Extra Questions and Answers_NEW.doc

EXTRA PROBLEMS New to 8th Edition 1. In July, a small chocolate factory receives a large order for chocolate bars to be delivered in November. The spot price for Cocoa is $2,400 per metric ton. It will need 10 metric tons of Cocoa in September to fill this order. Because of limited storage capacity and volatility in the world cocoa prices, the company decides the best strategy is to buy 10 call options for $53 each with strike price of $2,400 (equal to the current price) with a maturity date of September 2012. When the options expire in September, how much will the company pay (including the cost of the options) for cocoa if the spot price in September proves to be: a) $2,300, and b) $2,600? ($23,530, $24,530) 2. A trader invests in Facebook by buying 1000 shares in June for $27 per share. She also buys 1000 put options for $5 each as insurance in case the stock drops sharply. The put options have a strike price of $27 and a maturity date of December. What is the gain or loss if the spot price on December is: a) $20, b) $27, c) $32 and d) $37? ($5,000 loss, $5,000 loss, $0, $5,000 gain) 3. The spot price for Google stock is $578 on June 6. A trader considers two alternatives: buy 100 shares of the stock, or buy 100 European call options on Google for $38 each with a strike price of $575 and maturity date of September 2012. For each alternative, what is: a) the upfront cost? b) the total gain if the stock price at maturity is $650? c) the total loss if the stock price is $500 at maturity? ($57,800 and $3,800; $7,200 and $3,700; -$7,800 and -$3,800) 4. A trader takes the long position and a hedge fund takes a short position on ten 1-month S&P 500 futures contracts at 1300. A single S&P 500 futures contract equals ($250) x (Index Value). The initial margin is $325,000 and the maintenance margin is $245,000 for both accounts. Ten trading days later, the futures price of the index drops to 1,260 triggering a margin call for the trader. What is the change margin account balance (indicate gain or loss) for: a) the trader and b) the hedge fund? What is the margin call for the trader? (trader: $100,000 loss, hedge fund: $100,000 gain, margin call: $100,000) 5. A speculator sells a July 2013 wheat futures contract at 721 cents per bushel. Each futures contract is for 5,000 bushels. The futures price drops to 676 on December 31, 2012 and rises to 712 in May 2013 when she closes the contract. What is the gain or loss for accounting purposes in 2013? ($180,000 loss) 6. In December 2011, a company expects to buy 100,000 MMBtu of natural gas before the end of March 2012, but does not know exactly when. To hedge against volatile gas prices, it implements a rolling forward hedge by taking a long position on 10 two-month natural gas futures (only held for 1 month). One futures contract is for 10,000 MMBtu and is quoted in $ per MMBtu. The commodity is purchased in March 2012. What is total dollar gain/loss from the rolling hedge? Assume a hedge ratio of 0.8. ($84,000 loss) Date Dec 2011 Jan 2012 Feb 2012 Mar 2012 Feb 2012 Futures Price 3.65 3.00 - - Mar 2012 Futures Price - 2.95 2.70 - Apr 2012 Futures Price - - 2.65 2.50 Spot Price 3.67 2.50 7. A trader owns 55,000 troy oz of silver and decides to hedge with 6-month silver futures contracts. Each futures contract is on 5,000 troy oz. The standard deviation of the change in the spot price of silver is 0.43. The standard deviation of the change in silver futures prices is 0.40. The coefficient of correlation between the two is 0.95. a. What is the minimum variance hedge ratio? b. What is the optimal number of futures contracts without tailing the hedge? c. What is the optimal number of futures contracts with tailing the hedge? (1.02, 11.23, 12.08) 8. For an interest rate compounded annually of 7%, what is the equivalent interest rate compounded: (6.88%, 6.82%, 6.78%, 6.77%, 6.77%) a. Semi-annually b. Quarterly c. Monthly d. Weekly e. Daily 9. Given the zero rates and cash flows for a bond (see table below): a. What is the theoretical price? ($986.23) b. What is the bond yield? (3.19%) Maturity(Years) Treasury Zero Rates (%) Coupon Payments Principal 0.5 2.0% $10 - 1.0 2.3% $15 - 1.5 2.7% $10 - 2.0 3.2% $15 $1000 10. A stock provides a dividend yield of 5.0% paid semi-annually (equivalent to 4.94% continuously compounded). The spot price of the stock is currently $500, and the risk-free rate is 7.5% with continuous compounding. a. What is the two-year forward price for a stock? ($526.27) b. What is the continuously compounded cost of carry for the stock? (2.56%) 11. A US investor sees an arbitrage opportunity in the currency markets. The spot exchange rate between the Swiss Franc and US Dollar is 1.0404 ($ per CHF). Assume the continuously compounded interest rates in the US and Switzerland are 0.25% and 0%, respectively. The 3-month currency forward price is 1.0300 ($ per CHF). What is the theoretically correct forward price. What is the investor’s total profit (in CHF), assuming she begins by borrowing 1,000 CHF? (1.04105, 10.73) 12. Continuously compounded LIBOR rates per annum for 6, 12, and 18-months are given in the table below. The 2-year swap rate is 3% per annum with payments made semi-annually. What is the 2-year LIBOR/swap zero rate for 2 years? Use LIBOR discounting (2.99%) Maturity (Years) LIBOR/Swap Zero Rates (%) 0.5 2.0% 1.0 2.4% 1.5 2.6% 2.0 ? 13. Consider a currency swap with 3 years remaining. A financial institution receives 3.0% per annum in sterling (GBP) and pays 1.5% per annum in dollars once a year. The LIBOR/swap interest rate with continuous compounding is flat in both countries. The British rate is 2.5% per annum and the US rate is 2.0% per annum. The principal amounts are £10 million pounds and $15 million dollars, and the current exchange rate is $1.5 = £1. By valuing the currency swap as fixed-rate bonds, what is: a. The value of the dollar bond in $? ($14.78 Million) b. The value of the sterling bond in £? (£10.13 Million) c. The value of the currency swap in $? ($0.4255 Million) 14. Given the ABS & ABS CDO shown, what is the minimum loss on the portfolio of underlying assets when a. Lower two ABS tranches have a 100% loss of principal? (30%) b. Senior ABS tranche a 50% has loss of principal? (65%) c. Equity ABS CDO tranche has a 100% loss of principal? (6.25%) d. Mezzanine ABS CDO tranche has a 100% loss of principal? (12.5%) e. Senior ABS CDO tranche has a 50% loss of principal? (21.25%) f. Senior ABS CDO tranche has a 100% loss of principal? (30%) ABS Senior Tranche (70%) AAA ABS Equity Tranche (5%) Not Rated ABS CDO Senior Tranche (70%) AAA ABS CDO Mezzanine Tranche (25%) BBB ABS CDO Equity Tranche (5%) Not Rated Assets ABS Mezzanine Tranche (25%) BBB 15. An investor buys 5 call option contracts, each on 100 shares with a strike of 60. There is a 6-for-5 stock split. Give the following: a. The new strike price (50) b. The new number of shares underlying the 5 contracts (600) 16. The price of a European call and put on a stock are $2 and $5, respectively. Both have a strike price of $45 and an expiration date of 6 months. The current price of the underlying non-dividend-paying stock is $40? What is the implied risk-free interest rate? (9.09%) 17. An investor creates a butterfly spread by trading 9-month call options with strike prices of $115, $125, and $135. The prices of the options are $20.50, $14.50, and $9.50, respectively. (Note: Total payoff does not include initial investment) a. What is the initial investment? ($1 paid out) b. What is the total payoff when the stock price in 9 months is 110? ($0) c. What is the total payoff when the stock price in 9 months is 120? ($5) d. What is the total payoff when the stock price in 9 months is 125? ($10) e. What is the total payoff when the stock price in 9 months is 128? ($7) f. What is the total payoff when the stock price in 9 months is 140? ($0) 18. A 1-year option is offered on a non-dividend-paying stock. The stock price is $85. The exercise price of the option is $90 and the volatility is 18% per annum. The continuously compounded risk-free rate is 6% per annum. When the Black-Scholes-Merton model is used a. What is the value of d1? (0.106) b. What is the value of d2? (-0.074) c. What is the price of a call option, c? ($6.21) d. What is the price of a put option, p? ($5.97) Now, assume that the stock pays a dividend after 3-months and 9-months of $1.50. e. What is the present value of the dividends? ($2.91) f. What is the new value of d1 with dividends (-0.088) g. What is the new value of d2 with dividends (-0.268) h. What is the value of a call option? ($4.74) 19. Discuss the pros and cons of executive stock options versus paying executives directly with stock. 20. A two-step binomial tree is used to value an option on the Australian dollar. The strike price is 1.00 USD per AUD and the expiration date is in 6 months. Each step is 3 months. The current price of one AUD is 1.04 USD. The US risk free rate is 2.0%, and the AUD risk-free rate is 2.5%. The exchange rate has a volatility of 6% per annum. a. What is the proportional up movement, u, for the currency (1.0305) b. What is the probability of an up movement, p? (0.4717) c. What is the price of an American call option on the currency? ($0.0427) 21. The spot price of an index is 250. The dividend yield on the index is 3% per annum. The risk free rate is 4%. If price of a 3-month European call option is $16 when the strike price is 240, what is the implied volatility per annum? (20.4%) 22. Use Black’s model to value a European put option on the spot price of a commodity when the strike price is $30 and the expiration is in 12 months. The current futures price of commodity for a contract lasting 12 months is $35. The risk free rate is 5% per annum and the volatility is 25%. ($1.26) 23. A trader decides to hedge her portfolio against large market moves by taking positions in the underlying asset and two options (see table below). a. How many units of options 1 and 2, respectively, are needed to make the portfolio gamma and vega neutral? (300, -25) b. How many units of the underlying asset are needed to make the hedged portfolio delta neutral (indicate long/short position)? (11 long)   Delta Gamma Vega Portfolio 0.50 -1000 -500 Option 1 -0.03 10 2.5 Option 2 0.10 80 10 24. A trader decides to protect her portfolio with a put option. The portfolio is worth $150 million and the required put option has a strike price of $145 million with a maturity of 24 weeks. The volatility of the portfolio is 15% and the dividend yield on the portfolio is 3% per annum. The risk-free rate is 4%. Because the option is not available on exchanges, the trader decides to create an option by maintaining a position in the underlying portfolio with the required delta. What percentage of the original portfolio should be sold and invested at the risk-free rate: a. Initially at time zero? (sell 32.9%) b. After one week, when value is $145 million? (sell an additional 12.7%) c. After two weeks when value is $148 million? (buy back 7.99%) 25. A Cox-Ross-Rubinstein binomial tree is used to value an option on the Dow Jones Industrial Average (DJIA) index. The dividend yield is 3% per annum, the index volatility is 14% per annum, the time step is 2 months, and the risk-free interest rate is 5% per annum. What is the probability of an up move? (0.5149)