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GUIDE TO FUTURES AND OPTIONS

Most people have heard of futures and options but for many they remain shrouded in mystery, forever to beknown as dangerous instruments that should be left to the professionals. Well, the time has come to explainwhat these strange instruments are all about

Futures

Lets say that you have a 100 note and I asked to borrow it for a year and return the 100 note. Would youdo it? Of course not because you could put the money in the bank and get a riskless rate of return of, say,6% per year. That would mean that in a years time that 100 note is actually worth 106 to you. The futurevalue of the 100 is 106 (assuming inflation is zero).

That is the basic idea of a future, hence the name! What is the value to us now of the index/stock at theexpiry date of the future? The expiry date is the date that the future ceases to exist

The Definition:

A futures contract is the obligation to buy the underlying instrument at a pre-determined price and date in thefuture.

In the UK we only have futures on Index levels (some countries have futures on stocks). The standardcontract size is 10 per index point - which means that each futures contract is worth the level of the indexmultiplied by 10, e.g. 6200 x 10 = 62,000 - but LIFFE have recently introduced a mini-future with acontract size of 5 per point that is aimed at the private investor. There are four expiry months March,

June, September and December and the final value of the future is calculated on the third Friday of themonth using what is called the EDSP (Exchange Derivative Settlement Price). This is calculated as follows:

Between 10:10am and 10:30am the value of the index is taken every 15 seconds. Out of the total of 81prints the highest and lowest 12 are discarded. The remaining 57 are averaged and this becomes thesettlement price for the future.

A calculation:

E.g. its the 1st

November and the FTSE 100 index is currently trading at 6200.

What is the fair value of the December 2000 FTSE 100 index future?

To work this out we need to know what the FTSE 100 index is worth to us on December 15th

(3rd

Friday inDecember). For that we need the interest rate so lets assume that you can borrow at 6%. There are a totalof 44 days between the 1

stof November and expiry day. So 6200 now is worth:

V0*(1+Rt) (I.e. the value now + the interest you would get at 6%)

V0 is the value of the index now.

R is the rate you can borrow at.

t is the time between now and the expiry date, expressed as a fraction of a year.

This works out to be 6245. So the future should be trading at 6245, right? Wrong. We have forgotten thatstocks pay dividends and if we buy the future we get no dividends because we do not own a part of anycompany. This is where it gets complicated you find all the stocks that go ex-div between now and expiryand turn them into index points (in the same way as you turn company market capitalisations into index

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points). Since you dont know how much the dividend will be you use forecast estimates. Lets assume thatthere are 20 dividend points.

Therefore the future should be trading at 6225. The difference between the level of the market and thetheoretical value of the future is known as the basis. The future does not have to trade at theoretical value,but it must be close. Otherwise you could buy one and sell the other and make a riskless profit. This isknown as arbitrage.

Forwards:

A forward is much like a future, except that it is a contract drawn up by two people. Whereas a future isguaranteed by the exchange, a forward is not. A future has four expiry months, but the two people drawingup the forward contract agree an expiry date. The place, time, quantity, price are all set by the two peopledrawing up the contract and it is also very unusual for a forward contract to be sold on, but of course you cansell a future.

Some points about futures:

1. Since the basis is dependent on the interest rate if interest rates were to change the future wouldchange. That means that if you trade futures you have exposure to interest rates.

2. The basis is also dependent on dividends. If these are different from forecasts, again the basis willchange. Therefore, you have dividend risk too. People also have different forecasts, so whatappears to be fairly valued to one investor may be cheaper/more expensive to another who usesdifferent dividends forecasts.

3. The near-month FTSE 100 future (the one with the closest expiry date) is very liquid, meaning thespread is usually only a point or two.

4. Futures are often used to hedge since it is easier to trade a future and gain exposure to the wholemarket than buy every share in the FTSE 100, which would incur large transaction costs and meanlarger spreads.

5. Futures are used extensively in the commodities market for hedging. For example, if a wheat farmerwanted to guarantee his income at harvest he could hedge with a wheat futures contract.

Options

What if there was a way that you could gain exposure to a share/market for a small amount of capital, but ifit all went horribly wrong you would only lose that capital? Well, there is a way and its called an option.

There are two types of options calls and puts.

The Definitions:

A call is the right, but not the obligation, to buy the underlying asset at a pre-determined price and date.

A put is the right, but not the obligation, to sellthe underlying asset at a pre-determined price and date.

Exercising the option is converting the option into the underlying asset.

The strike price of an option is the price at which the option can be exercised; lets call this X.

An in-the-money option has value if exercised now.

An out-of-the-money option has no value if exercised now.

An at-the-money option is where the strike price of the option is the same (or as close as possible) to thecurrent underlying price.

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Valuing Options:

This is the tricky part!

Options in the market are priced using what is known as the Black-Scholes model (or derivations of) afterthe clever people who came up with it. Now thats a tad complicated so lets do it another way.

It can be said that there are two parts to the price of an option. They are most often referred to as the

intrinsic value and time value.

Lets say that I have an option to buy Vodafone stock at 200p with a December expiry date (i.e. 200p DecVOD call). Vodafone is currently trading at 240p in the market. If we exercised our call option (i.e. boughtVOD shares @ 200p) we could then sell them at 240p (ignoring the spread) and make 40p profit. Thatmeans that our 200p call already has 40p ofintrinsic value.

Time really is money in the case of an option the longer the time to expiry, the greater chance an optioncan be in the money and the greater the price. The volatility of the underlying asset also adds to the value ofan option. The greater the volatility, the more uncertainty there is so the higher the option price.

What if a stock pays a dividend while we hold an option on it? We do not receive the dividend because we

do not hold the stock so the value of the option should be reduced by the size of the dividend to compensateus.

Then there is the fact that we have not paid for the stock, but a smaller amount for the right to trade the stockat a price in the future. That means that we need to take into account the fact that we have earned intereston the money we would have used to buy the stockah, thats the basis again! So we need to add thebasis onto the value of the option.

These four factors contribute to the time value of the option.

A recap:

The intrinsic value is what we would get if exercised the option now and then closed out that position.

The time value is a combination of the time to expiry, volatility of the underlying asset and basis whichincludes dividend stream.

But thats not all because we have had to pay something for this option. That means that we need todiscount the value of the option because we could have put the money we paid for it in the bank and earnedinterest on it.

The Greeks :

Options have various properties that are quantified using Greek symbols. They are as follows:

1. Delta this is the change in option price relative to change in the price of the underlying asset. Thedelta of a call option can be between 0 and +1. The delta of a put option can be between 0 and 1.The deltas of at the money options are approximately (they have equal chance of being in or out-of-the-money at expiry). E.g. a call option is valued at 20p and has a delta of 0.2. The underlyingasset goes up by 1p so the call option is now worth 20.2p.

2. Gamma The delta of an option is not constant. For a deep in-the-money call (put) it is unlikely thatit will be out-of-the-money at expiry so it moves like the underlying asset and has a delta of +1(-1).Similarly, if the option is deep out-of-the-money it is unlikely to end up in-the-money so has a delta ofnearly 0. Gamma is the change in the delta of an option relative to the underlying asset. E.g. a calloption has a delta of 0.6 and gamma of 0.08. If the underlying moves up 1p the delta of the call isnow 0.68.

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3. Tau The price of an option is dependent on the volatility of the underlying asset. Tau is a measureof how the option value changes for changes in the volatility of the underlying asset.

4.Theta

As the option expiry moves closer, there is less uncertainty about the final value of theoption so the option value decreases. Theta quantifies the decrease in option value over time. Notethat it is not constant, but rather increases as the time to expiry decreases.

5. Rho Since the option value includes basis there is some dependence on interest rates. If interestrates rise the basis increases. Rho quantifies the exposure to interest rates.

Some Points About Options:

1. In general, private investors tend to want to use options as punts. They buy a deep out-of-the-money option for a relatively small amount in the hope that the underlying asset will move greatly inone direction or the other and the option suddenly becomes worth a lot more than was initially paid.Deep out-of-the-money options are called Tiny options.

2. Investment banks on the other hand trade the volatility value in the option. They hate selling Tinyoptions because of the huge leverage so tend to price them with large spreads.

3. Various combinations of options can be used to create various payoffs at expiry. These strategies are useful for different situations and include Straddles, Butterflies, Call Spreads, Put Spreads andmany others. (See a book for what these are and what the payoffs look like.)

Finally

Although that seems a lot, it really is only a brief summary. If you are interested in using futures and optionsthem we strongly advise that you undertake a course and/or read a few books. Options especially involve farmore than is described above and this article is meant only as a base for further study.

While both offer an exciting and useful dimension to the markets, both can be a painful way to lose a lot ofmoney if not understood and respected.

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