CHAPTER 15 HEDGING INSTRUMENTS: FUTURES, FORWARDS, OPTIONS AND SWAPS Understanding derivative products requires a thorough understanding of the basic concepts and practice via numerical exercises. As a result, the questions below attempt, in terms that are as straightforward as possible, to help students understand the basic motivation behind hedging instruments. More exotic questions are best left to more advanced texts. The aim here is to provide an introduction ONLY. PROBLEMS 1.

a. b.

(1050 - 950)/950 = 0.105 or 10.5% $950 US a year later represents 1050(1.10) = $1155 C. If the exchange rate was $1 US = $1 C today the cost (excluding transactions costs) of $950 US is $950 C. The yield in Canadian dollars is then (1155 - 950)/950 = .2158 or 21.58%

c.

$1050 US (0.90) = $945 C. The yield in Canadian dollars is then (945 - 950)/950 = -.005 or -0.5%

2.

The investor should rely on a short-hedge. See the Hedging in Interest Rate Futures table 15.3 for a numerical example.

3.

Current spot rate = $1.15 Current forward rate = $1.20 Because one anticipates needing more Canadian dollars to purchase each U.S. dollar, the Canadian dollar is expected to depreciate. Suppose there were no costs (transactions, etc...) to obtaining a forward contract and also suppose interest rates are the same in the U.S. and in Canada. In this fashion there is no loss of interest income if the investor decides, say, to buy U.S. dollars today or hold Canadian dollars until U.S. dollars will be needed. If expectations are correct, however, holding Canadian dollars until U.S. dollars are needed will cost 4.35% ([1.20 - 1.15]/1.15) due to exchange rate risk. But suppose the future spot rate falls below the current spot rate. Then it will have been advantageous to hold Canadian dollars to buy U.S. dollars cheaper in the forward market. Of course, one other possibility for holding Canadian dollars today is if Canadian interest rates are at least 4.35% higher than U.S. rates. Risk considerations, other than exchange rate risk, are also ignored.

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4.

The question continues to ignore transactions costs. Typically, the investor pays for only a fraction of the cost of buying the currency forward but in the answer below this consideration is ignored. Suppose that the entire $2 million U.S. has to be paid up front For a 3 month period, a 10% annual rate translates into 2.5% per quarter (ignoring compounding). This implies an opportunity cost of .025 (3,100,000) = $77,500 since it cost $3,100,000 in Canadian funds to buy $2M US at the current forward rate. If the future spot rate proves to be correct, and the investor chose to hold Canadian dollars, the cost would be $100,000 as shown in the Table less the $80,000 interest that could have been earned on $3,200,000, or for a net cost of $20,000. Because it has been assumed that the full cost of the forward contact was paid up front the above calculations understate the net costs.

5.

Since interest rates have peaked, in the opinion of the investor, it must be because they are expected to fall. Therefore a strategy such as that depicted in the Hedging in Interest Rate Futures table 15.3, namely engage in a long hedge, should be adopted.

6.

In the cash market the gain is 79 - 71 = 8 per bond, or $80 if the bond is one with a $1000 face value. But if the investor did not have the cash (as in the long-hedge example) then the 8 would represent a loss that can hopefully be recouped in the futures market since the buying price would be 72 and the selling price 78 for a gain of 6. Clearly, if the investor believes interest rates have peaked, thereby leading to a future rise in bond prices, and has the cash then a strategy of entering the cash market only would be the superior one. Transaction costs and some interest costs have been ignored in the above calculations.

7.

If the spot rate is £0.55, 90 days from today, the cost of buying $2,000,000 is £0.55 x $2,000,000 = £1,100,000 which is the wait-and-see position cost. If the option costs £20,000 the total cost is still £1,020,000. Since the latter is relatively less costly the option will be exercised.

8.

Since the investor is expecting a fall in interest rates the correct strategy is to select an option to buy, or a call, at a higher interest rate. In this fashion, the investor can purchase the right to a bond, whose price is expected to be higher in the future, at a relatively lower price today. A $1,000,000 treasury bill in the cash market would yield $25,000 over 90 days ($1,000,000 x .10 = $100,000 per year or $100,000/4 = $25,000 per quarter). If interest rates fall to 8% the same treasury bill would yield $1,000,000 x .02 (=.08/4) = $20,000 in the cash market. A measure of the loss in interest is $25,000 - $20,000 = $5,000 but since the option

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costs $10,000 and it is a sunk cost the option will be exercised. As before, we also ignore transactions costs. 9. After the fact spot exchange rate $1.30

Cost (in $C) of purchasing $US in the spot market $130,000

Gain (+) or Loss (-) on forward contract -$15,000

$1.40

$140,000

-$5,000

$1.45

$145,000

$0

$1.50

$150,000

+$5,000

10. If you kept the $C equivalent of $2,000,000 US then, in 3 months at 8% the interest earned would have been $3,000,000 CAD X.08/4 = $60,000 at the prevailing spot exchange rate ($1.50CAD=$1.00US). The resulting $3,060,000 CAD would buy $1,912,000 US at the spot rate of $1.60CAD anticipated 90 days from today and still $88,000US short of what is required. That would cost an extra $140,800 at the spot rate of $1.60CAD=$1.00US. An alternative would be to buy $2M US today at the current spot rate and invest at 6% to yield $30,000 US (=$2M X .06/4) for a net amount of $2,030,000 US. The $30,000 US would then be worth $48,000 if the anticipated spot rate 90 days from today is indeed correct. The Table below shows some the options: Cost in $CAD Wait and see $3,200,000 ($2MX1.6) Buying forward $3,100,000 (see Table 15.2) Invest in Canada then purchase US $ $3,140,800 (=$3+$140,800) Invest in US $2,952,000 (=$3M-$48,000)

11.

The cost of the unhedged purchase is $8 x 10,000 or $80,000. In the case of a hedged purchase one would buy 10,000oz. at $59,000 and sell at $84,500 generating a profit of $25,500. The nest cost then is $80,000 less $25,500 or $54,500.

12.

100-89 = 11% (100 times (1 - (90/360)(.11)) = 97.25 or $972,500.

13.

If returns are measured on the horizontal axis then probability distribution for calls would be xIFC while the distribution for puts would be OGHz reversing the case considered in the text. But this should not be surprising since the price of an asset moves in the opposite direction to its return.

14.

Clearly, one would have been better off buying US dollars back in 1996. The only other consideration is the differential in the return on US dollar denominated

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assets versus Canadian dollar denominated assets. The $C was worth 9.68% less than expected (1.4925/1.3608). 15.

If our expectations are correct and the contract does in fact end at 108, profit will be 8 (=108-100)-2.70 = 5.30. Given the prices in the Table a profit will be made whenever the exercise price is less than 110. In the case of 110 and 115 calls we should then prefer to be sellers. If a long position is taken then we make a profit whenever the price of the underlying contract rises; in the case of a short position, the situation is reversed. For each increase in the price of the underlying asset we lose.

DISCUSSION QUESTIONS 1.

In derivative markets one purchases relatively large quantities at a small fraction of the asset’s value. However, payments on losses are in terms of the total value of the asset so a small change in price in one day can lead to a large loss.

2.

Since options can be allowed to expire, what equation (15.3) and (15.4) do is provide a decision-making rule for when an option has value to an investor. Thus, in the case of a call, if one can buy an asset at a price (the exercise price) below its value in the spot market (the spot price) then it is clearly worthwhile to do so. The opposite holds on the case of a put.

3.

The principal reason for the importance of this issue is that the impact of policies, such as higher interest rates, can be delayed for a time through hedging behaviour. Thus, central banks might wish to raise rates even more than they otherwise would or maintain higher rates for a longer period of time. It is possible, therefore, that if central bank actions are believable, or credible, the announcement of an intention to raise interest rates might be sufficient to persuade markets that the central bank is serious and could, therefore, mitigate hedging behaviour. The reason is that markets know that hedging behaviour might force the central bank either to keep interest rates higher than necessary or to raise them for a sufficiently long time to undo the benefits of hedging behaviour.

4.

Because settlement is daily and the number of contracts involved was very large there were losses to make up every single day. More importantly, the trader(s) at Barings kept betting incorrectly on the direction the market would take thereby increasing the losses all the time. To add insult to injury the same trader(s) would buy more contracts all the time hoping to make up the losses in one big shot but it was not to happen.

5.

Since derivative products are purchased on margin there is a risk that the investor will not be able to make up a loss in the case of an unfavourable change in price. By settling gains and losses daily the inherent liquidity risk is lowered somewhat.

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6.

Open outcry presumes that buyers and sellers hear what they are supposed to hear. Open outcry requires traders to keep their word. Moreover, open outcry results in only as many transactions as a trader is able to complete within a specified time. Computer trading, on the other hand, leaves a trail of evidence about bid and ask quotes, and can handle many more transactions than a human is capable of. Arguably, computer trading may be less prone to errors.

ONLINE APPLICATIONS 1. 2.

3.

4.

Answers will vary according to the particular simulation chosen. Answers will vary according to the chosen instrument. Note that you must download an Excel spreadsheet to address this question. See answer to Question 4 for a view of the website. Answers will vary according to the parameters chosen in the simulation experiment. The website is as shown below.

The location on the Montreal Exchange’s web site is shown below:

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a. As explained in the chapter, hedgers want to reduce risk while speculators are willing to trade-off higher to obtain higher returns. Margin requirements, which are mark-to-market, reflect these differences in risk tolerance. b. Since speculators are more tolerant of risks, and therefore of losses, relatively larger margin requirements are necessary. It is instructive to go to the web site’s Home page and click on glossary and look at the definition of speculator and hedger. 5. Answers will vary according to the chosen set of values entered on the web site. The web site where the calculator is found is shown below.

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