|
Article researched and written for Fill ya Boots!
by Daniel Turner
Most people have heard of futures and options but
for many they remain shrouded in mystery, forever to be known as dangerous
instruments that should be left to the professionals.
Well, the time has come for Fill ya Boots! to explain what these strange
instruments are all about…
Futures
Let’s say that you
have a £100 note and I asked to borrow it for a year and return the £100 note.
Would you do 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 year’s time that £100 note is
actually worth £106 to you. The future
value 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 the expiry 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 the future.
In the UK we only have
futures on Index levels (some countries have futures on stocks). The standard contract size is £10 per index point - which
means that each futures contract is worth the level of the index multiplied by
£10, e.g. 6200 x £10 = £62,000 - but LIFFE have recently introduced a
mini-future with a contract 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 the month 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 81 prints the highest and lowest 12 are discarded.
The remaining 57 are averaged and this becomes the settlement price for
the future.
A calculation:
E.g. it’s 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 in December). For
that we need the interest rate so let’s assume that you can borrow at 6%.
There are a total of 44 days between the 1st of 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
that stocks pay dividends and if we buy the future we get no dividends because
we do not own a part of any company. This
is where it gets complicated – you find all the stocks that go ex-div between
now and expiry and turn them into index points (in the same way as you turn
company market capitalisations into index points).
Since you don’t know how much the dividend will be you use forecast
estimates. Let’s assume that there are 20 dividend points.
Therefore the future
should be trading at 6225. The
difference between the level of the market and the theoretical 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 is known as arbitrage.
Forwards:
A forward is much like
a future, except that it is a contract drawn up by two people. Whereas a future is guaranteed by the exchange, a forward is
not. A future has four expiry
months, but the two people drawing up the forward contract agree an expiry date.
The place, time, quantity, price are all set by the two people drawing up
the contract and it is also very unusual for a forward contract to be sold on,
but of course you can sell a future.
Some points about futures:
- Since the basis is dependent on
the interest rate if interest rates were to change the future would change.
That means that if you trade futures you have exposure to interest rates.
- The basis is also dependent on dividends.
If these are different from forecasts, again the basis will change.
Therefore, you have dividend risk too. People also have different forecasts, so what appears to
be fairly valued to one investor may be cheaper/more expensive to another who
uses different dividends forecasts.
- The near-month FTSE 100
future (the one with the closest expiry date) is very liquid, meaning the
spread is usually only a point or two.
- Futures are often used to
hedge since it is easier to trade a future and gain exposure to the whole
market than buy every share in the FTSE 100, which would incur large
transaction costs and mean larger spreads.
- Futures are used
extensively in the commodities market for hedging.
For example, if a wheat farmer wanted 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 if it all went horribly wrong you would only lose that capital?
Well, there is a way and it’s 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 sell the 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; let’s 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 the current underlying price.
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) after the clever people who came up
with it. Now that’s a tad complicated so let’s 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.
Let’s say that I
have an option to buy Vodafone stock at 200p with a December expiry date (i.e.
200p Dec VOD call). Vodafone is
currently trading at 240p in the market. If
we exercised our call option (i.e. bought VOD shares @ 200p) we could then sell
them at 240p (ignoring the spread) and make 40p profit.
That means that our 200p call already has 40p of intrinsic value.
Time really is money
in the case of an option – the longer the time to expiry, the greater chance
an option can be in the money and the greater the price.
The volatility of the underlying asset also adds to the value of an
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 compensate us.
Then there is the fact
that we have not paid for the stock, but a smaller amount for the right to trade
the stock at a price in the future. That
means that we need to take into account the fact that we have earned interest on
the money we would have used to buy the stock…ah, that’s the basis again!
So we need to add the basis 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
which includes dividend stream.
But that’s not all
because we have had to pay something for this option.
That means that we need to discount the value of the option because we
could have put the money we paid for it in the bank and earned interest on it.
The “Greeks”:
Options have various
properties that are quantified using Greek symbols.
They are as follows:
- Delta
– this is the change in option price relative to change in the price of
the underlying asset. The delta
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 ½ (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 underlying asset goes up by 1p so the call option is now worth
20.2p.
- Gamma
– The delta of an option is not constant.
For a deep in-the-money call (put) it is unlikely that it 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 of nearly 0. Gamma
is the change in the delta of an option relative to the underlying asset.
E.g. a call option has a delta of 0.6 and gamma of 0.08.
If the underlying moves up 1p the delta of the call is now 0.68.
- Tau
– The price of an option is dependent on the volatility of the underlying
asset. Tau is a measure of how
the option value changes for changes in the volatility of the underlying
asset.
- Theta
– As the option expiry moves closer, there is less uncertainty about the
final value of the option so the option value decreases.
Theta quantifies the decrease in option value over time.
Note that it is not constant, but rather increases as the time to
expiry decreases.
- Rho
– Since the option value includes basis there is some dependence on
interest rates. If interest
rates rise the basis increases. Rho
quantifies the exposure to interest rates.
Some Points About
Options:
- 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 in one 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.
- Investment banks on the
other hand trade the volatility value in the option.
They hate selling “Tiny” options because of the huge leverage so
tend to price them with large spreads.
- 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 and many 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 options them we strongly advise that you
undertake a course and/or read a few books.
Options especially involve far more 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 of money if not understood and respected.
Article researched
and written by
Daniel Turner
|