Why derivatives?

Every candidate underlying asset will have a value that is affected by a variety of factors, therefore inheriting risk. Derivative contracts, due to the leverage that they offer may seem to multiply the exposure to such risks. However, derivatives are rarely used in isolation. By forming portfolios utilizing a variety of derivatives and underlying assets, one can substantially reduce her risk exposure, when an appropriate strategy is considered.

Derivative contracts provide an easy and straightforward way to both reduce risk -hedging, and to bear extra risk -speculating. As noted above, in any market conditions every security bears some risk. Using active derivative management involves isolating the factors that serve as the sources of risk, and attacking them in turn. In general, derivatives can be used to

• hedge risks;

• reflect a view on the future behavior of the market, speculate;

• lock in an arbitrage profit;

• change the nature of a liability;

• change the nature of an investment;

Example 1 (Sources of risk)   Suppose that a British investor holds a number of 10 year US T-Notes, and wants her investment to expire on the 1st December 01.^1.4 The face value of the notes is $\$10m$, and at the current market prices they are worth $\$10.38m$. The exchange rate today is $1.4726\$/\pounds$. Therefore, if she decides to liquidize the notes now, the investor would receive $\pounds 7.049m$. There are two sources of risk in this setting: Exchange rate risk and interest rate risk.

Example 2 (cont. Exchange rate risk)   The British pound might keep rising against the dollar. This is illustrated in figure 1.1. In this case, the value of the investment will decline. The investor examines the futures markets, and observes that the quote for a $\$/\pounds$ exchange rate future that expires on the 1st December 01 is $1.4834\$/\pounds$. By selling futures worth $\$10.38m$ she will ensure a payment of

$$\$10.38m/1.4834\$/\pounds =\pounds 6.997m$$.

The above does not describe the perfect hedge position! Since the investor keeps the money in the 10y note until next year, she will enjoy the interest -and the possible coupons, offered through that year. The right amount to be converted would be the one that will include those payments. But what is this value? The actual value of the notes will depend on the short rates that will be in place next year. This gives rise to the interest rate risk.

Figure 1.1: Alternative exchange rate events

Example 3 (cont. Interest rate risk)   If the US rates go up during the next year, the value of the investment will decline -the bond prices will fall. How can the investor hedge against this kind of risk? By selling T-Note futures. Setting up the portfolio for this hedge is not as easy for the investor as it sounds. Unlike the FX futures contract, there is no 10y T-Note futures contract available that expires on the 1st Dec 01. She investigates a bit more and collects some similar instruments that might be helpful: these are described in the following table.

$$\begin{tabular}{llll} Instrument & Expiration & Price & Premium \... ...0500 & 139 \\ 10y T-Note Put & 1st Sep 01 & 10200 & 51 \hline \end{tabular}$$

Unfortunately, the instruments on the 10y T-Note do not have the appropriate maturity, whereas the instruments that have the correct maturity have a different underlying. The 10y and 30y instruments move in principle in the same directions, but they do not move in exactly the same way. Using the 30y T-Bond will not hedge perfectly, the risk that remains from such situations is called the basis risk which will be discussed in chapter 2. A perfect hedge is feasible using options management, the investor could ensure a minimum price for the investment by buying puts, or she could construct some kind of collar using both calls and puts, but these instruments expire before the investment. The investor can proceed until new derivatives enter the market, or seek for over-the-counter forward contracts that are tailor made.

The purpose of the above example was to highlight the use of derivatives as a hedging tool, and the way that the different sources of risk which are combined to generate the underlying asset's uncertainty are decomposed in order to achieve the perfect hedge. It addition it has also made use of two very similar types of contracts, the futures and the forward contracts.