Chapter 9 Derivatives: Futures, Options, and Swaps Conceptual and Analytical Problems An agreement to lease a car can be thought of as a set of derivative contracts. Describe them. Answer: When someone leases a car, he or she agrees to make a series of fixed monthly payments; this is like a forward contract. At the end of the lease, the lessee can purchase the car; this is like an option. How is entering into a forward contract similar to barter? Can you think of costs associated with forward contracts that are minimized or eliminated with futures contracts? Answer: As in barter, when you engage in a forward contract, you must establish a “double coincidence of wants;” that is, you must find someone who “has what you want and wants what you have.” While barter usually is an immediate trade of one item for another, in a forward contract you must also agree on the timing of the transaction. Compared to futures contracts, forward contracts also are illiquid and involve default risk that is reduced when a centralized clearinghouse is the counterparty. In spring 2002, an electronically traded futures contract on the stock index, called an E-mini future, was introduced. The contract was one-fifth the size of the standard futures contract, and could be traded on the 24 hour CME Globex electronic trading system. Why might someone introduce a futures contract with these properties? Answer: The size of the contract allows small investors to purchase it. The fact that the contracts can be traded 24 hours a day makes the contract more liquid and allows investors to speculate using current information from markets around the world. It also makes it more convenient for foreign investors to trade the contracts. A hedger buys a futures contract, taking a long position in the wheat futures market. What are the hedger’s obligations under this contract? Describe the risk that is hedged in this transaction and give an example of someone who might enter into such an arrangement. Answer: The hedger has taken the long position, promising to purchase the wheat at a fixed price on a future date. He is hedging against the risk that the price of wheat will rise. Someone who anticipates needing wheat in the future, such as a miller or a maker of breakfast cereals, might enter into such a transaction. A futures contract on a payment of $250 times the Standard and Poor’s’ 500 Index is traded on the Chicago Mercantile Exchange. At an index level of $1,000 or more, the contract calls for a payment of over $250,000. It is settled by a cash payment between the buyer and the seller. Who are the hedgers and who are the speculators in the S&P 500 futures market? Answer: Hedgers are investors who own funds composed of stocks from the S&P 500; they will sell futures contracts to hedge against the risk that the market falls. Speculators are trying to profit from movements in the market; they will sell futures if they expect the market to fall, and buy futures if they expect the market to rise. Explain why trading derivatives on centralized exchanges rather than in over-the-counter markets helps to reduce systemic risk. Answer: The presence of a centralized counterparty (CCP) increases transparency, as the CCP has the ability and the incentive to monitor whether a trader is taking a large position on one side of a trade. This reduces the vulnerability of the financial system to the weakness of any one participant. The CCP reduces its own risk through economies of scale. With large volumes of transactions on both sides of a trade, its net exposure is relatively small. The standardization of contracts traded through CCP also increases transparency while the practice of marking to market quickly exposes a counterparty’s inability to pay, allowing for a timely resolution of the problem and the avoidance of knock-on effects. What are the risks and rewards of writing and buying options? Are there any circumstances under which you would get involved? Why or why not? (Hint: Think of a case in which you own shares of the stock on which you are considering writing a call.) Answer: Because option buyers incur no obligations, their losses are limited to the price paid for the option. Their potential gains, however, can be large. Sellers must buy or sell the underlying asset at the strike price if the option is exercised, so their losses are unlimited. When writing a call option, the seller can lose money if the price of the underlying asset rises; however, if the seller owns the asset, then he or she is insured against these potential losses and issuing a call option is not very risky. Suppose XYZ Corporation's stock price rises or falls with equal probability by $20 each month, starting where it ended the previous month. What is the value of a three-month at-the-money European call option on XYZ’s stock if the stock is priced at $100 when the option is purchased? Answer: Value of option = Option price = Intrinsic value + Time Value of the Option Intrinsic value = $0 as the option is at the money. To calculate the time value of the option, list all the possible outcomes for the stock price movement and identify those where the price goes up. If the stock price falls, the option will not be exercised.
Month 1 Month 2 Month 3 Total
+20 +20 +20 +60
+20 +20 -20 +20
+20 -20 +20 +20
-20 +20 +20 +20
+20 -20 -20 -20
-20 +20 -20 -20
-20 -20 -20 -60
-20 -20 +20 -20
1. Each of the outcomes is equally likely and so occurs 1/8 of the time. Focusing on the first four where the price goes up, Time Value of the Option = Option price = intrinsic value + time value of the option = $0 + $15 = $15 Why might a borrower who wishes to make fixed interest rate payments and who has access to both fixed- and floating-rate loans still benefit from becoming a party to a fixed-for-floating interest rate swap? Answer: If the company has a comparative advantage in borrowing in the floating rate market, it can reduce its overall interest costs by borrowing at a floating interest rate and entering a swap agreement where it makes fixed payments and receives payments that fluctuate with the interest rate. The net effect is that its payments are fixed but, because it exploits its comparative advantage in the floating rate market where it can borrow relatively cheaply, the overall cost is lower than borrowing directly from the fixed rate market. Concerned about possible disruptions of the supply of oil from the Middle East, the chief financial officer (CFO) of American Airlines would like to hedge the risk of an increase in the price of jet fuel. What tools could the CFO use to hedge this risk? Answer: The CFO could buy oil futures contracts, giving him or her a long position in oil and so protecting against a price increase. Alternatively, he or she could buy oil call options, which would confer the right to buy oil at the strike price on or before the expiration date of the option. How does the existence of derivatives markets enhance an economy’s ability to grow? Answer: The existence of derivative markets increases the economy’s capacity to carry risk by facilitating the transfer of risk to those best able to bear it. They allow risks to be hedged more efficiently and at a lower cost by those who do not wish to carry them. In the absence of these mechanisms to deal with risk, resources may not be allocated efficiently, hindering the ability of the economy to grow. Credit-default swaps provide a means to insure against default risk and require the posting of collateral by buyers and sellers. Explain how these “safe-sounding” derivative products contributed to the 2007-2009 financial crisis? Answer: Credit default swaps (CDS) are traded over the counter and financial institutions do not report their CDS purchases and sales. This contributed to a lack of transparency about who bears the default risk, making the financial system more vulnerable. (Recall Core Principle 3 from Chapter 1 – information is the basis for decisions.) Traders could not identify who might have large one-sided positions, making the system vulnerable to the collapse of one institution. During the 2007 - 2009 crisis, AIG was a large player in the market for credit default swaps. When the company’s credit rating was downgraded, the additional collateral requirements it faced brought it near to collapse, threatening the stability of the financial system as a whole and prompting the intervention of the Federal Reserve. What kind of an option should you purchase if you anticipate selling $1 million of Treasury bonds in one year’s time and wish to hedge against the risk of interest rates rising? Answer: You could purchase a put option that gives you (as the holder) the right but not the obligation to sell the bonds at a price determined today. Therefore, if interest rates rise and so the price of the bonds falls, you can exercise the option and sell the bonds at the pre-determined price. If, on the other hand, interest rates fall, you can let the option expire and enjoy the benefits of the increase in the price of the bonds. You sell a bond futures contract and, one day later, the clearinghouse informs you that it had credited funds to your margin account. What happened to interest rates over that day? Answer: Interest rates have risen. This reduced the price of the bonds and so as the holder of the short position you have gained. As the clearinghouse marks to market on a daily basis, this gain was posted to your margin account. You are completely convinced that the price of copper is going to rise significantly over the next year and want to take as large a position as you can in the market but have limited funds. How could you use the futures market to leverage your position? Answer: You should buy as many one-year copper futures contracts as you can afford. This will depend on the margin payment required. As the margin payment is a fraction of the value of the contract, you will leverage your exposure to market movements. The value of the futures contracts will rise in lockstep with the price of copper. Suppose you have $8,000 to invest and you follow the strategy you devised in Problem 16 to leverage your exposure to the copper market. Copper is selling at $3 a pound and the margin requirement for a futures contract for 25,000 pounds of copper is $8,000. Calculate your return if copper prices rise to $3.10 a pound. How does this compare with the return you would have made if you have simply purchased $8,000 worth of copper and sold it a year later? Compare the risk involved in each of these strategies. Answer: a. With $8,000, you can afford to purchase one copper futures contract. At $3 a pound, this is worth $75,000. The contract specifies that you will take delivery of 25,000 pounds at $3 a pound in one-year’s time. If the price in the market has risen by then to $3.10, you make a profit of $2,500 on the $8,000 margin you posted. This represents a return of 31.25% on your investment. b. If you purchased copper directly at $3 a pound, you could have afforded 2,667 pounds. If you sold it one year later for $3.10, you would have gained $267, a return of 3.3%. c. Speculating in the futures market can bring high returns (in this case returns almost ten times as large), but, as usual, these high returns come at the cost of bearing greater risk. Suppose, for example, your hunch about copper prices was incorrect and the price of copper fell to $2.90. You would have lost $2,500 over the year. If you were very unfortunate and the price of copper fell to $2.65, you would have wiped out your entire $8,000 and a bit more as well. In comparison, if you bought the copper at $3 and after a year you sold it at $2.90, you would have lost only $267. For your entire $8,000 to be wiped out, the price of copper would have to fall to zero! And, of course, once you own the copper (ignoring storage costs), you could always elect to hold onto it until the price rose again. Suppose you were the manager of a bank that raised most of its funds from short-term variable-rate deposits and used these funds to make fixed-rate mortgage loans. Should you be more concerned about rises or falls in short-term interest rates? How could you use interest-rate swaps to hedge against the interest-rate risk you face? Answer: Given that you make interest payments based on short-term interest rates and receive fixed-rate interest payments, you should be most concerned about increases in short-term rates. You would have to make higher payments while the payments you receive remain the same. You could hedge against this risk by entering into a fixed-for-floating interest rate swap where you make payments based on a fixed interest rate and receive payments that fluctuate with a reference floating interest rate. When interest rates rise, you receive higher payments from the swap to offset the losses on your underlying banking business. The table below shows the yields on the fixed and floating borrowing choices available to three firms. Firms A and B want to be exposed to a floating interest rate while Firm C would prefer to pay a fixed interest rate. Which pair(s) of firms (if any) should borrow in the market they do not want and then enter into a fixed-for-floating interest-rate swap.
Fixed Rate Floating Rate
Firm A 7% LIBOR + 50 bps
Firm B 12% LIBOR + 150 bps
Firm C 10% LIBOR + 150 bps
Note: LIBOR, which stands for the London Interbank Offered Rate, is a floating interest rate. Answer: Possible pairs: A and C or B and C. (As A and B both want floating, they won’t engage in a fixed-for-floating swap with each other.) Next, look at who has the comparative advantage in which market. A versus C: A has a 3% advantage over C in the fixed rate market and a 1% advantage in the floating rate market. Therefore, A has a comparative advantage in the fixed rate market and wants floating. A and C can reduce their overall cost of funds by A borrowing fixed, C borrowing floating and then entering into a fixed-for-floating swap to exchange the exposures. B versus C: C has a comparative advantage in the fixed rate market and wants fixed rate exposure. Therefore, there is no benefit to the swap. A and C are the only pair that should engage in a fixed-for-floating swap. Suppose, prior to the European financial crisis, you were considering investing in Greek Government bonds but had some concerns about the creditworthiness of the Greek Government. Why, despite your concerns, might you still make such an investment? Answer: Core Principle 2 states that risk requires compensation, so it is likely that you are attracted by a higher yield available on Greek Government bonds compared to less risky investment alternatives. You might also transfer the risk associated with a default by the Greek Governments by purchasing a credit default swap. While you would have to pay a fee for this insurance, the expected higher return on the investment might warrant it. You and a colleague both follow the movements of the VIX, an index based on options prices that reflects investors’ expectations for stock market volatility. Suppose, according to the VIX, implied volatility is expected to be low for a protracted period. Your colleague sees this as unambiguously good news. Why might you disagree? Answer: While you agree with your colleague that low levels of implied volatility might bring high stock valuations and a high level of stock market liquidity, you might be concerned that investors will become complacent and underestimate risk, causing risky assets to become mispriced and possibly destabilizing the financial system when prices correct. Data Exploration Central banks occasionally engage in “liquidity swaps” with each other. Plot and interpret the Fed’s provision of dollar liquidity swaps (FRED code: SWPT) to other central banks since 2007. To facilitate your interpretation, view the FRED “Notes” about this data series. Answer: The data plot is: These liquidity swaps occur when foreign banks need additional U.S. dollars to fund their dollar-denominated activities. The Fed exchanges dollars with the foreign central banks, which then in turn lend them to their member banks. The Fed supplies dollars and accepts foreign currency at the current exchange rate. The swap agreement includes an arrangement to reverse the transaction at a later date, when the dollars are returned to the Fed (with interest) at the initial exchange rate (so there is no currency risk to the Fed). The data plot shows that these swaps occurred first in the financial crisis of 2007-2009. In that period, foreign commercial banks needed dollars for transactions their customers wanted to undertake in U.S. currency. Normally, these banks would have borrowed from U.S. financial intermediaries, but interbank lending plummeted during the crisis – especially after the failure of Lehman in September 2008. As a result, foreign banks were compelled to seek dollar-denominated loans from their own central banks that (in turn) obtained dollar liquidity swaps from the Fed (see Chapter 3). The second occurrence of large swap lines between the Fed and foreign central banks occurred in 2012 at an acute stage of the sovereign and banking crisis in the euro area (see Chapter 16). In both cases, once the function of private markets improved, central bank liquidity swaps virtually disappeared. Define the swap rate and then plot the five-year swap rate (FRED code: MSWP5). Describe a transaction involving the swap rate and the actions of the participating parties. Answer: In an interest rate swap, the fixed-rate payer pays the swap rate, tied to a market rate such as a Treasury bond yield of the same maturity. The data plot is: As an example of an interest rate swap, consider a commercial bank (Bank A) that has issued five-year certificates of deposit on which it pays a fixed interest rate. At the same time, Bank A receives time-varying interest payments on its portfolio of short-term business loans. In contrast, Bank B receives fixed-rate payments on its long-term mortgage loans, but owes time-varying interest payments on its short-term checking and savings deposits. To better match its assets and liabilities, Bank B is willing to swap its variable-interest payment stream for Bank A’s fixed-interest payment stream. Bank B will then have fixed income from its mortgages and fixed expenses on the CDs, stabilizing profits. Bank A will have variable interest income from its business loans and variable interest expense for the checking and savings deposits. Because the interest rates to which bank A is exposed rise and fall together, its profits will be stabilized as well. Risk-averse investors care greatly about asset price volatility. Using the FRED “Notes” about the data series, briefly define the (VIX) Volatility Index (FRED code: VIXCLS) of the Chicago Board Options Exchange (CBOE). Plot since 2004 the VIX and the percent change from a year ago of the Wilshire 5000 stock market index (FRED code:WILL5000PR). Interpret the graph Answer: The VIX infers stock market participants’ collective expectation of stock price volatility from options prices. Because the price of an option increases as the value of the underlying asset is more uncertain and volatile, a rise in the VIX reflects greater expected market variability. Consistent with this interpretation, we see that the VIX was rising gradually as the recession approached and then rose sharply at the time of the financial panic in September, 2008. Note also that the VIX is inversely related to the performance of the equity market index: expected volatility is low when the stock market rises (and vice versa). The VIX spike in 2008 followed the collapse of Lehman.
The data plot is: Is the VIX volatility index (FRED code: VIXCSL) an indicator of broader financial market volatility? Using weekly data ending on Fridays, plot from 1994 the VIX, with its scale on the left axis, and the St. Louis Federal Reserve Bank index of financial stress (FRED code: STLFSI), with its scale on the right axis. Describe the financial stress index and comment on how closely related it is to the VIX. Answer: The St. Louis Fed’s financial stress index is based on eighteen data series, including seven interest rates, six yield spreads, volatility indexes of stocks and bonds (including the VIX) and the breakeven inflation rate implied by Treasury Inflation Protected Securities (TIPS). To the extent that options traders’ behavior reflects the assessments of financial market conditions embedded in these indicators, the co-movement between the VIX and the stress index is perhaps not surprising. Note that the two series appear to be more closely related from the onset of the financial crisis of 2007-2009. Note also that the financial crisis was preceded by an episode of very low volatility that tempted investors and users of funds to take greater risk The VIX has become a major focus of attention because it is, arguably, the single most important (and timely) indicator of financial stress. indicates more difficult problems. Solution Manual for Money, Banking and Financial Markets Stephen G. Cecchetti, Kermit L. Schoenholtz 9781259746741, 9780078021749, 9780077473075
