# 19 Questions on Derivatives

For each of the following 8 statements determine if it is true, false or uncertain. You must justify your answer with a one-sentence explanation.

1. The beta of a hedge fund is usually close to one.

2. Suppose you hold a share of stock and a put option on that share. If the stock price is below the exercise price when the option expires the value of your position is the value of the stock.

3. There is a much greater outstanding volume of futures contracts as opposed to forward contracts because futures contracts are much more flexible in terms of settlement dates, amounts, etc.

4. The CAPM (Capital Asset Pricing Model) would be an accurate way to estimate the cost of equity for a company like Federal Express.

5. Assume that all investors are risk averse and select portfolios based on mean and variance. Then the highest return portfolio is always on the efficient frontier.

6. It is easier to earn "abnormal returns," i.e., returns greater than what investments of similar risk earn, by investing in financial rather than real assets.

7. If the price of a stock has gone up for ten consecutive trading days then on the eleventh day we would expect its price to decline.

Assume that we have the following monthly return data on 2 U.S. equity mutual funds. Assume the riskless return is 0.4% per month and the SPX return was 1.4% and its standard deviation was 3.0% per month over this period. You must show your computation to get any credit for your answer.

Fund A Fund B

Realized return 0.012 0.015

Standard deviation of return 0.06 0.08

Beta 1.5 2

8. Give an example of an options position that increases in value as the time to maturity decreases.

9. If interest rates rise, the convexity of a puttable bond will increase ______ an otherwise equivalent non-puttable bond.

a. more than

b. the same as

c. less than

d. actually the convexity will decrease

10. Assume you are short 2 futures contracts for 100 ounces of gold with initial margin of $2,000 each; maintenance margin is $1,500 per contract. Assume the price is initially $500 per ounce. If the price at the end of day 1 is $495 and $493 on day 2, how much money do you have in your margin account (assuming no withdrawals and assuming you make all margin calls) at the start of day 3?

11. Which of the asset A or B has the higher volatility? Both calls have one year to expiration and the riskless rate is 3%.

Option Exercise price Stock price Option price

Call on asset A 95 100 13.7

Call on asset B 60 50 6.10

12. Briefly explain why you think the Palm/3COM story is relevant to the study of financial markets.

13. The following diagram shows the beta calculation for a given firm using weekly data. What can you say about its performance over the time period represented by these data? Why?

The diagram below plots the value of a put option with an exercise price of $100 and one year to maturity.

14. Draw the value of a put option on the same security as in the previous question with an exercise price of $100 and 6 months to maturity.

For each of the following 3 questions determine whether or not an arbitrage opportunity exists. If one exists, describe how you could exploit this arbitrage. All options are written on the same underlying stock, which has a current price of $100 with annual standard deviation of return = .3. The riskless return is 4%.

15. Call with exercise price of 100 costs $20; Call with exercise price of 110 costs $13; Call with exercise price of 120 costs $5. All three options have a one-year maturity.

16. Call with a one-year maturity and an exercise price of 100 costs $20; put with a 2-year maturity and an exercise price of 100 costs $16.

17. The current one-year riskless rate in the U.S. is .05 and the current one-year riskless rate in Canada is .04. The spot rate shows that a Canadian dollar is 0.846 US$. The 6-month forward rate for converting Canadian to US dollars is 0.88.

18. Data have shown that the implied volatility of SPX puts is higher than the historical volatility of the SPX. How could you take advantage of this phenomenon?

19. Suppose you enter into a floating to fixed swap (i.e., you want to have certainty in your interest payments). The current swap rate for a 3-year maturity is LIBOR for 4.9% fixed. Assume that you are borrowing $10 million at LIBOR. Assume the swap payments are made annually. If at the end of year 1 LIBOR is 4.0%, how much do you pay to (or receive from) the swap counterparty?

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#### Solution Summary

Answers to 19 Questions on Derivatives dealing with beta of a hedge fund, put option, CAPM, Capital Asset Pricing Model, investors, risk averse, portfolios, mean, variance, highest return portfolio, efficient frontier, abnormal returns, equity mutual funds, riskless return, options position, time to maturity, interest rates, convexity of a puttable bond, futures contracts, gold, initial margin, margin calls, volatility, Palm, 3COM, financial markets, beta calculation, value of a put option, exercise price, maturity, arbitrage opportunity, riskless return, call, 6-month forward rate, Canadian dollars, US dollars, implied volatility, historical volatility, SPX, floating to fixed swap, LIBOR, swap counterparty.

What is the arbitrage profit? Which of the following is NOT true? All of the following are types of traders in futures, forward, and options markets EXCEPT: What is the futures price above which there will be a margin call? What hedge ratio should be used when hedging a one month exposure to the price of commodity A? What position should the fund manager take to hedge exposure to the market over the next two months?

Question 1: The price of gold is currently $700 per ounce. Forward contracts are available to buy or sell gold at $900 for delivery in one year. An arbitrageur can borrow money at 10% per annum. What is the arbitrage profit?

Question 2: A trader enters into a one-year short forward contract to sell an asset for $60 when the spot price is $58. The spot price in one year turns out to be $63. What is the trader's gain or loss?

Question 3: Which of the following is NOT true?

a. When a CBOE option on IBM is exercised, IBM issues more stock.

b. An American option can be exercised at any time during its life.

c. A call option will always be exercised at maturity if the underlying asset price is greater than the strike price.

d. A put option will always be exercised at maturity if the strike price is greater than the underlying asset price.

e. All of the above are true.

Question 4: Which of the following is NOT true?

a. When a CBOE option on IBM is exercised, IBM issues more stock.

b. An American option can be exercised at any time during its life.

c. A call option will always be exercised at maturity if the underlying asset price is greater than the strike price.

d. A put option will always be exercised at maturity if the strike price is greater than the underlying asset price.

e. All of the above are true.

Question 5: A trader buys 100 European call options (one contract) 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 turns out to be $25 in one year. What is the trader's gain or loss?

Question 6: It is May and a trader writes a September European call option with a strike price of $20. The stock price is currently $18 and the option price is $2. In September, the stock price becomes $25. What is this trader's cash flow from the option in September?

Question 7: All of the following are types of traders in futures, forward, and options markets EXCEPT:

a. hedgers

b. speculators

c. hackers

d. arbitrageurs

e. All of the above are trader types

Question 8: Which of the following is true?

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 forward contracts nor futures contracts are traded on exchanges.

Question 9: Which of the following is NOT true?

a. Forward contracts always have zero values.

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 for futures contracts.

d. Forward contracts usually have one specified delivery date; futures contracts often have a range of delivery dates.

e. All of the above are true.

Question 10: 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?

Question 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 changes in 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?

Question 12: A fund manager has a portfolio worth $100 million with a beta of 1.20. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on the S&P 500 to hedge the risk. The current index level is 850 and one futures contract is on 250 times the index (i.e., the index multiplier is 250). The risk-free rate is 6.0% per annum and the dividend yield on the index is 3.0% per annum. The current three-month futures price is 852.34. What position should the fund manager take to hedge exposure to the market over the next two months?

Question 13: An interest rate is 15% per annum when expressed with quarterly compounding. What is the equivalent rate with continuous compounding?

Question 14: An interest rate is 8% per annum expressed with continuous compounding. What is the equivalent rate with semiannual compounding?

Question 15: The 6-month, 12-month, 18-month, and 24-month zero rates are 3%, 3.5%, 3.75%, and 4% with semi-annual compounding. What is the continuous compounding forward rate for the six-month period beginning in 12 months (i.e., F12,18)?

Question 16: 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?

Question 17: The spot price of an investment asset is $30 and the risk-free rate for all maturities (with continuous compounding) is 10%. The asset provides $2 income at the end of the first year. What is the three year forward price?

Question 18: The spot price of an investment asset is $30 and the risk-free rate for all maturities (with continuous compounding) is 10%. The asset provides a 4% continuous yield. What is the three year forward price?

Question 19: An exchange rate is 0.800 and the 2-month domestic risk free interest rate is 5%. The 2-month foreign interest rate is 2% (both rates are continuously compounded). What is the two month forward rate?

Question 20: Which of the following is a consumption asset?

a.The S&P 500 Index

b.The Canadian Dollar

c. Copper

d. IBM Shares

e. None of the above

Question 21: A five-year bond with a yield of 9% (continuously compounded) pays an 8% coupon at the end of each year. What is the duration of the bond?

Question 22: Suppose you enter into an interest rate swap where you are receiving floating and paying fixed. Which of the following is true?

a) Your credit risk is greater when the term structure is upward sloping than when it is downward sloping.

b) Your credit risk is greater when the term structure is downward sloping than when it is upward sloping.

c) Your credit risk exposure increases when interest rates decline unexpectedly.

d) Your credit risk exposure increases when interest rates increase unexpectedly.

Question 23: A trader writes two naked put option contracts. The option price is $3, the strike price is $40 and the stock price is $42. What is the original margin?

Question 24: It is January 15, 2009. The quoted price of a T-bond with a 12% coupon that matures on October 15, 2020, is 102-07. What is the cash price?

Question 25: Suppose Microsoft is paying LIBOR + 1% per annum to its lenders. If Microsoft enters into a interest rate swap with Intel to receive LIBOR and pay fixed 3.9%, what will be the net effect to Microsoft's payment?

Question 26: The current price of a stock is $94, and three-month European call options with a strike price of $95 currently sell for $4.70. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options (20 contracts). Both strategies involve an investment of $9,400. How high does the stock price have to rise for the option strategy to be more profitable?

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See attached file.