336 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 10.2 Portfolio insurance
line when the portfolio is at its initial value (100) or greater. This difference
represents the cost of performing the portfolio insurance. Otherwise, as the
portfolio falls in value, portfolio insurance provides a floor on the value of
the portfolio at a desired level (in this case, the present value of 100) minus
the cost of performing the strategy.
In a nutshell, portfolio insurance is akin to buying a put option on the
portfolio. Let’s suppose that the fund you are managing consists of only one
stock, which is currently priced at $100. Buying a put option on this stock,
with a strike price of $100, at a cost of $10, would replicate the dotted line
in Figure 10.2. The worst that could happen to your portfolio of one stock
and a put option on it is that you could exercise the put, which sells your
stock at $100, and you lose the value of the put, $10. Thus, the worst that this
portfolio can be worth is $90, regardless of how far down the underlying
stock goes.
On the upside, your insured portfolio suffers somewhat, in that the
value of the portfolio is always reduced by the cost of the put.
Now, consider that being long a call option will give you the same profile
as being long the underlying and long a put option with the same strike price
and expiration date as the call option. When we speak of the same profile,
we mean an equivalent position in terms of the risk/reward characteristics
at different values for the underlying. Thus, the dotted line in Figure 10.2
can also represent a portfolio composed of simply being long the $100 call
option at expiration.
Here is howdynamic hedgingworks to provide portfolio insurance.
Suppose you buy 100 shares of this single stock for your fund, at a price
of $100 per share. Now, you will replicate the call option by using this
underlying stock. The way you will do this is by determining an initial floor
for the stock. The floor you choose is, say, 100. You also determine an