41 lines
2.7 KiB
Plaintext
41 lines
2.7 KiB
Plaintext
Chapter 38: The Distribution of Stock Prices 799
|
||
thing that cannot be predicted with certainty. Nevertheless, any probability calcula
|
||
tor requires this input. So, one must understand that the results one obtains from any
|
||
of these probability calculators is an estimate of what might happen. It should not be
|
||
relied on as "gospel."
|
||
Additionally, probability calculators make a second assumption: that the volatil
|
||
ity one inputs will remain constant over the entire length of the study. We know this
|
||
is incorrect, for volatility can change daily. However, there really isn't a good way of
|
||
estimating how volatility might change in the course of the study, so we are pretty
|
||
much forced to live with this incorrect assumption as well.
|
||
There is no certain way to mitigate these volatility "problems" as far as the prob
|
||
ability calculator is concerned, but one helpful technique is to bias the volatility pro
|
||
jection against your objectives. That is, be overly conservative in your volatility pro
|
||
jections. If things tum out to be better than you estimated, fine. However, at least
|
||
you won't be overstating things initially. An example may help to demonstrate this
|
||
technique.
|
||
Example: Suppose that a trader is considering buying a straddle on XYZ. The five
|
||
month straddle is selling for a price of 8, with the stock currently trading near 40. A
|
||
probability calculator will help him to determine the chances that XYZ can rise to 48
|
||
or fall to 32 (the break-even points) prior to the options' expiration. However, the
|
||
probability calculator's answer will depend heavily on the volatility estimate that the
|
||
trader plugs into the probability calculator. Suppose that the following information is
|
||
know about the historical volatility of XYZ:
|
||
l 0-day historical volatility:
|
||
20-day historical volatility:
|
||
50-day historical volatility:
|
||
l 00-day historical volatility
|
||
22%
|
||
20%
|
||
28%
|
||
33%
|
||
Which volatility should the trader use? Should he choose the 100-day historical
|
||
volatility since this is a five-month straddle, which encompasses just about 100 trad
|
||
ing days until expiration? Should he use the 20-day historical volatility, since that is
|
||
the "generally accepted" measure that most traders refer to? Should he calculate a
|
||
historical volatility based exactly on the number of days until expiration and use that?
|
||
To be most conservative, none of those answers is right, at least not for the right
|
||
reasons. Since one is buying options in this strategy, he should use the lowest of the
|
||
above historical volatility measures as his volatility estimate. By doing so, he is taking
|
||
a conservative approach. If the straddle buy looks good under this conservative
|
||
assumption, then he can feel fairly certain that he has not overstated the possibilities |