4. Forward price for an asset with a known cash income: F = (S-I)*erT --- (5.2) 5. Forward price for an asset with a known dividend yield: F = S*e(r-q)T --- (5.3) 6. Valuing forward contracts: f = (F-K)*e-rT (long); f = (K-F)*e-rT (short) 7. Forward prices and futures prices: concepts 8. Stock index futures contracts and characteristics: ues (5.3) 9. Currency futures: use (5.3) 10. Commodity futures with and without storage cost 11. Cost of carry 12. Examples discussed in class and assignments 4. 5. 6. 7. Chapter 6 Day count convention Quotations T-bonds and T-bond futures contracts: concepts, applications, and calculations Cash price, quoted price, accrued interest, and cheapest to deliver T-bills and T-bill futures contracts: concepts and applications Duration and immunization: concepts and applications Duration-based hedge ratio: concepts and applications Examples discussed in class and assignments 1. 2. 3. 4. 5. 6. Chapter 7 Swaps: concepts Comparative advantage Interest-rate swaps: concepts and diagrams Currency swaps: concepts and diagrams The role of financial intermediary Examples discussed in class and homework problems 1. 2. 3. 2 Sample Problems Chapter 1 1. Problem 1-24 Trader A enters into a forward contract to buy gold for $1,000 an ounce in one year. Trader B buys a call option to buy gold for $1,000 an ounce in one year. The cost of the option is $100 an ounce. What is the difference between the positions of the traders? Show the profit per ounce as a function of the price of gold in one year for the two traders. Answer: Trader A makes a profit of ST Ӎ 1,000 and Trader B makes a profit of max(ST Ӎ 1,000, 0) – 100 where ST is the spot price of gold in one year. Trader A does better if ST is above $900 as indicated in Figure S1.3. Figure1.3: Profit to Trader A and Trader B in Problem 1.24 2. Assume that the spot price for gold is $1,200 per ounce and the gold futures contract for one year delivery is trading at $1,270. The risk-free interest rate is 5% per year. Can you arbitrage? How? Answer: Theoretical futures price F = 1,200*e(0.05*1) = $1,261.53 Since the actual futures price in the market is $1,270 > $1,261.53, it is overpriced so you can arbitrage Today: (1) Borrow $120,000 at 5% for one year to buy 100 ounces of gold at $1,200 (2) Sell a futures contract on gold at $1,270 per ounce (one year delivery) In one year: (1) Make the delivery and collect $127,000 (2) Repay the loan (principle plus interest) $126,153 = 120,000*e(0.05*1) (3) Take risk-free profit = $847 3 Chapter 2 1. Quiz 2.3 Answer: For a short position, if price drops, you gain; if price goes up, you lose Margin call: lose more than $1,000 or price goes up by more than 20 cents (5,000 ounces per contract) 2. Quiz 2.4 Answer: For a long position, if price drops, you lose; if price goes up, you gain 3. Problem 2.11 Answer: Margin call: to lose more than $1,500 if the futures price drops by more than 10 cents per pound (since the contract size is 15,000 pounds) Making $2,000 total or $1,000 per contact: if the price rises by 6.67 cents per pound Chapter 3 1. Quiz 3.6 Answer: see the textbook 2. Quiz 3.7 Answer: see the textbook 3. Consider the following stock portfolio: Stock Shares Price -------------------FV 30,000 34 GC 25,000 22 YH 20,000 17 Value ---------1,020,000 550,000 340,000 Beta -----1.25 1.00 0.80 If the S&P 500 index currently is standing at 1,000 ($250 time the index is the contract size), how many futures contracts must be bought or sold to hedge 50% of the market risk of this portfolio? How about reducing beta by 75%? Beta of the portfolio (value weighted average) = 1.098; F = 1,000*250 = $250,000 S = 1,020,000 + 550,000 + 340,000 = $1,910,000 Optimal contract size N* = 1.098*(1,910,000/250,000) = 8.39 contracts, a 50% hedge (or to reduce the portfolio beta to 0.55) means shorting 4 S&P 500 index futures contracts To reduce beta by 75% (meaning to reduce the beta to 0.27) implies shorting 6 futures contracts Chapter 4 1. Quiz 4.4 Answer: see the textbook 2. Quiz 4.5 Answer: see the textbook 4 Chapter 5 1. Quiz 5.3 Answer: see the textbook 2. Quiz 5.4 Answer: see the textbook 3. Problem 5.12 Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create? How can you arbitrage? Answer: Theoretical futures price F = 400*e(0.1-0.04)(4/12) = 408.08 and the actual futures price in the market F = 405 < 408.08, which is undervalued Arbitrage: Today: buy futures contracts at 405; short sell stock index at 400 and deposit short sale proceeds at 10% for four months After four months: collect 413.56; take the delivery and pay 405; return the asset plus dividend (5.37); arbitrage profit = 413.56 – 405 – 5.37 = 3.19, PV of profit = $3.08 Chapter 6 1. Quiz 6.2 Answer: see the textbook 2. Problem 6.9 Answer: AI = 6*98/181 = 3.2468 (there are 98 days between January 27 and May 5 and there are 181 days between January 27 and July 27) Cash price = 110.5312 + 3.2468 = 113.7798 3. Problem 6.10 Answer: Bond 1: net cost = 2.178 Bond 2: net cost = 2.652 Bond 3: net cost = 2.946 Bond 4: net cost = 1.874 Bond 4 is the cheapest to deliver Chapter 7 1. Quiz 7.1 Answer: see the textbook 2. Quiz 7.3 Answer: see the textbook 5