Having talked about the difference between hedging and speculating and
pointed out the contrasts in approach between a financial risk manager and a
portfolio manager (whose functions are generally familiar to most of the
readers of this site), this article will discuss in general terms the new
financial instruments called derivatives and the rationale for using them.
Key to understanding this rationale and a point that is crucial to
introduce early on is the notion of a premium. Some derivatives are compared to
insurance. Just as you pay an insurance company a premium in order to obtain
some protection against a specific event, there are derivative products that
have a payoff contingent upon the occurrence of some event for which you must
pay a premium in advance.
A derivative financial product is a contrived instrument, the value of which
depends indirectly on the price of a cash instrument. The price of the cash
instrument is referred to as the "underlying" price, quite often.
Examples of cash instruments include actual shares in a company, physical
stocks of commodities, cash foreign exchange, etc.
Why use derivatives and not just cash instruments? Derivatives exist to
solve specific positioning, accounting and regulatory problems. These reasons
may not be immediately clear to you but they will be after you read all of the
derivatives articles on this web site.
When one buys a cash instrument, for example, 100 shares of ABC Inc., the
payoff is linear (disregarding the impact of dividends). If we buy the shares
at $50 and the price appreciates to $75, we have made $2500 on a mark-to-market
basis. If we buy the shares at $50 and the price depreciates to $25, we have
lost $2500 on a mark-to-market basis.
Instead of buying the shares in the cash market, we could have bought a 1
month call option on ABC stock with a strike price of $50, giving us the right
but not the obligation to purchase ABC stock at $50 in 1 month's time. Instead
of immediately paying $5000 and receiving the stock, we might pay $700 today
for this right. If ABC goes to $75 in 1 month's time, we can exercise the
option, buy the stock at the strike price and sell the stock in the open
market, locking in a net profit of $1800. If the ABC stock price goes to $25,
we have only lost the premium of $700. If ABC trades as high as $100 after we
have bought the option but before it expires, we can sell the option in the
market for a price of $5300. The option in this case gives us a great deal of
positional flexibility with a different risk/reward profile. Mark-to-market is
a way of accounting for financial products in which an inventory of financial
products is revalued a pre-set interval (usually at the end-of-business on a
daily basis) at current market rates. The combination of realized and
unrealized profit and loss is booked to the profit-and-loss account.
Mark-to-market accounting is a good practice for the management of any
financial portfolio. It is mandatory for financial institutions to report their
financial accounts in this fashion. In the near future, initiatives like the
Financial Accounting Standards Board Statement No. 133 will require
mark-to-market accounting from non-institutional end-users, as well.
Another aspect of financial derivatives is the fact that they are carried
off-balance sheet, generally. When we speak of the size of a particular
derivative contract, we refer to the notional amount. The notional amount is
the amount used to calculate the payoff. For example, in our options example
above, the notional amount was 100 shares. However, the potential payoff and
the potential loss were both different from the value of 100 shares. Because
the payoffs of derivative products differ from the payoffs that their notional
amounts might suggest if they were cash instruments, they are kept off balance
sheet. Otherwise, the balance sheet could be distorted and inflated by even a
relatively small derivatives portfolio.
Finally, in terms
of the regulatory appeal of derivative products, there are a number of
different ways of looking at this issue. Derivative products, because of their
off-balance sheet nature, can be used to clear up the balance sheet. A mutual
fund manager who is restricted from taking currency plays by regulatory
requirements can buy a structured note whose coupon is tied to the performance
of a particular currency pair. Credit derivatives can be used to lay off and
manage a company's exposure to credit events, such as supplier default.
Most importantly, derivative products enable the end user to tailor their
risk profile in order to most closely match their exposure to their view of the
financial markets and their preferences for holding and managing risk.
There are two types of derivatives: linear derivatives and non-linear
derivatives.
A linear derivative is one whose payoff
function is a linear function. For example, a futures contract has a linear
payoff in that every one-tick movement translates directly into a specific
dollar value per contract.
A non-linear derivative is one whose payoff
changes with time and space. Space in this case is the location of the strike
with respect to the actual cash rate (or spot rate).
One example of a non-linear derivative with a convex payoff profile at some
point before the option's maturity is a simple plain vanilla option. As the
option becomes progressively more in-the-money, the rate at which the position
makes money increases until it asymptotically approaches the linear payoff of
the future. Similarly, as the option becomes progressively more
out-of-the-money, the rate at which the position loses money decreases until
that rate becomes zero.
With non-linear derivatives, therefore, it is possible to capture gains from
volatility by hedging a portion of the option's value (called the
"delta", given by a mathematical formula derived from the formula
used to determine price) and rebalancing the hedge as spot moves around and the
delta changes.
In the ABC Inc.
example from above, we could have purchased a 1-month $50 call option on ABC
giving us the right to purchase 100 shares. With the spot price at $50, the
option is said to be at-the-money. At-the-money options have a delta of 50%, so
to "delta-hedge" the option, we would have sold short 50 shares.
If the ABC price proceeded to $25 the next week, we could buy back some of
the 50 shares we were short (realizing a $25 profit on those shares). Any move
back to $50 subsequently and we could sell more shares short again.
If the ABC price went to $75 the next week, we could sell more shares short.
This would enable us to buy these shares back if the ABC price went lower
before maturity.
The more times we can delta-hedge the option (or "dynamically
hedge" the option), the more profit we will realize. Every time we realize
a profit, we help to pay for the option.
If you own an option and you delta hedge it, you will make money if the
stock price goes up. You will also make money if the stock price goes down. You
have to delta-hedge consistently in order to realize that profit, though. At
the end of the day, you will only make money if you have realized delta-hedging
profits that are greater than the premium you paid away for the option. The
more the stock price moves up and down, the more likely you are to realize
delta-hedging profits.
Conversely, if you sell an option and delta hedge it, you will lose money if
the stock price goes up and you will lose money if the stock price goes down.
Each time that you delta-hedge, you are realizing a loss. At the end of the
day, you will only make money if your delta-hedging losses are less than the
option premium you earned to sell the option in the first place.
If you can understand delta hedging, then you can understand the way options
are priced and what it means to determine good value in a premium.
If we buy an option, then we are arguing that we will make more money
dynamically hedging around it than we will pay in premium.
If we sell an option, then we are arguing that we will make more money in
premium than we will lose in dynamically hedging the option.
One of the prime determinants of the price of an option is the volatility.
Volatility is the measure of how much the spot rate is expected to move around.
Obviously, in a high volatility environment, the spot rate will be expected to
move around aggressively and options premiums are very high. In a low
volatility environment, the spot rate is expected to move around very little
and options premiums are very low. One of the key factors in making money in
options is to understand the nature of volatility.
There are two important characteristics of volatility one needs to
understand.
First, volatility is not constant. It changes over the course of time. There
might be specific events that will cause volatility to spike higher. For
example, the 1992 European Exchange Rate Crisis, triggered by votes on the
Maastricht Treaty, turned a relatively stable environment into a savagely
volatile one.
Second, volatility is statistically persistent. That is a fancy way of
saying that volatility trends. If it's volatile today, then it should continue
to be volatile. If it's calm today, then it should continue to be calm.
Making money in options often means realizing that the trend in volatility
has changed from calm to volatile (in which case you buy options at the
beginning of the volatile period when options volatilities are still low
compared to what you expect actual volatility will turn out to be) or selling
options when the trend changes from volatile to calm (and option volatilities
are higher than what you expect them to be).
In subsequent articles, we will elaborate on determining good value in
options and we will focus on the other key elements in making money in options:
understanding the behavioral characteristics of derivative products.
The biggest single problem with the use of derivative products today is the
lack of knowledge about these two factors.
Article by Chand Sooran, Principal Victory
Risk Management Consulting, Inc. |