Are jumbo gaps an oxymoron like "jumbo shrimp"? I found some similarity between shrimp sizes and normalized up-side gaps (see Chart 1). Do such jumbo gaps offer trading opportunities? I tried to quantify just that, and here is what I found. By the way, just as the number of shrimp per pound drops rapidly once the size goes above "Jumbo", similarly the frequency of occurrence of upside gaps (normalized by the 10-day average true range) drops rapidly past some critical "Jumbo" size. I decided to focus my exploration on such jumbo gaps.

*Figure 1: The visual is to remind me I am looking for a jumbo shrimp in a gap: a large gap in an otherwise ordinary string of stock prices.*

*Chart 1: I used the terminology of Shrimp Sizes to categorize my distribution of normalized gaps (see details below). The shrimps per pound drops meaningfully once we get past the Jumbo size, and so I had to calibrate my normalization parameters to the same scale for emphasis, so that gaps at and above the Jumbo size would offer meaningful opportunities to feast on price moves.*

**Up-side Gap Definition**

I focused on up-side gaps only for this exploration. The recent upside jump in Staples (SPLS) illustrates the general concept. The low of the last bar is above the high of the previous day. I want to measure this gap, and find some way to normalize it. For example, I used the 10-day average True Range (from the previous day) as the reference in Chart 1. But, I could have used the x-day standard deviation, y-day average high-low difference, z-day highest high-lowest low range or any other measure of price action I choose.

Chart 2: The gap on the right is more than the previous day's 10-day average True Range. (A discussion of True Range is here.)

**Why Up-side Gaps Occur**

Gaps occur because there is a supply-demand imbalance at the current price, and hence the next price paid must be well above (or below) the previous close to clear the market. For example, after a strong earnings report, there may be "excess" demand to buy a stock. Say the "demand" is for 10,000 shares, and the average volume of the past 30-days is just 1000 shares. Thus, unless many new sellers appear very quickly, the existing sellers can ask for a higher price, and buyers must decide if they are willing to buy at that higher price a seller is asking. Thus, shares will be marked up to clear the market (match supply with demand). Naturally, the reverse can occur to produce a down-side gap.

Gaps occur frequently, and can sometimes be only momentary, lasting for just minutes or hours. We need to study the distribution of gaps to develop a trading strategy or process.

**Normalizing the Gap**

I will use the 10-day average true range (ATR10) as my measure of price movement to calibrate the gap. The daily True Range measures the price range allowing for gaps. (A discussion of True Range is here.) Thus, if a gap occurs today, I will use yesterday's value of ATR10 to normalize today's gap. Thus, I will say today's gap was x-times yesterday's ATR10 for the stock. In equation form,

Today's Normalized Gap (NG) = (Today's Low - Yesterday's High)/Yesterday's ATR10.

Naturally, if today's low is below yesterday's high, there is no gap, i.e., NG must be greater than zero. Also, the yesterday's ATR10 must not be zero, otherwise NG is undefined. Given those two conditions, (NG > 0; ATR10 > 0), we can "normalize" every gap in every market and compare them on an apples-to-apples basis. This means we can properly compare a normalized gap today to any other normalized gap in the past in the same market, or to any other normalized gap in any other market.

**Long-Term Distribution of 81,535 Gaps**

I studied more than 900 stocks from the Russell-1000 universe and went back up to 13 years to quantify the distribution of gaps seen in those stocks. These stocks represent a large chunk of the market, and the very long time period ensures that I have included the crash of 2008. I each case, I normalized the gap using the ATR10. This is a very broad and deep study in order to quantify the distribution of gaps that have been observed in the market. Naturally, the data I use for the stocks will affect the distribution I find. I expect that the very large amount of data I am using will overcome random effects of data errors which may exist in the data. The distribution I found is shown in Chart 3 (you got a preview of the data in Chart 1 above).

*Chart 3: The distribution of gaps observed in the Russell 1000 universe dating back to 2005. The gaps are normalized by the previous day's 10-day average True Range. The sample had 81,535 gaps of various sizes. The histogram has increments of 0.25 ATR10. The smallest gaps on the left were smaller than 0.25*ATR10. The largest gaps on the right were more than 2*ATR10. The frequency of occurrence (blue line) is on the left. The cumulative frequency (red line) is on the right-hand Y-axis. Only about 5.6% of the sample had normalized gap greater than the previous day's 10-day average true range.*

The red-line in Chart 3 shows that fewer than 6% of all gaps in the sample were "Jumbo" gaps i.e. greater than 1*ATR10. Hence, I will study the profitability of gaps equal to or greater than ATR10.

**Model: Enter on Following Open, Buy-and-Hold for 5-days or 50-days **

I used a very simple model to test the basic idea of the profitability of jumbo gaps. The model is summarized as follows:

1) Check to see if we have a jumbo gap after today's close (Low > yesterday's high + yesterday's 10-day average true range).

2) If true, buy on tomorrow's open.

3) If in trade, exit on the close 5-days from entry day, or 50-days from entry day.

I did not use any specific trade sizing rule, but just computed the 5-day and 50-day percent gain or loss to get a sense for the distribution of gap performance. This is clearly not a system test, since it treats each gap as a separate event and just focuses on gap-by-gap profitability, rather than look at the overall portfolio performance. The results themselves do not include the effects of trading costs or taxes, since we are just trying to understand the effect of gap size on the distribution of profitability over the holding period. The model does not include the effect of risk-control measures such as trailing stops at this particular step.

**Distribution of Returns**

Table 1: Sample Size = 4,446 Events: Jumbo Gap on Russell 1000 Universe (Data back to 2005 where available) |
||

5-day Holding Period | 50-day Holding Period | |

Percent Profitable | 53.73% | 61.24% |

Average Gain/Loss | 0.43% | 3.08% |

Worst Loss from Entry | -36.80% | -76.04% |

Largest Gain from Entry | 50.83% | 124.15% |

Std. Dev. Across All Gaps | 4.98% | 14.30% |

The overall results are summarized as follows (see Table 1). The sample size is quite large, at 4,446 events, with about 54% profitable at the 5-day holding period, and about 61% profitable at the 50-day holding period. As we should expect, the average gain is greater for the longer holding period (0.43% vs 3.08%), and the maximum losses and gains also increase with holding period. As is to be expected, the standard deviation (i.e. variability) in returns is much greater for the longer holding period (14.23% vs 4.98%). The distribution of returns is shown in Chart 4. The blue-line (for 5-day holding period) is clearly more peaked i.e. the returns are grouped more tightly together, since the market can only move so much in five days.

*Chart 4: A distribution of returns of gap-by-gap test of profitability. The blue line is for a 5-day holding period, and the red line is for a 50-day holding period. The horizontal axis shows the gains or losses in percent, and the vertical axis shows the number of gaps with their gains or losses in each horizontal interval. The shorter holding period is more peaked, i.e., the range of returns is smaller than the 50-day holding period (red line) as we should expect.*

**Gaps in ETFs**

So far I have only discussed gaps in individual stocks. Naturally, you could look for gaps in portfolios, such as those encapsulated in ETFs. It is even harder to move entire portfolios over large gaps, so one could argue that gaps are perhaps more significant in ETFs. I tested the iShares and SPDR ETF universes, and found a bit higher profitability around 67% for the longer holding period. As is to be expected, the sample of gaps found was smaller, since it is difficult to shift entire portfolios across gaps.

**Gap Test Has No Market Specific Features**

An important detail to recognize is that my test had no market specific information, and hence the trading system based on it can be very robust. For example, I did not limit my testing to a single market, or use any market-specific evaluation rules. In other words, I did not treat any one stock differently from any other. Many trading systems are based on market specific features, or a small combination of market indexes (say SPY and VIX), or have market-specific entry, exit or profit conditions. Since I have normalized the gap, the sizing, trailing stops etc. can be also be written in terms of the average true range, for a market-independent trading system.

**Gaps Are Not Dependent on Trends in Market Indexes**

The occurrence of gaps is related to news about a particular stock, and not to the market as a whole. Thus, this is not a trend-following system such as using moving averages on a market index. The holding period clearly affects the returns as well as the correlation of this strategy to other strategies. The longer the holding period, the more the returns will look like a trend-following system. Naturally, it is possible that jumbo gaps are more profitable during major uptrends in the market as a whole, but it is important to recognize that the gaps themselves are not related to broad trends in market indexes.

**Design of Trading Systems with Jumbo Gaps**

On the whole, trading jumbo gaps could be profitable, but one has to design a system around it. It can get complicated, so I will not go into a full exploration here. For example, a trailing stop can set from Chart 4 to avoid the worst losers. The trailing stop may also cut off some profitable trades, so this is a tradeoff that will depend on your risk preferences. Since there are a large number of stocks, you will have to decide how many positions you are willing to put on, and how you will size them. You can try a variety of entry strategies. You could try other exit strategies, such as a trailing stop, or a profit target. There is also the research track of adding filters, to look at jumbo gaps in rising (or falling) stocks or markets and so on. Thus, starting with the jumbo gap concept, you could construct many different trading strategies. Naturally, the distribution of returns for a trading system will look quite different from say Chart 4. Since every trading system needs some tradeoffs, and reflects the needs of the trader, it is up to you to decide how you will pair a jumbo gap with other rules to create a system.

**Scan Code for Jumbo Gap**

Here is my quick scan code for Jumbo Gaps.

The results of a scan after yesterday's close look like this:

*Chart 5: A scan of the NYSE stocks with jumbo gaps on June 22.*

The charts for the four stocks and ETFs identified in Chart 5 clearly show large gaps (see Chart 6).

*Chart 6: The objects from the overnight scan all show jumbo gaps. They all show strong to very strong trend strength via CTM.*

**Summary**

Jumbo gaps can be used as a robust building block to create well diversified trading systems.

I hope this discussion will whet your appetite for trading jumbo gaps.

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Enjoy!

Tushar