Introduction
One of the words you will hear most on a trading floor is the word hedge. A
hedge, quite simply, is some way to reduce or remove the unwanted risk of a
position, like hedging a bet. A proverb among trades is that "The only
perfect hedge is in a Japanese garden". Although I cannot comment on Japanese
horticulture, I can comment on the quality of some hedges, so that is what
I will do. I will then explain why a hedge is very important in finance.
Basis risk
If you have a position in one asset, and do a trade in the same asset that perfectly
compensates this position, one could say one has a perfect hedge. However, this is
commonly just known as having no position. As such, having a hedge position almost by
definition implies that the hedge is not perfect; a perfect hedge is not called a
hedge, but a flat position. However, when a hedge is not perfect, we introduce
basis risk.
Basis risk has its own node, but in principle, it just means that there is a
remaining position. Consider, for instance, that one has a position in oil to be
delivered in Europe. Now, for some reason, this is hedged with oil to be delivered
in Oklahoma. This normally is a very good hedge - unless for some reason, the cost
of transport between Europe and Oklahoma skyrockets.
Basis risk can be subtle or obvious, and large or small. People have been killed -
even literally - by the smallest of basis risks, such as a difference between the A
and B shares of a company, in which the A shares have options on them but the B
shares don't, but are otherwise identical. Especially combined with liquidity risk,
a basis risk can be devastating.
Static versus dynamic hedging
There are hedges that you can do and then forget about. For instance, the oil hedge I
just mentioned is one you could probably just forget about (unless the basis risk
kicks in, but then it's probably too late to do anything about it).
These are probably the most "obvious" examples of hedges.
There are, however, also products which require dynamic hedging. An example of this
are options. Without going too much into detail about the fine art of
hedging options, we can state than an option is the right to buy or
put a share (or other underlying) at a certain price, known as the
strike, and before a certain time. This time is called the expiration The owner
of a call will buy the share if it is above the strike at expiration, because that
would lock in a profit. If it were below the strike, he would do nothing. So, if
you have a clue on the chance you are actually going to buy or sell that share, you
might as well buy or sell those shares beforehand, right? Imagine, for instance, that
I have a 1050 call on the S&P 500 index, which is today trading at 1090. This call
will expire in 2 years. Well, I think it's fair to say that we have about a roughly
even chance that it will end above 1000 - perhaps a little bit more than even - so
we might sell 50 or 55 shares. However, if the option expires tomorrow, we are almost
sure to exercise and we might sell 95 or 100 shares.
Now, there obviously has been a transition between the 50 or 55 shares sold initially
and the 95 or 100 shares sold eventually. This means we would have had to adjust our
hedge. This would, incidentally, also be the case if the value of the S&P 500 would
have changed. If the S&P 500 drops, we should buy shares, and if it were to go up, we
would sell shares.
The above example, which is oversimplified - the actual hedge of an option is a lot
more complex to compute - is but one example of a case in which dynamic hedging is
necessary. It is noted that dynamic hedges are in a sense never very good. The hedge
might turn out to be bad in the near or far future, and in the mean while, it was not
optimal.
Hedging only unwanted risk
Okay, so we have seen it is possible to hedge a risk. By choosing an appropriate
hedge, it is possible to only have exposure to one specific risk. Consider, for
instance, an investor that thinks that Exxon will outperform the general market. Of
course, she could buy Exxon shares. However, if the entire stock market tanks, she
could, even if Exxon does relatively well. A possibility is to sell a basket of
other stocks to remove this risk, for instance by selling an index. For
example, she could sell the S&P 500 index, which is a broad index of large US
companies. This should be a good hedge.
It is even possible she has a more narrow vision, namely that Exxon will outperform
other oil companies. In this case, she could sell (go short) other oil companies,
such as Royal Dutch Shell, Gazprom and Petrobras. By a proper choice of hedge, one
can tailor the exposure one has. In fact, the basis risk is something which is
deliberately chosen. As such, an investor does not consider it a risk in the sense
that it is an undesirable risk. With good hedging, it should be possible to just
have exposure to the one variable one hopes to profit from, such as the relative
performance of oil stocks, India versus China, or Euro versus dollar.
Hedges in finance
This, however, is not the only reason why a hedge is important. Consider, for
instance, a structured product. This product has the following payoff:
- 1000 if the S&P 500 is at or below 1000 in one year
- The value of the S&P if it is between 1000 and 1250 in one year
- 1250 if the S&P is at or above 1250 in one year.
Such products are very popular in
Europe. What should one pay for this? Well, this
product essentially consists of a
risk reversal, a
long put and a
short
call, and the S&P 500 index. This
put and this
call are
liquid products, that
have a well-defined price. As this
product can be replicated exactly using the
call, the
put and the
index, its
price is simply equal to the price of the
long
put, the
index, minus the
premium received for the
short call. More
importantly, it can be (nearly) exactly replicated. As such, a
bank can
issue
these
products,
hedge them, and if they are
sold for more than the value
of the
hedge, they pocket the difference, with essentially no risk. The people that
sold the
put and bought the
call have the
risk, and they have their own way of
hedging it.
This is a general principle: if a product can be created from a combination of other
products, it can be hedged by buying these other product if one sells the
product. As such, its value is uniquely determined by the value of the hedge. This
principle is the cornerstone of the valuation of all derivatives.
Conclusion
A hedge is a trade that reduces the risk of a position. In general, a hedge is
understood to only remove part of the risk; if the exact same asset is used, a
perfect risk reduction is achieved, but this is called closing rather than
hedging a position.
Hedging is important for managing risk. It can be used to obtain an exposure to only
the desired part of a position, for instance an exposure to the relative performance
of an oil company by hedging the general performance of the stock market
by selling the index. Hedging can also be used to value derivatives; the price of
a derivative is equal to the (expected) cost of hedging it.