Daily Bias

Is there one day that is statistically better to trade verses another?

I’m hoping the answer is no, otherwise something will be a skew with my perception of the option market, but I have to run a test to be sure.

I created a test that allowed each scenario to open a trade a specific number of days from expiration. The days ranged from 1 to 90 days testing all the days in the front three months. The test created all permutations of those days and the deltas

0.05, 0.07, 0.1, 0.15, 0.18, 0.2, 0.22, 0.25, 0.27, 0.3, 0.35, 0.40

For instance, the first scenario could open up trades 1 day from expiration but only with a 0.05 delta on the short strikes. This resulted in 1068 different scenarios. All trades were held to expiration.

After the test results were generated, I created a heatmap of the number of trades for each delta and day range (ignoring any that had less than 25 trades).


A very interesting pattern emerges. The green shows high number of trades, and the red lower numbers. There is a definite pattern where we find lots of trades for short expiration and small delta increasing linearly as days from expiration and delta are both increased. Conversely, trades are harder to find for low delta/long duration and high delta/short duration.

Another peculiar pattern emerges. Notice every 5 days or so the entire chain for that day it is harder to find acceptable trades compared to a day before or after. These bands all occur on Mondays. But after (too much) analysis, it turns out that these abnormalities are due to holidays. Many of the days when the market are closed are generally Mondays or Fridays leading to lower trades on those days. This confirms that my tests are finding the correct number of trades.

Next I create a heatmap of the average profit factors for every Delta and Day. I then eliminated all trades with excessively low number of trades (under 25). The results were a little surprising. In general, I would not except any particular days to stand out as being particularly good or bad to trade on. The map shows that generally, the higher delta trades perform worse; since these trades are held to expiration this is inline with the results we found in the baseline test. However, several anomalies also appear in the data.


First, look at the Day 2 row. This row actually reflects trading on the Thursday before expiration (expiration actually being Saturday, and no trading on Friday).  A value of 100.0 for the PF reflects that there were only winning trades. But the entire row has a very high PF. These are very low expected return trades, but consistently winners. These would be relatively binary trades that largely depend on the opening price the next day. A gap up/down on the expiration day could incur a big loss, but historically, has not.

It is also apparent from the first table that these trades are harder to come by. Usually the day before expiration, the frequency of deltas changes dramatically and less variety can be found.

Now I am not sure how easy it would be to get fills with low deltas just 1 day before expiration. Strictly speaking, these are trades that are assuming that there is negligible gap up or down the following Friday morning.

There are a few hotspots around the Delta-5 trades during days 10, 16, and 47. If I take a deeper look at the biggest hotspot (day 16) it turns out that it was just a statistical fluke. The days before and after (days 14 and 15) both incurred one more loss than did day 16. Day 16 had just 1 loss, and during the downturn in Nov 2008 it managed to eek out a profit when its neighbors took a loss. There were large swings in prices those days. And because of that, I can conclude that there was nothing special about trades on this day. The other days fall into very similar patterns. Just one less loss was able to catapult the profit factor for these scenarios.

I look at one final heat map on the data. This time, I want to look at which trades are profitable or not. I use the last heat map, but color all cells green that have a PF >1, otherwise red:


This is very similar to the last heat map, but the patterns are much more stark. Clearly, low delta trades do better when held to expiration than do high delta trades. There are a few outliers, but they have relatively close distance to their neighbors that they do not stand out as anomalous.


There appears to be no daily bias from the historical RUT data. Certainly, trades on the day prior to expiration day may statistically have an advantage, but for our test cases they have no room for management or adjustment.

Data Files

Daily Bias Test Excel Data


Permutations 1056
Profitable Scenarios 522 49%
Total Trades 67366
Profitable Trades 49815 74%
Expired 67366 100%
Test Duration 2.06(min)

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