Suppose you own 50,000 shares of stock valued at $35.50 per share. You are interested in protecting it with a put that would have a delta of 0.62. Assume however, that the put is not available or is unfairly priced. Illustrate how to construct a dynamic hedge using a risk-free debt instrument that would replicate the position of having the put. Ignore the cost of the puts. Show how the hedge works by explaining what happens if the stock falls by one dollar.
> Suppose you buy a stock index futures contract at the opening price of 452.25 on July 1. The multiplier on the contract is 500, so the price is $500 452 25 $226,125 You hold the position until selling it on July 16 at the opening price of 435.50. The ini
> An option dealer needs to finance the purchase of a security and holds an inventory of U.S. Treasury bills. Explain how the dealer can use the repo market for financing the security purchase?
> A short stock can be protected by selling a put. Determine the profit equations for this position and identify the breakeven stock price at expiration and maximum and minimum profits.
> Contrast dollar return and percentage return. Be sure to identify which return is more useful when comparing investments.
> Assume that you have an opportunity to visit a civilization in outer space. Its society is at roughly the same stage of development as the U.S. society is now. Its economic system is virtually identical to that of the United States, but derivative tradin
> Using an example, compare and contrast physical delivery and cash settlement.
> Why is speculation controversial? How does it differ from gambling?
> What are daily price limits and how are they used by futures exchanges?
> Give an example of an in-the-money call and put and an out-of-the-money call and put.
> What is storage? Why is it risky? What role does it play in the economy?
> Suppose you are shopping for a new automobile. You find the same car at two dealers but at different prices. Is the law of one price being violated? Why or why not?
> Define arbitrage and the law of one price. What role do they play in the U.S. market system? What do we call the “one price” of an asset?
> Explain the differences among the three means of terminating a futures contract: an offsetting trade, cash settlement, and delivery?
> A short position in stock can be protected by holding a call option. Determine the profit equations for this position and identify the breakeven stock price at expiration and maximum and minimum profits.
> Repeat problem 10, but close the position on August 1. Use the spreadsheet to find the profits for the possible stock prices on August 1. Generate a graph and use it to identify the approximate breakeven stock price.
> What is an efficient market? Why do efficient markets benefit society?
> Consider a call option on an asset with an exercise price of $100, a put option on that same asset with an exercise price of $100, and a forward contract on the asset with an exercise price of $100, all expiring at the same time. Assume that at the expir
> What responsibilities does senior management assume in a risk management system?
> What is the purpose of risk management industry standards?
> Summarize in one sentence how each of the following organizations failed to practice risk management: a. Metallgesellschaft b. Orange County c. Barings d. Procter & Gamble
> Describe the primary differences between accounting for fair value hedges and accounting for cash flow hedges.
> Explain how an organization determines whether a hedge is sufficiently effective to justify hedge accounting.
> Why is hedge accounting used, and how can it be misused?
> Explain how cash flow hedge accounting is applied in principle. Specifically, identify how this accounting treatment is different from the typical way cash flow transactions accounting is handled.
> Explain why the traditional auditing function cannot serve as the risk management function.
> We briefly mentioned the synthetic call, which consists of stock and an equal number of puts. Assume that the combined value of the puts and stock exceeds the value of the actual call by less than the present value of the exercise price. Show how an arbi
> Explain the basic differences between open outcry and electronic trading systems.
> Explain the accounting of hedging currency translation of a firm’s foreign subsidiary.
> ACB, Inc., engages in a forward transaction and is applying fair value hedge accounting. ACB holds the underlying instrument and hedges it by selling this forward contract. During the hedge period, the underlying instrument increases in value by $250,000
> Define and explain what is meant by independent risk monitoring. How can senior management improve independent risk monitoring?
> Explain the advantages for senior management having detailed written policies for financial risk management.
> Suppose that a firm plan to purchase an asset at a future date. The forward price of the asset is $200,000. It hedges that purchase by buying a forward contract at a price of $205,000. During the hedging period, the forward contract incurs a paper loss o
> Suppose that a firm engages in a derivative transaction that qualifies for fair value hedging. The firm holds a security and hedges it by selling a derivative. During the course of the hedge, the security increases in value by $20,000, whereas the deriva
> Identify and discuss five problems with regard to the application of FAS 133.
> One responsibility of senior management is to identify acceptable risk management strategies. Identify three categories of risk, focusing on broad classifications and not on specific types of risks.
> Briefly explain how speculative derivatives transactions are treated from an accounting perspective.
> You have inherited some stock from a wealthy relative. The stock had poor performance recently, and analysts believe it has little growth potential. You would like to write calls against the stock; however, the will stipulates that you must agree not to
> Distinguish between the front office and the back office of a derivatives dealer. Explain why it is important to keep the front and back offices separate.
> What is the difference between an initial margin and a maintenance margin? What is the variation margin?
> Compare and contrast view-driven risk management with needs-driven risk management.
> Identify and discuss benefits for managing financial risks.
> How does the legal system impose risk on a derivatives dealer?
> Explain how closeout netting reduces the credit risk for two firms engaged in several derivatives contracts?
> Comment on the current credit risk assumed for each of the following positions. Treat them separately, that is, not combined with any other instruments. a. You are short an out-of-the-money interest rate call option. b. You entered into a pay-fixed, re
> Critique each of the three methods of calculating value at risk, giving one advantage and one disadvantage of each.
> A company has assets with a market value of $100. It has one outstanding bond issue, a zero coupon bond maturing in two years with a face value of $75. The risk-free rate is 5 percent. The volatility of the asset is 0.30. Determine the market value of th
> Suppose you enter into a bet with someone in which you pay $5 up front and are allowed to throw a pair of dice. You receive a payoff equal to the total in dollars of the numbers on the two dice. In other words, if you roll a 1 and a 2, your payoff is $3
> Suppose an investor is considering buying one of two call options on a particular stock with the same maturity. The only difference between the two call options is the strike prices. The rate of return on a call option is its profit divided by the invest
> Company CPN and dealer Swap Fin are engaged in three transactions with each other. From Swap Fin’s perspective, the market values are as follows: Explain the consequences to SwapFin if CPN defaults with and without closeout netting. In
> How can one make a profit from a transaction in light of the bid–ask spread, assuming the spread remains constant?
> Identify and explain four forms of netting.
> The following table lists three financial instruments and their deltas, gammas, and vegas for each $1 million notional amount under the assumption of a long position. (Long in a swap or FRA means to pay fixed and receive floating.) Assume that you hold a
> Calculate the VAR for the following situations: a. Use the analytical method and determine the VAR at a probability of 0.05 for a portfolio in which the standard deviation of annual returns is $2.5 million. Assume an expected return of $0.0. b. Use the
> Consider a portfolio consisting of $10 million invested in the S&P 500 and $7.5 million invested in U.S. Treasury bonds. The S&P 500has an expected return of 14 percent and a standard deviation of 16 percent. The Treasury bonds have an expected return of
> Suppose the periodic payments made by a CDS buyer to a CDS seller are worth $1 per $100 notional value of debt per quarter. Explain how this figure is related to the value of the debt and the value of an otherwise equivalent bond that is default free.
> Suppose your firm is a derivatives dealer that has recently created a new product. In addition to market and credit risk, what additional risks does it face that are associated more with new products?
> Identify the five types of credit derivatives and briefly describe how each works.
> Another consideration in evaluating option strategies is the effect of transaction costs. Suppose that purchases and sales of an option incur a brokerage commission of 1 percent of the option’s value. Purchases and sales of a share of stock incur a broke
> Explain how the stockholders of a company hold an implicit put option written by the creditors.
> Consider a firm that has assets that generate cash but which cannot be easily valued on a regular basis. What are the difficulties faced by this firm when using VAR, and what alternatives would it have?
> Compare and contrast total return swaps, credit default swaps, and interest rate swaps.
> Referring to problem 15, suppose transaction costs amounted to 0.5 percent of the value of the stock index. Explain how these costs would affect the profitability and the incidence of index arbitrage. Then calculate the range of possible futures prices w
> Identify and explain the primary methods of managing credit risk for derivatives dealers.
> Determine the prices of lookback and modified lookback calls and puts. For the modified lookbacks, use an exercise price of 95.
> Determine the price of an average price Asian call option. Use an exercise price of 95. Count the current price in determining the average. Comment on whether you would expect a standard European call to have a lower or higher price.
> Use the information in problem 9 to set up a dynamic hedge using stock index futures Assume a multiplier of 500. The futures price is 496.29. The volatility is 17.5 percent. The continuously compounded risk-free rate is 3.6 percent, and the call delta is
> On July 5, a market index is at 492.54. You hold a portfolio that duplicates the index and is worth 20,500 times the index. You want to insure the portfolio at a particular value over the period until September 20. You can buy risk-free debt maturing on
> In modern financial derivatives markets, there are many exotic options. Briefly explain compound options, multi-asset options, shout options, and forward start options.
> Suppose the call price is $14.20 and the put price is $9.30 for stock options, where the exercise price is $100, the risk-free interest rate is 5 percent (continuously compounded), and the time to expiration is one year. Explain how you would create a sy
> Explain how weather derivatives could be used by an electric utility to manage the risk associated with power consumption as affected by the weather.
> Demonstrate that the payoffs of a chooser option with an exercise price of X and a time to expiration of T that permits the user to designate it as a call or a put at t can be replicated with two transactions. Specifically, by (1) buying a call with an e
> A convertible bond is a bond that permits the holder to turn in the bond and convert it into a certain number of shares of stock. Conversion would, thus, occur only when the stock does well. As a result of the option to convert the bond to stock, the cou
> Suppose you are asked to assist in the design of an equity-linked security. The instrument is a five-year zero coupon bond with a guaranteed return of 1 percent, compounded annually. At the end of five years, the bond will pay an additional return based
> In this chapter, there are two equations presented for the implied repo rate related to the following bond futures contracts. Explain these equations and discuss the differences between them (1/T) ((CF)[fo(t) + AlT + Clo,r -1 and Bo + Al, CF(t)]fo(t)
> Contrast lookback options and barrier options and explain the difference between in- and out options.
> Derive the terminal stock price of a portfolio insurance strategy with put options such that the upside capture exactly equals 100 percent.
> Suppose an investor owns 1,000 shares of Pear, Inc., stock that is trading at $100 per share. Design a portfolio insurance strategy assuming a strike price of $100, time to maturity of one year, and a put price of $9.35 per share. Compute the number of p
> An investment manager expects a stock to be quite volatile and is considering the purchase of either a straddle or a chooser option. The stock is priced at 44, the exercise price is 40, the continuously compounded risk-free rate is 5.2 percent, and the v
> Consider a ten-year, fixed-rate mortgage of $500,000 that has an interest rate of 12 percent. For simplification, assume that payments are made annually. a. Determine the amortization schedule. b. Using your answer in part a, determine the value of bot
> Using BlackScholesMertonBinomial10e.xlsm, compute the call and put prices for a stock option, where the current stock price is $100, the exercise price is $100, the risk-free interest rate is 5 percent (continuously compounded), the volatility is 30 perc
> A stock is priced at 125.37, the continuously compounded risk-free rate is 4.4 percent, and the volatility is 21 percent. There are no dividends. Answer the following questions. a. Determine a fair price for a two-year asset-or-nothing option with exerc
> Consider a stock priced at 100 with a volatility of 25 percent. The continuously compounded risk-free rate is 5 percent. Answer the following questions about various options, all of which have an original maturity of one year. a. Find the premium on an a
> A portfolio manager is interested in purchasing an instrument with a call option-like payoff but does not want to have to pay money up front. The manager learns from a banker that one can do this by entering into a break forward contract. The manager wan
> Determine the prices of the following barrier options. a. A down-and-out call with the barrier at 90 and the exercise price at 95. b. An up-and-out put with the barrier at 110 and the exercise price at 105. c. Select any other barrier option but base
> Explain the advantages and disadvantages of implementing portfolio insurance using stock and puts in comparison to using a fiduciary call.
> Assume that on December 2, YY, the cheapest bond to deliver was the 6 1/4s maturing on August 15, YY 18. The March contract is priced at 112, and the conversion factor is 1.0269. The June futures price is 111.75. The conversion factor for the 6 1/4s deli
> Suppose a firm plan to borrow $5 million in 180 days. The loan will be taken out at whatever LIBOR is on the day the loan begins and will be repaid in one lump sum90 days later. The firm would like to lock in the rate it pays, so it enters into a forward
> Suppose you work on an interest rate derivatives trading desk and observe the following market quotes. Long (short) $100,000,000 interest rate cap, 90/360-day count, 4 percent strike rate priced at $4,950,000 ($4,925,000). Long (short) $100,000,000 inter
> Suppose you are long a 180-day LIBOR-based FRA (receive floating) with notional amount of $50,000,000. At expiration, LIBOR is 4 percent and the strike rate (the agreed-upon rate) is 3 percent. Assuming a 360-day year, what is the dollar profit or loss o
> Suppose you are long a 90-day LIBOR-based FRA (receive floating) with notional amount of $50,000,000. At expiration, LIBOR is 4 percent and the strike rate (the agreed-upon rate) is 3 percent. Assuming a 360-day year, what is the dollar profit or loss on
> The Black–Scholes–Merton option pricing model assumes that stock price changes are log normally distributed. Show graphically how this distribution changes when an investor is long the stock and long the put.
> Explain how a forward swap is like a swaption and how it is different.
> Explain how a bank could use a swaption to hedge the possibility that it will enter into a pay floating, receive-fixed swap at a later date.
> Explain how the two types of swaptions are like interest rate options and how they are different.
> Consider a call option with an exercise rate of x on an interest rate, which we shall denote as simply L. The underlying rate is an M-day rate and pays off based on 360 days in a year. Now consider a put option on a $1 face value zero coupon bond that pa
> A firm has previously issued fixed-rate nonsalable debt. Because interest rates are perceived to be temporarily high, the firm would like to have the flexibility of calling the debt later when rates are expected to fall and replacing it with floating rat
> Suppose your firm had issued a 12 percent annual coupon, 15-year bond, callable at par at the eighth year. It is now two years later, so the bonds are not callable for another six years. At this time, new bonds could be issued at 8 percent, which is hist
> Explain the impact on the implied repo rate of changing from the bid to the offer futures price, of the longer-dated futures contract.
> Explain how a swaption can be terminated at expiration by either exercising it or settling it in cash. Why are these procedures financially equivalent?
> A company wants to enter into a commitment to initiate a swap in 90 days. The swap would consist of four payments 90 days apart with the underlying being LIBOR. Use the following term structure of LIBOR to solve for the rate on this forward swap Term
