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Many
times it is in an investor�s best interest to lock in recent gains or to
protect a portfolio of stocks from a decline beyond a certain price. One way to
do this would be to purchase a put option contract on each of your various
holdings (this would essentially allow you to "lock in" a particular
sale price on each stock, so even if the market crashed, your overall portfolio
wouldn't suffer much). However, if you hold a large, diversified portfolio of
stocks, then it is probably not cost-effective to insure each and every position
in this manner.
As an alternative, you might want to consider using index options
to hedge the risk in your portfolio. Index options are options not on an
individual stock, but rather on an entire index. Many different indices have
options available, including the Nasdaq 100, the Dow Jones Industrial Average
and the S&P 500. For the purposes of today's example we will use the S&P
500-- ticker symbol "SPX"--as a proxy for the overall market's return.
With some careful planning, you should be able to offset a sharp decline in your
portfolio by hedging your overall position with index options. Though it is
impossible to forecast exactly how your portfolio will perform during a
steep market sell-off, you can calculate this out fairly close to the
actual result.
Before you can hedge your portfolio against a major market correction, however,
you'll need to figure out two key items. First, you'll need to determine which
particular index to use as a proxy for your portfolio. If you hold primarily
high-tech stocks (or if you just want to hedge against a downfall in your
technology holdings), then you might want to consider trading options on the
Nasdaq 100. Alternatively, if your portfolio consists mainly of blue-chip
companies, then you might want to use the Dow Jones Industrial Average. Again,
since we're going to assume that your portfolio consists of a well-diversified
mix of different stocks, for the purposes of today's example we'll use the
S&P 500 as our proxy.
Next, you'll need to find the correct number of options to use as a portfolio
hedge. Along those lines, here are a few important items to consider:
-- You first need to derive an estimate of beta (β). This may
sound like an obscure technical term, but beta simply measures the amount of
variance in a portfolio in relation to the market. If you were using the S&P
500 as a proxy for the market, then β would indicate how much your
portfolio moves when the S&P 500 changes by 1%. For example, if you notice
that, in general, your portfolio changes by 2% whenever the S&P moves up 1%,
then your portfolio has a β of 2.0. If the portfolio changes by 0.5%, then
β = 0.5. If the portfolio changes by 1%, then β = 1.0. (Beta is an
important component of all options, so it would be a useful exercise to try this
with your portfolio or individual stocks to become more comfortable with this
term.)
-- The next step is finding the risk-free rate. As the name
implies, this is the rate of interest that can be obtained without incurring any
risk. For the short-term, we usually use the appropriate three-month T-bill
rate.
-- If your portfolio pays any dividends, then you
need to formulate the portfolio�s dividend yield. This can be
found by adding the amount of dividends paid during the year and dividing that
figure by the value of your portfolio. For example, if you receive roughly
$40,000 in dividends per year on a $1 million portfolio, then your portfolio's
dividend yield is 4% (40,000 � 1,000,000).
Now consider the following example:
Suppose you own a $1 million portfolio of stocks and you wish to insure this
portfolio against a decline of greater than -6% during the next three months. In
other words, you want to put a hedge in place to make certain that your
portfolio does not fall below $940,000. To make the calculations fairly simple,
let's assume that the S&P 500 index is currently trading at 1000. Let's also
assume that your portfolio is volatile and generally doubles the S&P 500�s
gains or losses. Therefore, the β is 2.0. Finally, let's assume that the
risk-free rate is 4% and the dividend yields on both your portfolio and the
S&P 500 are also 4%. The assumed return of the SPX is 12% per year. (We
should note that it is not necessary to have an accurate forecast of the
market's return for this hedge to work correctly.) In this example, if you
want to employ SPX put options as a hedging tool, then here's how to calculate
how many contracts you need to purchase:
Total Return of SPX in Three Months:
In three month�s time you expect a 3% return (assuming a 12% annual rate) and
a 1% dividend (assuming a 4% annual yield) for a total return of 4%.
Excess Return of SPX:
The excess return of any asset is the amount it returns over the risk-free rate.
In this case, the risk-free rate would be 1% (assuming a 4% annual rate) in
three months. The excess return is therefore 3% (4% total return � 1%
risk-free).
Total Return of Portfolio in Three months:
For this example we stated that the β of the portfolio is 2, which implies
that if the market returns 3%, then your portfolio will double that amount by
returning 6%. The expected dividend is still 1% during the next three months, so
the total expected return will be 7%.
Excess Return of Portfolio:
The expected excess return is 7% and the risk-free rate is 1%, so the excess
return here will be 6%. This is the return you expect in three month�s time.
The table below illustrates how the portfolio is expected to behave in relation
to the market:
| Value
of S&P 500 Index in Three Months |
Value
of Portfolio in Three Months |
| 1060 | $1,120,000 |
| 1030 | 1,060,000 |
| 1000 | 1,000,000 |
| 970 | 940,000 |
| 940 | 880,000 |
From this chart we can see that the portfolio
will perform twice as well, or twice as poorly, as the market. In this example,
you do not want to let your portfolio fall below $940,000 in the next three
months. Using the table, you can see that buying SPX puts with a strike price of
970 will accomplish this. To find the optimal number of put option contracts to
purchase, use this formula:
Portfolio Value � [(100 x Current Strike Price) � β] = number of put
contracts
In this example, where the portfolio value equals $1,000,000 and the current
strike price is 1000, the calculation would be as follows:
$1,000,000 � [(100,000) � 2] =
$1,000,000 � 50,000 = 20 put contracts
This means you should buy 20 SPX 970 Put contracts that expire in three months
to insure your portfolio against a decline below $940,000.
To see that this is correct, suppose the SPX finishes at 940 when the options
expire in three months. This implies from the chart that your portfolio would be
worth just $880,000. However, the SPX 970 Put contract will expire "in the
money" and will be worth $30 (970 � 940) at expiration. In this scenario,
your 20 options contracts (each contract is for 100 options) will now carry a
value of $60,000. When you add that figure to the $880,000 that your portfolio
is now worth, this equals exactly $940,000. You can perform this procedure for
any decline in the SPX, and in every case you will find that your overall
portfolio will still be worth a minimum of $940,000 at expiration.
Conclusion
Portfolio hedging is an important technique to learn. Although the calculation
of β must be correct to ensure an exact result, most investors find that
even a reasonable approximation will deliver a satisfactory hedge. This
technique is especially helpful when an investor has experienced an extended
period of gains and feels this increase might not be sustainable in the future.
Like all option strategies, portfolio hedging requires a little planning before
executing a trade. However, the security that this strategy provides could make
it well worth the time and effort in a period of declining stock prices.
Please visit the link below to read the next installment of this multi-part
options series In it, we'll introduce you to spread trades and a few other more
advanced topics.
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Good options trading! |
-- Jeff Bishop
Staff Writer
StreetAuthority.com
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