RUN YOUR PLAYS
Let’s put it all into practice. Say a stock has
rallied from $80 on Monday to $85 on Tuesday. On Monday, the stock had an overall vol
of 30%. So, 0.0618 x 0.30 x $80 = $1.48. And
$1.48 is one standard deviation based on
Monday’s price and volatility. Theoretically,
68% of the time, the stock might have closed
in a range between $78.52 (down $1.48) and
$81.48 (up $1.48) on Tuesday. But instead, it
rose $5 on Tuesday. Divide the $5 change in
the stock price by the $1.48 theoretical standard deviation to see how many standard
deviations it rallied ($5/$1.48 = 3. 38 standard
deviations). Theoretically, with 99% of the
potential stock prices being up or down three
standard deviations, a 3. 38 standard deviation price change is pretty unusual.
If the vol of that
$80 stock was 60%
on Monday, then
0.0618 x 0.60 x $80
= $2.97. That’s theoretically one standard deviation, and
$5/$2.97 = 1.68. A
1.68 standard deviation price change is
big, but not unusual, theoretically.
The $5 price change in the $80 stock is
that same p/l for 100 shares. But in statistical terms, it means different things. The $5
change when vol was 30% is worthy of some
excitement. The $5 change when vol was
60%, not so much. In other words, when vol
was 60%, the market was perhaps expecting
a big price change, and the $5 move wasn’t as
big as it might have been.
To get the vol and stock price numbers
to do this analysis, hit the Charts page of
thinkorswim (Figure 1).
1—From “Studies,” add the “Imp Volatilty” study to
the Charts, which shows the overall implied vol
of a stock’s options.
2—Set the cursor over a date that’s before the price
change in question.
3—You'll now see the closing price of the underlying
stock or index on the upper left of the chart, and
the overall implied vol of the stock or index in
the upper left-hand corner of the Imp Volatility
Then consider the stock or index’s price
after a big change, and subtract the closing
price of the previous date from that post-move price to get the price change.
Adjust the vol for time, do some multipli-
cation and division, and determine the price
change’s standard deviations.
Why do you have to adjust vol by the square
root of the time frame? If a stock moves up
+1% one day, and down -0.999% the next, the
stock price has had almost zero net change.
But was it volatile? Yes. To make sure positive price changes don’t offset negative price
changes (which would give the impression
that there’s no vol), all the price changes are
squared to make them positive. By averaging
squared changes, you get a variance that’s
directly related to time. Because it’s a square
of the stock returns, that variance is harder
to interpret. So, we take its square root to get
back to the vol of stock returns. If you take
the square root of the variance, you must take
the square root of time, too. That’s why vol is
related to the square root of time.
Now, past performance does not guarantee future performance, and vol’s not a
perfect predictor of future potential returns.
Sometimes it can underestimate a stock’s
potential price changes, while other times it
can overestimate. In other words, vol might
predict a stock’s 3% move in a month, when it
actually moved 5% (underestimating). Or vol
might predict a stock’s 10% move in a month
when it actually moved 8% (overestimating).
Also keep in mind that the normal distribu-
tion at the base isn’t a perfect descriptor of
returns. In practice, returns are rarely dis-
tributed along a “clean” normal distribution.
All in all, this analysis gives price move-
ment a context. Going back to the $80 stock,
if the $5 rise in price represented a statis-
tically less likely 3. 38 standard deviation
change, a contrarian bearish trader might
seize that potential opportunity to enter
a trade, while a momentum bullish trader
might wait for the stock to drop before enter-
ing. If the $5 price rise represented a statis-
tically more likely 1.68 standard deviation
change, the contrarian bear might wait for
the stock to rally before shorting it, while a
momentum bull might get long at that point
and see more upside potential.
NO FREE THROWS
Use vol and statistics as one more metric in
your trading toolbox. It’s not a strategy in and
of itself. But it may help you determine entry
and exit points for certain trades by quantifying the “bigness” of price changes.
For more on the general risks of trading and trading
options, see page 37, #1– 2.
TAKE AC TION
For an overview on
volatility, read “Markets
Move. Get Over It.
An Options Volatility
Primer.” Go to the
online at tickertape.
FIGURE 1: Sizing up standard deviation of price change. Hover your cursor over a price bar before and after the
price change in question. Next, get the closing price and overall implied vol of the underlying stock or index. Then
plug the numbers into the formula and figure out the standard deviation of the price change. Source: thinkorswim® from
TD Ameritrade. For illustrative purposes only.
price of price
of price bar