Mark Hulbert’s 9/5/07 column addresses the 9-to-1 up day event, a bullish technical signal publicized by Martin Zweig in a 1986 book. It occurs when at least 90% of daily NYSE volume belongs to advancing issues. When the signal occurs in multiples over short periods, as it has recently, prospects for equities are “quite bullish” according to Mark Hulbert. A reader comments and inquires:
“A statistician [David Aronson, author of Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signals] confirms the significance of Zweig’s original observation. I don’t know whether he considered all possible confounding factors, such as low volume days, effect of externalities on the market, and others I can’t think of. This analysis sounds like so much epidemiological research, finding associations but never proving causality. For example, in the decade of the 1980s, alternate papers found that coffee consumption (greater than three cups per day) is and is not associated with increased risk of cancer of the pancreas. How much credence do you place in Hulbert’s article?”
Using S&P 500 index data for 1942-2006 (67 years), David Aronson finds an average return of about 5.2% in the 60 trading days after double 9-to-1 up days, significantly greater than the average return of about 1.1% during intervals of 60 trading days when there has not been such a signal. To follow up, we pose some questions to David Aronson and then consider strategies an investor might employ to exploit double 9-to-1 up day signals, as follows:
First, note that a large enough sample should allow the random variations of any interfering but unrelated factors to self-cancel. Statistical significance is a way to express the level of assurance that such self-cancellation has occurred.
Next, the Q&A with David Aronson:
Q: How many independent double 9-to-1 up day signals are there in the 67-year sample?
A: The longer the holding period after a signal, the fewer the number of independent double 9-to-1 up day signals. For a one-month holding period, there were about 65 signals.
Q: Did you notice whether the effect weakens after 1986, when Martin Zweig’s book came out?
A: As I recall, the signal did not weaken after its publication by Zweig.
Q: Do the excess returns systematically relate to the underlying (momentum) concept? Do double 8-2 and 7-3 up days have diminishing but still excess 60-day returns compared to double 9-to-1 up days? Do single 9-to-1 up-volume days have lesser excess returns? Do triple 9-to-1 up-volume days have greater returns? Do double 9-to-1 down-volume events have negative excess returns?
A: I did not investigate the signal’s effectiveness as a function of the ratio of up to down volume.
Q: Might there be any data snooping biases in the specifications of “double” or “9-to-1” or “60-day” return?
A: I wrote to Martin Zweig to ask how much he played with the ratio (9-to-1), the number of threshold events (double) and the maximum time between events (65 trading days) in settling on the double 9-to-1 up day signal, but he did not respond.
We conclude that: (1) double 9-to-1 up days are statistically significant signals of abnormal short-term mean returns at an average frequency of no greater than one event a year; and, (2) signal strength has not diminished over time despite publication.
Finally, how might an investor exploit the signal?
One possible strategy, ensuring the capability to exploit double 9-to-1 up day signals fully, is to hold funds patiently in 13-week Treasury bills (T-bills) until getting a signal and then buying and holding a broad market exchange-traded fund for 60 trading days before shifting back to T-bills. Assuming an average of one signal per year, this approach would in the past have captured an average capital gain in equities of roughly 5% plus a T-bill yield of perhaps 2%-4% annually. Trading costs would have been small. Total annual return would have approximately matched buy-and-hold on average, with lower volatility. However, all capital gains for the double 9-to-1 up day strategy would be short-term.
A more aggressive strategy of extending a buy-and-hold position with margin for 60 trading days after double 9-to-1 up day signals might make sense, provided one can tolerate the variability of returns after signals. Statistical trading means sticking with the strategy for many events (many years for this signal) to realize reliably the mean return.
An investor might assume the existence of other indicators that signal opportunities for abnormal mean returns during times when no double 9-to-1 up day signal is in effect. However, David Aronson’s study finds slim pickings during non-signal periods. Other kinds of signals therefore may well conflict with the double 9-to-1 up day signals such that funds are already committed based on one kind of signal when the other kind occurs.
In summary, double 9-to-1 up day events may reliably signal abnormal short-term returns, but designing a system to exploit such rare and unpredictable signals is problematic.
Frequently Asked Questions
What is a double 9-to-1 up day signal in the stock market?
A double 9-to-1 up day signal is a bullish technical indicator in which at least 90% of daily NYSE volume belongs to advancing issues on two occasions within a short period (Martin Zweig's rule uses a maximum of 65 trading days between events). A single 9-to-1 up day was publicized by Martin Zweig in a 1986 book. Multiple occurrences in a short span are viewed as especially bullish for equities.
Do double 9-to-1 up days predict higher stock market returns?
Double 9-to-1 up days have historically preceded higher short-term S&P 500 returns. David Aronson found an average return of about 5.2% over the next 60 trading days, versus about 1.1% for 60-day intervals without such a signal, using 1942-2006 data. The difference is statistically significant, and the signal did not appear to weaken after its 1986 publication, though signals occur at no more than about one per year.
How is the double 9-to-1 up day signal tested for statistical significance?
The double 9-to-1 up day signal was tested by comparing average S&P 500 returns over the 60 trading days after signals with average returns over 60-day intervals without signals, across 67 years (1942-2006). Statistical significance expresses assurance that random variations from unrelated factors have canceled out in a large enough sample. For a one-month holding period there were about 65 independent signals, and fewer independent signals exist for longer holding periods.
How does trading on double 9-to-1 up day signals compare to buy-and-hold investing?
A strategy of holding 13-week T-bills until a double 9-to-1 up day signal, then holding a broad market ETF for 60 trading days, would historically have approximately matched buy-and-hold total returns on average with lower volatility. Assuming about one signal per year, it would have captured roughly 5% in equity gains plus a T-bill yield of perhaps 2%-4% annually, with small trading costs. All capital gains would be short-term, and a more aggressive margin-based variant would require tolerance for variable post-signal returns.
What are the limitations of using the double 9-to-1 up day signal?
The double 9-to-1 up day signal is limited by its rarity, its unpredictability, and possible data snooping bias, since it is unknown how much Martin Zweig tuned the 9-to-1 ratio, the 'double' threshold and the 65-day window; Zweig did not respond to Aronson's inquiry. Aronson also did not test whether variants such as 8-to-2 or triple events behave consistently, and non-signal periods offered slim pickings, so other signals may conflict with it when funds are already committed. Exploiting the signal requires sticking with it over many years, so designing a system around it is problematic.