| | | 9.12% Question 4 What is the current spot price of gold if the lease rate on the contract is 1.25%, the risk-free rate is 3%, and the 9-month forward price is $1,000? | | | $986.96 | | | | $1,052.54 | | | | $964.37 | | | | $1,080.92 Question 5 A non-dividend paying stock is currently valued at $100. The option strike price is $100, the risk-free rate is 2%, and the stock volatility is 30%. Using 2 binomial periods, what is the 1-year call option price? | | | $10.47 | | | | $9.23 | | | | $12.89 | | | | $11.94 | | Question 6 Suppose we want to construct a duration-matched portfolio of two bonds. We have a long position in a 10-year, 6.5% annual coupon bond that yields 5.5% and has a duration of 7.9366 years. For each contract we are long, how many contracts do we have to short if the other bond is an 18-year, 4.75% annual coupon bond that yields 10% and has a duration of 10.5104 years? (Hint: You must compute each bond price first) | | | -0.74 | | | | -0.81 | | | | -1.67 | | | | -1.49 Question 7 Suppose Samsung produces 800 phones and each requires 2 oz. of silver to produce. The standard deviation of the phone price is 0.15 and the standard deviation of the silver price is 0.55. The correlation between silver and the phone price is 0.65. One silver contract calls for delivery of 25 oz. of platinum. How many contracts are needed to minimize the variance of profit? Round to the nearest whole number. | | | 41 | | | | 23 | | | | 35 | | | | 58 Question 8 A non-dividend paying stock is currently valued at $100. The option strike price is $100, the risk-free rate is 2%, and the stock volatility is 30%. If there are 2 binomial periods, what is the delta of a 1-year call option at time 0 (today)? | | | 0.5784 | | | | -0.6596 | | | | 0.3878 | | | | -0.4563 Question 9 A non-dividend paying stock is currently trading for $100 and has a standard deviation of 0.10. The strike price on the 2-year call option is $120 and the continuous risk-free rate is 5%. How much borrowing (B) is needed with the purchase of delta shares assuming 1 binomial step? | | | -42.71 | | | | 42.71 | | | | -29.10 | | | | 29.10 Question 10 Consider a 5-year zero-coupon bond with a 5% yield to maturity. The bond price per $1,000 of face value is $862.61. What is the modified duration of this bond? | | | 4 years | | | | 4.85 years | | | | 5 years | | | | 4.76 years | Question 11 A non-dividend paying stock is currently trading at $50. Over the next year, its stock price can increase by 30% or decrease 20%. What is the value of lending amount (B) with strike price equal to $60 if the continuous risk-free rate is 2% and assuming 1 binomial step? | | | -50.97 | | | | 42.38 | | | | 50.97 | | | | -42.38 Question 12 A non-dividend paying stock is currently trading at $40. The 6-month call option has a strike price of $38. If the stock has a standard deviation of 0.15 and the continuous risk-free rate is 4%, what is the elasticity of the call option? | | | 6.33 | | | | 9.17 | | | | 12.65 | | | | 5.90 Question 13 The price of a 3-year zero coupon government bond is 85.16. The price of a similar 4-year bond is 79.81. What is the yield to maturity (effective annual yield) on the 4-year bond? | | | 4.6% | | | | 5.5% | | | | 5.8% | | | | 6.7% Question 14 Consider a bond that makes semiannual coupon payments. The bond is an 8% coupon with 6 years to maturity, a price of $95.44 per $100 of face value, and yield of 9%. What is the conversion factor of this bond? | | | 1.0436 | | | | 1.0995 | | | | 1.0691 | | | | 1.0801 Question 15 If a stock price increases from $63 to $65 and the price of a call option with a delta of 0.60 (gamma of 0.05) is $4.30 (at $63), then what is the approximate price of the call option after the stock price increase using only a delta approximation? | | | $4.90 | | | | $3.70 | | | | $5.50 | | | | $5.90 Question 16 A long position in a T-note contract is an obligation to buy a 6% bond with between 6.5 and 10 years to maturity. True False Question 17 A non-dividend paying stock currently sells for $125.00. A 12-month call option with a strike of $130.00 has a premium of $4.00. Assuming a 5% continuously compounded risk-free rate, what is the price of the associated put option? | | | $2.66 | | | | $3.17 | | | | $1.04 | | | | $3.53 Question 18 A non-dividend paying stock is currently trading at $50. Over the next year, its stock price can increase by 30% or decrease 20%. What is the delta of a put option on this stock with strike price equal to $60 if the continuous risk-free rate is 2% and assuming 1 binomial step? | | | 0.50 | | | | -0.80 | | | | -0.50 | | | | -0.65 Question 19 What is the current spot price of gold if the lease rate on the contract is 2.25%, the risk-free rate is 4.5%, and the 1-year forward price is $950? | | | $1,014.63 | | | | $928.86 | | | | $1,052.54 | | | | $880.92 Question 20 The Black-Scholes option price is the binomial option price as the number of binomial steps approaches infinity for a given fixed time to expiration. True False Question 21 Which of the following statements is false? | | | American options are at least as valuable as European options. | | | | All else equal, a 2-year American call option is at least as valuable as a 1-year American call option. | | | | A call with a lower strike price is at least as valuable as a call with a higher strike price. | | | | A put with a lower strike price is at least as valuable as a put with a higher strike price. Question 22 A non-dividend paying stock is currently trading at $50. Over the next year, its stock price can increase by 30% or decrease 20%. What is the value of a put option on this stock with strike price equal to $60 if the continuous risk-free rate is 2% and assuming 1 binomial step? | | | $8.41 | | | | $12.33 | | | | $10.97 | | | | $9.07 Question 23 If a stock price increases from $63 to $63.80 and the price of a call option with a delta of 0.50 (gamma of 0.04) is $2.30 (at $63), then what is the approximate price of the call option after the stock price increase using a delta-gamma approximation? | | | $2.71 | | | | $3.70 | | | | $1.96 | | | | $2.25 Question 24 The S&P 500 Index is priced at $1800. The annualized dividend yield on the index is 2.40%. The continuously compounded annual risk-free interest rate is 4.40%. What is the price of a forward contract that expires 9 months from today? | | | $1,937.48 | | | | $1,942.66 | | | | $1,827.20 | | | | $1,801.69 Question 25 A non-dividend paying stock is currently trading at $40. The 6-month call option has a strike price of $38. If the stock has a standard deviation of 0.15 and the continuous risk-free rate is 4%, what is the Black-Scholes call option price? | | | $2.71 | | | | $5.46 | | | | $4.68 | | | | $3.36 Question 26 A non-dividend paying stock is currently trading for $100 and has a standard deviation of 0.10. The strike price on the 2-year call option is $120 and the continuous risk-free rate is 5%. What is the price today of the 2-year call option assuming 1 binomial step? | | | $3.06 | | | | $3.96 | | | | $6.14 | | | | $5.60 Question 27 The 1-year and 2-year forward prices for platinum are $900/oz and $920/oz, respectively. A firm recently purchased a small platinum mine for $1,200 and they expect the mine to produce 1 ounce of platinum each year for 2 years. The marginal cost of operating the mine is $75/oz. If the risk-free rate is 5%, what is the net present value of this mine? | | | $349.35 | | | | $1,549.35 | | | | $502.17 | | | | $749.35 Question 28 The prices of 1, 2, 3, and 4-year zero coupon government bonds are 95.42, 90.36, 85.16, and 78.81, respectively. What is the par coupon on a 3-year coupon bond selling at par? | | | 5.02% | | | | 5.48% | | | | 5.81% | | | | 6.06% Question 29 Given a 12-year, zero-coupon bond with a face value of $100, what is the bonds Macaulay duration if the yield to maturity is 6.5%? Question 30 Consider a 5-year zero-coupon bond with a 3% yield to maturity. The bond price per $1,000 of face value is $862.61. What is the price value of a basis point for this bond? | | | -$0.1943 | | | | -$0.4187 | | | | -$0.2765 | | | | -$0.3433 | | | | | | | | | | | | | | | | | | | | | |
