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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. Its the sum of the changes in the S&P 500 ($INX) over a set period of days.
Why does it work? Lets 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 stocks 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 markets 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 markets 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.
Heres an example: Lets 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 Exchanges 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 markets 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.
Lets 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 |
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As can be seen in the table, the VICs lowest levels have an average change of about -1 S&P point in the next three to five days. The VICs 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 500s 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 |
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*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 |
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*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 Bacons 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 publics 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 Mondays 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 packaging salesman for Sonoco -- is available at our Dailyspeculations.com 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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