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Wednesday, May 2, 2018

The Best Day of the Week to Buy Index Funds

This post is inspired by a similar article from Rob@MustardSeedMoney. In his article Rob identifies the best day for investing in stocks as Monday. As someone who does a lot of passive investment and dollar cost investing I was intrigued by his conclusion. I decided to do the math to figure out if Monday is indeed the best day for dollar cost averaging on a weekly basis. Are you ready?







The data for this analysis is taken from Google Finance. We look at the price of VFINX (Vanguard S&P 500 Index Fund) between 1/3/2000 and 4/27/2018. Between these two dates there is a reasonably equitable distribution of Monday, Tuesday etc. We ignore Saturday’s & Sunday’s as it is not possible to execute an order on those days. The above time frame has 4,506 days and is distributed as show below. The difference in the number of days is due to trading holidays falling on weekdays.

Let’s say we have 1,000$ to invest per week. We try out different scenarios e.g. investing $1,000 every Monday, Tuesday etc. We are interested in finding out if investing on a particular day of the week has any effect on our final performance. The table below shows the results of investing on specific day of the week.

The distribution of the days is not uniform and as such the money invested also varies. It looks like the best day for investing is Monday with 99.13% (+0.61%) returns. In terms of absolute amount Wednesday is better at $912,168.77. This is because a lot more of money is invested. This kind of makes sense as holidays are likely to occur at the beginning or end of a week. So, to maximize the amount invested it makes sense to invest on a Wednesday.






How could we normalize this data? To make the days equally distributed I made a small switch to my algorithm. Now, for any particular holiday I assume the value for the fund from its previous close i.e. the price did not change on that day. With this change the 4,780 days get split equally across Monday, Tuesday etc. I now redo the math. Obviously the total amount invested remains the same across any of the investment scenarios.

Clearly there is no benefit whatsoever associated with investing on a particular day of the week. The gains are marginal at best. Seems like Monday scores the best return this time around with 99.82% returns (+0.13%).

Why does investing on Monday provide us better returns? Our data looked at 4,780 days or 956 weeks. Out of the 956 weeks the lowest price in a week was on a Monday 317 times or 33.16% of all the weeks.

Monday is the highest in terms of weekly lows but is not always the lowest. As a matter of fact on 66.84% of the times the lowest value was not on a Monday. Our greedy solution is not the best possible solution after all.

How do we improve the odds? For one we should not be greedily picking every Monday. Instead we replace it with a probability model. In a given week we chose the day to invest with a probability e.g. we have a 23.01% chance of picking Friday, 16.95% chance of Tuesday etc. Obviously we give a higher weight to Monday i.e. 33.16%.

The results are from a probability simulation. They depend heavily on random number generation and as such results vary from run to run. I am sharing the results of five such runs.

In all the 5 runs we have outperformed the returns from our greedy solution i.e. investing on a Monday. Is it possible we could also under-perform? The answer is yes. But, the likely hood is less.






Now to complete this analysis we need to run our model one more time. This time we randomly chose a day of the week to invest in i.e. each day has an equal probability.

On an average the returns obtained by investing on a random day of the week is as good (if not superior) as the returns obtained by using a simple probability distribution or investing on Mondays.

Just for completeness I also wanted to provide a distribution of the day in a week where the market is at its highest. Friday seems to be the most probable date on which a weekly high might be hit. A greedy approach would be to schedule all sells on a Friday. As we have seen before with buy orders it might not be the most optimal solution.

Another way to look at this data would be to look at the spread between the highest and lowest days.

Based on the above analysis it does look like Monday might be the best day to buy and Friday the best day to sell. But as we saw that would be a greedy solution and could be sub-optimal. The more optimal solution would be to build a probability distribution. The distribution that I used is very naïve. I am sure better models can be built with additional data facets like interest rates etc.

It might be interesting to consider the effects of macroeconomic trends on a particular sector. Federal Reserve has its weekly meetings on a Wednesday and typically come out with some information on benchmark interest rates (increase or decrease). In the last 5 years it’s been about an actual increase or likelihood of an increase. This would have a sizable impact on a utility ETF i.e. a rate hike would cause the price of the ETF to fall (in the process increasing yield).

Does it then make sense to invest in utility ETFs on Wednesday? Time to do the numbers and this time around we will be looking at the last 6 years (2012 to 2018). We consider 1,589 days.






The returns are the same across all 5 days. Seems like Monday, Wednesday and Friday might be the best days to buy utilities.

In general over a sustained period of time the choice of day does not have a sizable impact on the returns. That being said macroeconomic trends might dictate specific dates for buying specific stocks (e.g. utilities). In those cases it makes sense to execute buys on a particular day.

The purpose of this article is to refute the claim that investing on a particular day of the week provides better returns. We have see that this is not necessarily true over a long duration of time.

What are your thoughts? Do you agree with my assessment? Please leave a comment.













10 comments:

  1. Hey DG. I read Rob's post also and will leave a similar comment. I've read with interest research like this in the past and at times tried to execute a strategy to purchase on the "best day". I found it was more than I cared to think about so I fall back to sooner is better. And, it will never be sooner than today. Tom

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    1. Thanks Tom. I wanted to solidify my own thoughts i.e. the day of the week does not have any effect on the final returns. I was hoping my math would make it clear. I think it did. But, I agree with you say...Best day is today!

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  2. Interesting article. I never thought the day of the week has an impact on your investment.

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    1. Hi PS. As a matter of fact it does not. That is the conclusion of my article :-)

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  3. Love the concept of this. That debate been thrown around forever. We actually ran some calculations of this exact same thing in my statistics class a while back and the outcome was inconclusive. According to the stats we had anyway, there is no significantly statistical evidence to show one day is better than the rest.

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    1. Totally agree. I don't think the day matters at all. As Tom mentioned the best day to invest is today :-)

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  4. Interesting analysis! I remember us doing some analysis of the day of the week effect on investment returns at the business school, and while there was some evidence of potential correlations...the conclusion was that it was insignificant. Studies have shown that when any form of market "inefficiencies" or correlations are found out by market participants, they all try to utilize it (some form of arbitrage) and they end up making the market even more efficient because that "inefficiency" in the market simply fades away over time.

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    1. Very true Enoch. Reinforces my idea to invest in index funds :-)

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  5. This is very interesting, thanks for sharing- I do the DCA approach (monthly basis) but don't have a particular day that I hit buy.

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    1. Yes GYM. Interestingly the day has not impact whatsoever. So, one less thing to be worried about.

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