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Practise Questions (Optional) (Note: As additional materials, the quick answers are given and assist you to understand concepts and some calculations. You are encouraged to work out procedures by yourself. You should review that week lecture notes and text chapter/s.) 1. List three types of traders in futures, forward, and options markets 1. (i) ................. 2. (ii) ................ 3. (iii) ............... 1. hedgers, speculators, arbitrageurs2. A trader buys 100 European call options with a strike price of $20 and a time to maturity of one year. The cost of each option is $2. The price of the underlying asset proves to be $25 in one year. What is the trader's gain or loss? ............ 2. $300 gain 3. A one-year call option on a stock with a strike price of $30 costs $3; a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option. (i) What is the breakeven stock price, above which the trader makes a profit? ………. (ii) What is the breakeven stock price below which the trader makes a profit? ………. 3. (i) $35; (ii) $20. 4. Which of the following is not true (circle one) (a) Futures contracts nearly always last longer than forward contracts (b) Futures contracts are standardized; forward contracts are not. (c) Delivery or final cash settlement usually takes place with forward contracts; the same is not true of futures contracts. (d) Forward contract usually have one specified delivery date; futures contract often have a range of delivery dates. 4. (a) 5. In the corn futures contract a number of different types of corn can be delivered (with price adjustments specified by the exchange) and there are a number of different delivery locations. Which of the following is true (circle one) (a) This flexibility tends increase the futures price.1

(b) This flexibility tends decrease the futures price. (c) This flexibility may increase and may decrease the futures price. (d) This has no effect on the futures price 5. (b); 6. A company enters into a short futures contract to sell 50,000 pounds of cotton for 70 cents per pound. The initial margin is $4,000 and the maintenance margin is $3,000. What is the futures price above which there will be a margin call? ……….. 6. 72 cents; 7. A company enters into a long futures contract to buy 1,000 units of a commodity for $20 per unit. The initial margin is $6,000 and the maintenance margin is $4,000. What futures price will allow $2,000 to be withdrawn from the margin account? ………….. 7. $22 8. Who determines when delivery will take place in a corn futures contract (circle one) (a) The party with the long position (b) The party with the short position (c) Either party can specify a delivery date (d) The exchange specifies the exact delivery date. 8. (b); 9. Which of the following is true (circle one) (a) Both forward and futures contracts are traded on exchanges. (b) Forward contracts are traded on exchanges, but futures contracts are not. (c) Futures contracts are traded on exchanges, but forward contracts are not. (d) Neither futures contracts nor forward contracts are traded on exchanges. 9. (c) 10. On March 1 the spot price of a commodity is $20 and the July futures price is $19. On June 1 the spot price is $24 and the July futures price is $23.50. A company entered into a futures contracts on March 1 to hedge the purchase of the commodity on June 1. It closed out its position on June 1. What is the effective price paid by the company for the commodity? ………. 10. (a)2

11. Suppose that the standard deviation of monthly changes in the price of commodity A is $2. The standard deviation of monthly changes in a futures price for a contract on commodity B (which is similar to commodity A) is $3. The correlation between the futures price and the commodity price is 0.9. What hedge ratio should be used when hedging a one month exposure to the price of commodity A? ………….. 11. 0.6 12. Futures contracts trade with all delivery months. A company is hedging the purchase of the underlying asset on June 15. Which futures contract should it use (circle one) (a) The June contract (b) The July contract (c) The May contract (d) The August contract 12. (b); 13. A company has a $36 million portfolio with a beta of 1.2. The S&P index is currently standing at 900. Futures contracts on $250 times the index can be traded. What trade is necessary to achieve the following. (Indicate the number of contracts that should be traded and whether the position is long or short.) (i) Eliminate all systematic risk in the portfolio ………… (ii) Reduce the beta to 0.9 ………….. (iii) Increase beta to 1.8 ……………. 13. (i) 192 short; 48 short; 96 long14. The spot price of an investment asset that provides no income is $30 and the risk-free rate for all maturities (with continuous compounding) is 10%. What is the three-year forward price? ……… 14. $40.50 15. Repeat question 14 on the assumption that the asset provides an income of $2 at the end of thefirst year and at the end of the second year……….. 15. $35.84 16. An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 5% and 7% (both expressed with continuous compounding). What is the six-month forward rate? ………… 16. 0.69303

17. The spot price of an asset is positively correlated with the market. Which of the following would you expect to be true (circle one) (a) The forward price equals the expected future spot price. (b) The forward price is greater than the expected future spot price. (c) The forward price is less than the expected future spot price. (d) The forward price is sometimes greater and sometimes less than the expected future spot price. 17. (c); 18. The one-year Canadian dollar forward exchange rate is quoted as 1.4000. What is the corresponding futures quote? ……………… 18. 0.7143 19. Which of the following is a consumption asset (circle one) (a) The S&P 500 index (b) The Canadian dollar (c) Copper (d) IBM shares 19. (c) 20. Consider an exchange traded put option to sell 100 shares for $20. Give (a) the strike price and (b) the number of shares that can be sold after (i) A 5 for 1 stock split (a) ………….(b) …………… (ii) A 25% stock dividend (a) ……….. (b) …………. (iii) A $5 cash dividend (a) ………. (b) …………… 20. (i) $4 and 500; (ii) $16 and 125; (iii) $20 and 100 21. Which of the following are always positively related to the price of a European call option on a stock (circle three) (a) The stock price (b) The strike price (c) The time to expiration4

(d) The volatility (e) The risk-free rate (f) The magnitude of dividends anticipated during the life of the option 21. (a), (d), and (e); 22. What is the lower bound for the price of a two-year European call option on a stock when the stock price is $20, the strike price is $15, and the risk-free interest rate is 5% and there are no dividends? …… 22. $6.43 23. What is the lower bound for the price of a six-month European put option on a stock when the stock price is $40, the strike price is $46 and the risk-free interest rate is 6%? ………… 23. $4.64 24. A call and a put on a stock have the same strike price and time to maturity. At 10:00am on a certain day, the price of the call is $3 and the price of the put is $4. At 10:01am news reaches the market that has no affect on the stock price, but increases its volatility. As a result the price of the call changes to $4.50. What would you expect the price of the put to change to? …………. 24. $5.50. 25. A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European put option with a strike price of $95. The risk-free interest rate is 8% per annum (i) What is the risk-neutral probability of a 10% rise in each quarter? ……………… (ii) What is the value of the option? …………….. (iii) What is the value of the option if it is American? ……………… (iv) What is the value of the option if it is a call rather than a put? ………….. 25. (i) 0.601; (ii) 2.14; (iii) 2.14; (iv) 10.87. 26. Consider a six month put option on a stock with a strike price of $32. The current stock price is $30 and over the next six months it is expected to rise to $36 or fall to $27. The riskfree interest rate is 6%. (i) What is the risk-neutral probability of the stock rising to $36? …………… (ii) What position in the stock is necessary to hedge a long position in 1 put option? ……………5

(iii) What is the value of the put option? ………… 26. (i) 0.435; (ii) Long position in 0.556 shares; (iii) 2.74; 2. 27. For a call option on a non-dividend-paying stock, the stock price is $30, the strike price is $29, the risk-free interest rate is 6% per annum, the volatility is 20% per annum and the time to maturity is three months. Expressed in terms of the cumulative normal function, N(x), (i) What is the price of the option? ……………………………………………. (ii) What is the price of the option if it is a put? ……………………………. 27. (i) 30N(0.5390)−28.57N(0.4390);(ii) 28.57N(−0.4390)−30N(−0.5390) 28. A portfolio of derivatives on a stock has a delta of 2400 and a gamma of −100. (i) What position in the stock would create a delta-neutral portfolio?..................... (ii) An option on the stock with a delta of 0.6 and a gamma of 0.04 can be traded. What position in the option and the stock creates a portfolio that is both gamma and delta neutral?................. 28. (i) Short 2,400; (ii) Long 2,500 options; Short 3,900 shares 29. The delta of a European call option on a non-dividend-paying stock is 0.6, its gamma is 0.04 and its vega is 0.1 (i) What is the delta of a European put option with the same strike price and time to maturity as the call option?.................... (ii) What is the gamma of a European put option with the same strike price and time to maturity as the call option?.................... (iii) What is the vega of a European put option with the same strike price and time to maturity as the call option?........................ 29(i) −0.4; (ii) 0.04; (iii) 0.1. 30. As time passes, the spot price and the futures price do not necessarily change by the same amount, a decrease in basis is referred to as? (a) strengthening b) improving (c) weakening (d) none of the above 30 (c)6