CISCO Futures
1-303-306-1521 1-800 800 7227
http://www.cisco-futures.com
dljones@cisco-futures.com
Volatility is extremely useful in evaluating risk and trading potential in
auction markets. It is used by day, swing and option traders as well as long
term investors. Only the investors have enough data to find a statistically
valid measure, the standard deviation of several hundred days of price range.
Even here, there is the limiting assumption of equilibrium. In the shorter
timeframes of a day or two, equilibrium is not present. In fact, traders are
looking for disequilibrium (moving value); that's where the
opportunity is. The trader needs to know yesterday's volatility and the
day before, not the average for the year. Changes in local, day-to-day,
volatility alerts the daytrader to potential changes in price.
It is often observed that markets begin moving internally before starting
to trend. Once movement is underway, volatility usually continues to increase
for a period and then tends to relax back, decreasing as the market moves back
into congestion. When the move is over, volatility goes back to longer term
average values. If you know the volatility is increasing or decreasing
you have a valuable decision tool. The size and direction of the volatility
prepares you for price change and lets you quantitize and time your risk.
We will first define exactly what short time frame volatility is and
then show how to compute it on a day-to-day basis. Day, swing and
option traders can have a realistic value and history within which to set their
trading strategy.
Volatility Defined
Volatility is simple in concept, surprisingly complex in it's determination.
Gordon Gustafson in the June 2001 Stocks and Commodities defined the short
timeframe volatility as the ATR (a days true range). Kevin Lund in the May
2002 Stocks and Commodities defined volatility as "rate of change in price
over a specific time period". Both err. Volatility is an (average) price
fluctuation, not a velocity. It is created by differences in opinions about
value. Mixed in with a volatility measurement is random noise, a fluctuation
due in part to the tick size. If a market is in a trend, volatility (and
noise) rides along, helping to obscure the change in value.
Option traders often use implied volatility, a value that is backed out
of the traded option price. Since price itself contains noise and other fluctuations,
implied volatility includes "real" volatility plus an unknown fluctuation
factor. Implied volatility is prone to all those errors associated
with price variation (noise, manipulation, large trader's strategies, etc).
Long Term Capital Management which lost $1.3 trillion, had its largest
positions in implied volatility trades (R. Lowenstein, When Genius
Failed....., Random House, 2000).
Sampling
The definition of volatility is straightforward since it is just
a measure of price range variability (average range). Making the measurement
with limited data is not so trivial. It depends
on appropriate sampling. Statisticians have much to say about sampling
theory, which for this work boils down to "have enough data to get a
realistic average". Noise (random fluctuation) is the second factor in
market fluctuation and must be understood. If it is minimal it can be
ignored, if not it must be sorted out of the final result.
The problem we solve is "what was yesterday's volatility". As noted, the key
to finding a days volatility lies in being able to validly break the day down
into its constituent parts. Fortunately we have some experience with the Market
Profile data base, which is developed from half-hour sampling. So we start
with the Meta-Profile data and its half-hour bars. From
there we will generalize, showing that half-hour bars are quite good for the
purpose, but 25 minute bars are probably somewhat better.
Volatility from Half-Hour Meta-Profile Bars
At CISCO we have calculated volatility from the half-hour bars in the
Meta-Profile for many years. Our use of 30 minute range bars rests on the
fact that the Meta-Profile is a mature methodology for describing market
value. (Meta-Profile volatility is displayed in reference 4., as are
volatility history tables.)
Practically, we develop Meta-Profiles for other purposes, so it is
a convenient database. Questions
have arisen from time to time about whether a 15 or 20 minute time frame, say,
might be a better descriptor. In this report, I will show
you the results of a study that validates the 30 minute time frame as quite
good, with the optimum time frame around 25 minutes. Also, these new
calculations are divorced from the CBOT Market Profile, so that anyone with a
ticker can find the volatility.
Quantitative volatilities benefit the trader by replacing the general
"hmmm, I think the SP volatility is increasing" with the specific ("SP volatility
on Monday 12/16/02 is 28.1, on Tuesday it is 28.1, and on Wednesday it is
37.9") (ref 5). In this example, the market was balancing
on Monday, Tuesday and Wednesday (ref 5). The increase in volatility on
Wednesday is a
tip-off that new trading interest came into the market on Wednesday. You would
be alerted to look into your trading methodology for Thursday's market. Maybe
something is afoot.
In fact, the close on Wednesday was 89150, Thursday closed at 88480, so
the big jump in volatility gave you advance notice of a possible trading
opportunity.
Volatility from the Meta-Profile
You can understand volatility measurement easiest with an example from
a Meta-Profile and it's half hour bars. We use the eMini S&P to show
that the volatility obtained for December 18 (39.82) is essentially the
same as for the SP cited above (37.9). The eMini and the big SP contract
differ primarily in their minimum tick size, so the volatilities should
differ to some degree. The half hour bars in
Figure V1 will be used to calculate the volatility in Figure V2.
META-PROFILE REPORT FOR 12 18 02
AND SEGMENTED AUCTION
COMMODITY -- Mini S&P 500 (CME-IOM)MAR 03
Price Brackets Half-Hour Bars
89750 B B
89725 B B
89700 B |B
89675 B |B |
89650 B |B | |
89625 B |B | |
89600 B |B | |
89575 B |B | |
89550 B >B | |
89525 B |B | |
89500 BCI |B |C | |I
89475 BCI |B |C | |I
89450 BCI |B |C | |I
89425 BCI |B |C | |I
89400 BCI B |C | |I
89375 BCIK B >C | |I |K
89350 BCIK B |C | | |I | |K
89325 BCIK B |C > | |I | |K |
89300 CHIK |C | | | |H |I | |K | |
89275 CHIKL |C | | | |H |I | |K |L |
89250 CHIKL |C | | | | |H |I | |K |L | |
89225 CHIKL |C | | | | |H |I | |K |L | |
89200 CGHIKLP |C | | | |G |H |I | |K |L | | |P
89175 CGHIKLP |C | | | |G |H |I | |K |L | | |P
89150 CGHIKLP C | | | |G |H |I | |K |L | | |P
89125 CDGHIJKLNP C |D > | |G |H |I |J |K |L | |N |P
89100 CDFGHIJKLNP C |D | >F >G >H >I >J >K >L | |N |P
89075 CDFGHIJKLMNP C |D | |F |G |H |I |J |K |L >M >N >P
89050 CDFGHIJKLMNP C |D | |F |G |H |I |J |K |L |M |N |P
89025 CDFGHIJKLMNP C |D | |F |G |H |I |J |K |L |M |N |P
89000 CDFGHIJKLMNP C |D | |F |G |H |I |J |K |L |M |N |P
88975 CDFGIJKLMNP C D | |F |G | |I |J |K |L |M |N |P
88950 DFJKLMNP D | |F | | | |J |K |L |M |N |P
88925 DEFJKLMNP D |E |F | | | |J |K |L |M |N |P
88900 DEFJLMNP D |E |F | | |J | |L |M |N |P
88875 DEFJLMNP D |E |F | | |J | |L |M |N |P
88850 DEFLMNP D |E |F | | | |L |M |N |P
88825 DEFLMNP D |E |F | | | |L |M |N |P
88800 DEFLMNP D |E |F | | | L |M |N |P
88775 DELMNP D |E | | | L M |N |P
88750 DELMNP D |E | | | L M N |P
88725 DEMN D |E | | | M N
88700 DEMN D |E | | M N
88675 DEM D |E | | M
88650 E |E | |
88625 E |E | |
88600 E |E |
Figure V1. Meta-Profile of eMini S&P, December 18, 2002. The
half-hour bars on the right show the cumulative POC
(point of control) identified with the > symbol. The
vertical line (|) delineates the Value Area as it changes
throughout the day. B is 8:30 to 9, C is 9 to 9:30 and
so on. Meta-Profile from CISCO archives.
Calculation of Volatility from half-hour bars (MP)
Half-hour bar range
B 89750 - 89325 425
C 89500 - 88975 525
D 89125 - 88675 450
E 88925 - 88600 325
F 89100 - 88800 300
G 89200 - 88975 225
H 89300 - 89000 300
I 89500 - 88975 525
J 89125 - 88875 250
K 89375 - 88925 450
L 89275 - 88750 525
M 89075 - 88675 400
N 89125 - 88700 425
P 89200 - 88750 450
TOTAL 5575
VOLATILITY 5575/14 = 398.21 VTY = 39.82 (basis index)
$VTY = 199
Figure V2. Half-Hour Bars of eMini S&P, December 18, 2002. The
volatility for the day is 39.82 ($199).
A more general view of volatility for the day trader opens the question
of the source of the fluctuation included in our measurement. There
are two components,
noise from random market movement and the signal from the differing
opinions of traders. Noise is always there at about the same level.
The real change in volatility we wish to measure comes from changing
market forces, or "traders interest".
Noise
Calculating volatility from the Meta-Profile bars, of course,
includes any background noise. Noise will always
be additive to the fluctuation caused by trader's differing opinions.
Noise results in large part from the size of the minimum tick. Figure V3
shows a few seconds of ticks for the eMini on December 18, 2002.
8:30: 0 89600
8:30: 0 89625 +25
8:30: 0 89600
8:30: 0 89625 +25
8:30: 0 89600
8:30: 0 89625 +25
8:30: 0 89600
8:30: 2 89625 +25
8:30: 3 89600
8:30: 3 89625 +25
8:30: 3 89600
8:30: 3 89625 +25
8:30: 3 89600
8:30: 3 89625 +25
8:30: 3 89600
8:30: 6 89575
8:30: 7 89600 +25
8:30: 7 89575
8:30: 7 89600 +25
8:30: 7 89575
8:30: 7 89600 +25
8:30: 7 89575
8:30: 8 89600 +25
8:30: 8 89575
8:30: 8 89600 +25
8:30: 8 89575
8:30:10 89550
8:30:10 89575 +25
8:30:11 89600 +25
8:30:11 89575
8:30:11 89550
8:30:11 89575 +25
8:30:11 89600 +25
8:30:11 89575
8:30:11 89600 +25
8:30:11 89575
8:30:13 89600 +25
8:30:13 89575
8:30:13 89600 +25
8:30:13 89575
8:30:14 89600 +25
8:30:14 89575
8:30:14 89600 +25
Figure V3. Ticks, eMini S&P, December 18, 2002, first few seconds.
Randomness display. Only up ticks listed for clarity.
This market first ticked at 89600; ticked up, ticked down and forty three
ticks later was back where it started. A range measurement would show
an average of somewhat more than 25, all of which is noise. This short
sample does not treat the actual noise level. It must be greater than
25, the minimum tick. How much greater is difficult to know since it is
random. We will devise a way to make the estimate.
Figure V1 shows that from 8:30 to 9:00 price
traded in the range of 89750 to 89325. Very little of that 425 range is
due to noise because the bar is probably quite large compared to the noise,
as will be made clear by figure V4 and discussion.
Length of Bar, a Time Effect
Another effect that will alter a volatility calculation is the time length
of the price bar. Longer times naturally have wider ranges.
At longer times the increase in length dominates. At the limit of a single
bar for the day, we end up with the day's range 89750 - 88600 or 1150. Recall
that Gustafson defined the volatility as the ATR, in this case 1150. For the
investor, ATR is one day's input to the year total. For the trader, the local
volatility is embedded in the ATR and is a fractional part of it.
Shortening the bar to one-half or one-quarter of the day still leaves the
volatility measure dominated by the length of the bars, as explained in
figure V4.
If the volatility calculation is made with shorter bars, say
one minute, the noise could be significant. If the time bars are short
enough, only noise will be measured.
The volatility analysis from tick bars that range from very short to very
long pass through three distributions. Short bars are strongly affected
by the noise and generate a parabolic distribution. Long bar results are
dominated by the length of the bar, forming a linear distribution.
In the transition from bars that are too short to those too long
is a region
where the volitility is dominant. The short bars describe a parabola,
the long ones create a straight line. The transition between too long and
too short forms a very clear transition, a "knee". The knee is obvious in
figure V4.
Figure V4. Volatility calculated with tick bars of varying length for
eMini day trading (8:30 to 15:15) on December 18, 2002.
At very short times (1, 3, 5, 10, 15 and 20 minutes) the
calculated volatility forms an arc with increasing time.
Between 20 minutes and 30 minutes the arc transitions
into a straight line. The beginning of the transition
area (the knee) is where the noise has become small relative
to the volatility being measured. The end of the transition is
where the time effect (larger bars) has overcome the
volatility.
Evaluating the Volatility Measurement
The knee region, bars from 20 to 30 minutes, is where the noise has become
small compared to the market volatility and bar length is not yet
dominant. The middle of the knee is around the 25 minute bar. So, if
you wish to measure volatility, you need to only average the 25 minute bars.
If you are currently using Meta-Profiles and the volatility from 30 minute
tick bars, you are using volatilities that are slightly too high, but still
acceptable for most purposes.
Other commodities we studied behave the same way, with the knee
in about the same place. The level of volatility differs from commodity to
commodity and for a particular commodity, from day to day.
One limitation of the measurement is the need for an adequate tick rate,
adequate trading.
You are measuring time bars. If there are not enough ticks, not enough
trading, the measurement is invalid. You would not want to try to measure
the volatility of lightly traded futures with this methodology.
Value of a Quantified Measure
If you have a numeric value of volatility, you have an important piece of
information for evaluating your trading risk. A general rule is to not
set stops within the volatility envelope. If you do, market fluctuation
may well stop you out. This is different from being wrong on your trade.
It is simple statistics. Traders do sometimes set their risk within
the volatility, thinking that they are limiting risk. This is self
defeating, since it ensures an elevated number of losses.
For many trading purposes, the volatility absolute value is not so important
as the relative value. In the example above, going from 28 to 38 is a
35 percent jump. If you did not have a calculated number, still such
a change might catch your eye. What you are looking for is the alert that
a change in value is in the wind.
You should gain several significant pieces of information from this article
that will help your trading.
First, you can use quantitative volatilities in your trading. You cannot
use the classical annualized volatility because it is not timely.
Secondly, if you have a ticker, you can create your own volatility and you
now know which time bars to use.
Third, you are aware of the effect of noise and impliedly, you know that
looking too close at the market may mean merely looking at noise.
Fourth, you now have a feel for the utility of quantative versus qualitative
uses of volatility.