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Posted
12/19/2002 |
The Speculator
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The Speculator
A
buy signal that's as easy as 2 + 2
Analysts often look to the
options-based volatility index, the VIX, when they're betting on the
market's volatility. We propose a simpler -- and more profitable --
gauge.
By Victor
Niederhoffer and Laurel Kenner
Investors take on risk only when there is extra
return in it. That is the main idea in investing and in much of
life. It is also the foundation of a new, highly accurate market
indicator developed by The Speculator.
Like most
things that work, our new indicator is based on a simple
calculation. It’s the sum of the changes in the S&P 500
($INX)
over a set period of days.
Why does it work? Let’s start
with the basis of modern finance theory, the capital asset pricing
model. The basic equation, true for a wide variety of assumptions in
theory and practice, is that the expected extra return on an
individual stock is proportional to the difference between the
market return and Treasury bills (say 6%), multiplied by its
sensitivity (or beta) to market moves. For example, if a stock’s
sensitivity to the market is 1.5, the extra return above Treasury
bill rates will be 1.5 x 6% = 9%.
For the market as a whole,
the relation is similar. The expected extra return of the market
portfolio is directly proportional to the variability of the market
multiplied by a factor relating to the average degree of risk
aversion of the market. As uncertainty increases, the market’s price
drops to compensate buyers for the uncertainty. This increases the
expected return, which on average is equal to the ex post
facto return.
Thousands of articles have been written on
this subject. The theory is encapsulated and documented in all
current corporate finance or investment textbooks and now makes its
way into most modern economics texts. (Our preferred references are
Investments by Zvi Bodie, Alex Kane and Alan Marcus, and
Principles of Corporate Finance by Stewart Myers and Richard
Brealey.)
Because the market’s return is proportional to its
variability, the return should be higher when variability is high
and lower when variability is low. The normal way to define
variability is with standard deviations. But just as good is the
simpler absolute value of the changes relative to the mean -- the
absolute deviation.
Here’s an example: Let’s say the S&P
500 on five consecutive days is 1,000, 1,010, 980, 1,020 and 1,000.
The absolute changes are 10, 30, 40 and 20. The sum -- the VIC
reading -- is 100.
The indicator we have developed is based
on counting the running total of the absolute variability in the
market -- the sum of day-to-day point changes, up and down, in
S&P 500 futures. The higher the value, the higher the expected
future returns.
Introducing the
VIC
We have taken the liberty of naming this indicator the
VIC, since it represents a simple improvement over the Chicago Board
Options Exchange’s Volatility Index, commonly referred to as the
VIX ($VIX.X).
The
VIX measures the implied volatility of options as a proxy for
investor sentiment. The general idea is that the higher the VIX, the
greater the return that can be expected in the future. Bullish
levels are said to be in the 30%-50% range, and bearish levels are
said to be in the 15%-25% range.
We have written about the
VIX ourselves. We showed that if you buy the market when the VIX
goes above 30% and cover your longs when it drops below 25%, you do
better than you would with a simple buy-and-hold strategy. The
results are somewhat non-random, but there are certain problems with
the strategy. The last buy signal was on June 20, when the S&P
500 was at 1,012. (We wrote about it then; click here
for that column.) The S&P 500 soon went down to 777, and is
still well below 1,000.
Even before this year, the VIX was
not wholly reliable. As the aftermath effects of the 1987 crash wore
off, the VIX went down to very low levels, hovering between 10% and
25% from 1991 to 1995. The indicator thus missed the entire 125%
rally in those five years.
An indicator based on options is
intrinsically problematic. VIX is based on the implied volatilities
of near-the-money options in the nearest months, and it becomes more
volatile as options expiration days approach. This leads to
anomalous and unstable readings. For example, on June 21, the VIX
was at 33.49. On the day after expiration, it dropped to 29.87.
Furthermore, option prices are set with a view to ensnaring
different market participants with varying degrees of strength and
capitalization. Thus, option prices -- and VIX levels -- often show
unusual spikes relating to the raging battle between the various
participants in the market firmament. A simpler, and therefore
preferable, method of measuring market uncertainty is to take
account of the actual uncertainty in the market over a period of
days.
Putting VIC to the
test
A simple enumeration of one-, five-, 10- and 20-day
moves over the last six years proves the value of the VIC. A typical
result is that the correlation between the 10-day VIC and the
market’s move over the next five days is approximately 0.10. Using
simulation techniques (since there is a degree of overlap in the
1,500 observations), we find that the odds against a value at least
as high as this occurring by chance variations alone are some 4 in
100.
Putting it all together, the natural extension is to buy
the market when the VIC is at a relatively high level and to sell it
at a relatively low level. To come with an ideal indicator, one has
to compute the VIC in the last one, three, five, 10 and 20 days, and
develop a specific classification scheme to signify when it is
bearish and when it is bullish. We developed a retrospective system
of classification, and found very good results if one buys the
S&P 500 when the 10-day VIC is above 90 and sells when it is
below 60.
Let’s focus on those 10-day VIC levels:
| 10-day VIC and expected moves in the
S&P |
| VIC level |
Observations |
Next 3 days |
Next 5 days |
| 0-30 |
45 |
-1 |
-1 |
| 30-60 |
259 |
1 |
2 |
| 60-90 |
395 |
0.5 |
0 |
| 90-120 |
435 |
-2 |
-2.5 |
| 120+ |
600 |
3 |
5 | |
As can
be seen in the table, the VIC’s lowest levels have an average change
of about -1 S&P point in the next three to five days. The VIC’s
highest level has an average change of some 4 points over the next
three to five days.
The correlation between 10-day VIC and
the S&P 500’s change over the next three days is 0.09. The
probability of a correlation this high, with overlapping intervals
based on some 2,500 observations, turns out to be about 3 in 100.
Similar results, though less strong, would occur from a
study of the VIX. However, for the reasons given above, the VIC is
theoretically and empirically likely to be less subject than the VIX
to noise and manipulation. The correlation between the 10-day VIC
and the VIX level that day is 0.56. We ran our system by James
Altucher, who runs the hedge fund Subway Capital out of Cold
Springs, N.Y. He took the sum of highs minus lows for periods from 1
to 20 days and found similar correlations between the VIC and the
VIX, ranging from 0.45 to 0.65.
Taking it a bit further, we
tested market indicators based on the VIC. We wanted to keep it
simple and symmetrical while holding to our fundamental theme: "High
is a good time to buy."
The table below gives buy and sell
dates over the past six years for a 10-day VIC system. The buys
showed an average appreciation of 23 points to the next sale, and
the sells showed an average appreciation of 1.7 points to the next
buy. Simulating this with random buy-and-hold periods of comparable
durations, we find that profits as great as this would occur by
chance on slightly less than 1 in 15
occasions.
Unfortunately, the next-to-last trade, a buy at
1,496, lost 329 points, and the last one is down 243 points, marked
to market. Thus, the VIC is by no means the easy street to riches.
10-day VIC
| Buy S&P when VIC is above 90, sell
below 60 (Prices are S&P futures) |
| Date |
Buy |
Sell |
Profit/Loss |
| 4/1/1997 |
765 |
|
|
| 5/22/1997 |
|
840.25 |
75.25 |
| 6/24/1997 |
905 |
|
|
| 8/1/1997 |
|
953 |
48 |
| 8/15/1997 |
898.8 |
|
|
| 10/31/1997 |
|
976.35 |
77.55 |
| 10/24/1997 |
944 |
|
|
| 12/9/1997 |
|
978.9 |
34.9 |
| 1/9/1998 |
929.5 |
|
|
| 2/4/998 |
|
1,009.70 |
80.2 |
| 4/27/1998 |
1,093.50 |
|
|
| 5/22/1998 |
|
1,114 |
20.5 |
| 6/5/1998 |
1,117.40 |
|
|
| 7/16/1998 |
|
1,191.20 |
73.8 |
| 7/30/1998 |
1,146.10 |
|
|
| 7/19/1999 |
|
1,418 |
271.9 |
| 7/22/1999 |
1,367.80 |
|
|
| 8/24/2000 |
|
1,515.20 |
147.4 |
| 9/8/2000 |
1,496.60 |
|
|
| 3/18/2002 |
|
1,167.20 |
-329.4 |
| 4/16/2002 |
1,129.70 |
|
|
| 12/13/2002* |
|
886.5 |
-243.2 |
|
|
Average |
23.3 |
|
|
St dev |
151.53 | | *marked to market
| Sell S&P when VIC is above 90, buy
below 60 (Prices are S&P futures) |
| Date |
Buy |
Sell |
Profit/Loss |
| 1/16/1996 |
610.9 |
|
|
| 4/1/1997 |
|
765 |
154.1 |
| 5/22/1997 |
840.25 |
|
|
| 6/24/1997 |
|
905 |
64.75 |
| 8/1/1997 |
953 |
|
|
| 8/15/1997 |
|
898.8 |
-54.2 |
| 10/13/1997 |
976.35 |
|
|
| 10/24/1997 |
|
944 |
-32.35 |
| 12/9/1997 |
978.9 |
|
|
| 1/9/1998 |
|
929.5 |
-49.4 |
| 2/4/1998 |
1,009.70 |
|
|
| 4/27/1998 |
|
1,093.50 |
83.8 |
| 5/22/1998 |
1,114 |
|
|
| 6/5/1998 |
|
1,117.40 |
3.4 |
| 7/16/1998 |
1,191.20 |
|
|
| 7/30/1998 |
|
1,146.10 |
-45.1 |
| 7/19/1999 |
1,418 |
|
|
| 7/22/1999 |
|
1,367.80 |
-50.2 |
| 8/24/2000 |
1,515.20 |
|
|
| 9/8/2000 |
|
1,496.60 |
-18.6 |
| 3/18/2002 |
1,167.20 |
|
|
| 4/16/2002 |
|
1,129.70 |
-37.5 |
|
|
Average |
1.7 |
|
|
St dev |
69.05 | | *marked to market
The system shown
in the table is not the best way of splitting the data or the best
interval for computing the VIC. With some fine-tuning, we can triple
the profits. However, we must be mindful of the timeless principle
of ever-changing cycles laid down in Robert Bacon’s Secrets of
Professional Turf Betting, an out-of-print 1956 classic that we
can never quote often enough:
In actual racing, the percentage of winners does
not remain constant, as the public’s play beats down the prices of
horses picked by any set scheme. Some well-to-do horsemen who sent
their horses out to do their best for probable betting prices of
3-to-1 “cooled off” as the prices sank below 5-to-2. Instead of
trying their hardest to win, they sent the horses out to win if
they could win easily. But the boys were told not to punish the
animals, told to pull them back out of the money in the stretch if
they saw an easy winning was not possible.
The horsemen
knew that this pulling back out of the money would make a bad race
show as the last outing in the past performance charts, thus
putting the public off the horse for next time. We
believe one of the virtues of the VIC is that it can be applied to
individual stocks, by computing the running total of absolute
changes for, say, the last 10 days. Mr. Altucher of Subway Capital
has kindly performed such an extension and reports very promising
results.
The challenge: you need to run statistical tests on
each stock over time. There's no set gauge to start with -- it's a
concept for experimentation.
As of Monday’s close, the last
10 days’ absolute S&P 500 change is 85.3, a somewhat neutral
level. We will report the bullishness or bearishness of 10-day VIC
in future columns and make daily updates available on our Web site.
End Note
We generally avoid all seasonal
trades in our activities. We have found too often that in practice
the future seasonality is completely different from whatever past
seasonality we find up our sleeve. However, as Christmas approaches,
we plan to buy the market on Dec. 19 or Dec. 20 at the close with
the idea of holding until a few days after Christmas. This trade has
an expectation of some 1%, a two-thirds chance of being profitable
and a 90% shot that the actual change will be between 0 and 2%,
based on past data. The full workout -- inspired by natural
philosopher and trader Duncan Coker, formerly a paper salesman for
Sonoco -- is available at our Daily Speculations Web
site.
Also, a reader writes to Vic: "You seem to be a well
meaning person who has made every mistake in the book. Can you
recommend how I can avoid same?"
Yes, we believe that we have
succumbed to every past mistake it's possible to make. However, for
the future, there are doubtless other pitfalls and snares waiting
for us. To try to minimize these, may we encourage our readers to
write to us through our Web site so that we can learn together. We
will share all education we receive and reward you with a cane for
particularly good ones.
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