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Derivatives in their Golden Days (1994 to 2007)
The years between 1994 and 2007 have seen a period of low inflation and low interest rates in most developed economies. With the exception of Japan, these years have also seen staggering rises in the prices of stocks and real estate. The periodic crises (e.g. the Asian crisis which began around July 1997, the bursting of the dotcom bubble in March 2000, or the terrorist attacks on 11 September 2001) have not significantly altered the financial landscape for the worst, at least when compared with the stagnation of the late 1960s, the periodic recessions throughout the 1970s and early 1980s, coupled with sky-high inflation in the late 1970s. The current economic climate since the burst of the sub-prime bubble in August 2007 might herald a less benign era, but that is still something unfolding at the time of writing. Nevertheless, we must approach the explosive growth of derivatives in the light of what could be considered the last two golden decades.
Derivatives are simply products whose payoffs depend on the values of other underlying market variables. For example, an agreement to buy a stock 1 year from now at a pre-agreed price is a derivative since its value depends on the value of the underlying stock.
Since the publication of the Black-Scholes model in 1973, a new framework for understanding derivatives and managing risk has taken shape. Derivatives have existed for a long time (e.g. rice futures in Japan in the 1700s) and have been used to transfer risk. The concept of the traditional insurance, which has also been around for some time, is really also based on risk transfer. However, with an improved framework for pricing and managing risk post-1973, substantial innovations in derivatives occurred as more players entered the field. The advances in technology which allowed for high-powered computing of the prices of derivatives also contributed significantly to their growth on an industrial scale.
Ultimately, however, the economic environment contributed heavily to the demand for derivatives from the investing public. In particular, in a low interest rates environment, can one be blamed for seeking higher yields through other means? And if, as policy-makers would have you believe, the boom-bust cycle has been tamed and we are now in a period of steady growth, is it not appropriate to leverage up with derivatives in our pursuit of yield? Further, corporates with hedging needs have certainly welcomed customised solutions that deal with projected cashflows.
In the following sections, we shall be visiting various products and concepts. Please do not be too bothered if you cannot follow all the products and features mentioned. They are meant more to show the myriad of innovations in derivatives stemming from the environment of the last decade or so. And the concepts will be fully discussed in the remainder of the book. Please note that there is a glossary at the end of the text in case you need to remind yourself of the definition of a new term.
1.1 USES OF DERIVATIVES
Put simply, there are two main purposes of derivatives
1. hedging
2. speculation
Hedging
Hedging is where an individual or firm takes a position, with the aim of protecting against an adverse movement in the market environment. As a simple example, suppose you are a US dollar investor and need to pay €100 for some item 1 year from now. It is unclear what spot EUR/USD would be worth 1 year from today. Figure 1.1 shows that as spot EUR/USD (1 year from today) varies between 0.5 and 2, the dollar cost of the €100 payment varies between $50 and $200.
Figure 1.1 As the EUR/USD spot FX rate (1 year from today) varies from 0.5 to 2, the dollar cost of a €100 position varies from $50 to $200.
(Note that the usual style of FX quotation in ccy1/ccy2 is number of units of currency 2 per unit of currency 1. So, EUR/USD refers to number of dollars per euro. The “/” symbol can be misleading for one with mathematical training, as it wrongly suggests itself as the number of euros per dollar.)
You might want to lock in the rate of exchange by entering a 1-year forward, agreeing to buy EUR/USD at 1.3 (i.e. to pay $130 for €100), rather than wait until 1 year from now and be at the mercy of the exchange rate at that time. Figure 1.2 shows that as EUR/USD varies from 0.5 to 2, the forward contract has payoff varying from $80 to $70. Notice that you incur a loss on the forward contract itself if EUR/USD 1 year from now is less than $130. However, the forward contract offsets the dollar cost of buying euros, so that the net cost is always $130 (see Figure 1.3).
Suppose, instead, you are not sure you would need to enter the transaction and just want the right (but not obligation) to buy €100 for $130 at the end of 1 year. This is a call option. Figure 1.2 shows that the call option and the forward have the same payoff if EUR/USD is above 1.3, but otherwise the payoff of the call option is 0. Since you could walk away if EUR/USD is less than 1.3, the call option must cost something up front. This cost is referred to as the premium. Figure 1.3 shows that the call option allows you a lower cost of euro purchase if EUR/USD drops below 1.3, while still ensuring that you never pay more than $130.
Figure 1.2 Dollar payoffs of a forward and a call option on EUR/USD based on different realised values of EUR/USD. Both the forward and the call option have increasing payoffs as EUR/USD increases but the payoff of the option does not go below zero when EUR/USD falls below 1.3.
Perhaps you think the option costs too much. Could you give away some protection for a cheaper option? Perhaps you could have the same option with a knockout barrier so that the option expires worthless if EUR/USD drops below 1.15 any time before the end of the year. In this case, you will be unprotected if EUR/USD drops to 1.14 after 6 months and then rises back above the strike of 1.3 by the end of the year. (See Figure 1.4 for an illustration of this.) But then, nothing in life is free.
Figure 1.3 Resultant dollar payoffs when we superimpose the hedges (either forward or call option) on the short EUR/USD position (from the requirement to purchase €100). For the forward contract, the net effect is that you buy €100 at $130. For the call option, the net effect can lead to a cheaper cost of euro purchase if EUR/USD drops below 1.3.
Figure 1.4 Path of spot FX. Knockout call option has barrier level 1.15. Option is knocked out at 2 months. Thus, even though at expiry of 1 year EUR/USD is above the strike of 1.3, the payoff is 0.
I hope, nevertheless, that you get the point that derivatives can be used for hedging - and optionality costs money. You can also sell some optionality, thus making the existing product cheaper.
But hedging can also be imperfect. As another example, suppose you are a huge grapefruit producer. You want to hedge your profits by entering a forward contract to sell grapefruit (i.e. a contract to sell grapefruit at a pre-agreed price in the future), so that a bumper harvest world wide in August next year will not cause depressed prices to affect you. However, you feel that orange juice contracts are much more liquidly traded, whereas the forward market cannot accommodate the volume of grapefruit you wish to sell. You also believe (or have observed historically) that grapefruit prices and orange juice prices tend to move together (at least most of the time). So instead you sell futures on orange juice (i.e. you enter into an agreement on an exchange to sell a certain quantity of orange juice next August for a pre-agreed price).
There is a significant basis risk (i.e. risk due to hedging using related assets) in that there might be a blight in oranges but a bumper harvest for grapefruit. After all, the historical relation between harvests of grapefruit and oranges may change. In this case, your grapefruit harvest will be sold at reduced prices, and yet you will lose money on the orange juice futures you have sold, since orange juice prices will spike upwards sharply. That could very well lead to ruin, so you can see that hedging may not always be the perfect solution.
It is worth pointing out that hedging tends to involve simpler products than speculation, since here you are trying to generate cashflows which protect against movements of market variables that adversely affect you, based on your existing exposure. And such exposures tend to be the result of prior simpler arrangements.
Speculation
Speculation involves taking a position in the hope of making money. If I am a dollar hedger and think that the euro will rise, I can buy euros. However, if I were a euro investor, how should I buy more euros? Perhaps, I could sell the dollar, or buy the euro by taking a long position (i.e. an agreement to buy the asset) in a 1-year EUR/USD forward contract. What differentiates me from the dollar hedger is that I have no need to buy euros, nor to sell any dollars.
No doubt huge risks can result from speculation. For instance, you could sell short a share (i.e. borrow a share you do not own to sell it) and be exposed to unlimited loss from any rises in its price. (This has nothing to do with derivatives. Going short a forward, however, involves derivatives.) But if you have bought an option, your losses are limited to the initial premium (since you are not obliged to enter the transaction at expiry).
This rather curiously takes us to the point that derivatives need not be risky in themselves. Indeed, many (but not all) retail notes are str...
