My not so profound valuations and observations on Markets
My not so profound valuations and observations on Markets
During the March 2020 draw-down, I remember looking at the premarket returns to see whether the day is an up or a down day. While I was panicking, I was wondering if the premarket returns would tell us anything about the present day returns. I decided to find out, so I download the historical SPY price data from 1993 to 2021.
The US stock market starts trading from 9:30AM to 4:00 PM, this is when most people trade. Then since 1991 some stock exchanges started to allow institutional investors to trade after 4:00PM this is called after hours trading, now days after hours can run as late as 8:00PM. Then there is premarket trading, where trading occurs from 8:00 AM to 9:30 AM.
I first choose to use Close instead of Adj.Close because Adj.Close accounts for dividends and I decided that since I just wanted to compare the return during the night and day, so dividends shouldn't be included.
"Day returns" refer to the returns made during the day from 9:30 AM to 4:00 PM, and it is calculated by market close divided by market open so 4:00 PM price divided by 9:30 AM price.
Then on line 20, in day Returns I got rid of the first entry just so I can match with premarket returns. So the first day return is 1993 Feb 2nd.
In my code when I use "night returns" it is referring to "after hours and premarket returns". After hours and premarket returns is defined as 9:30 AM price divided by yesterday 4:00 PM price, so day open divided by previous day close. When I say "if you saw the premarket to be up", this premarket has already incorporated the returns of yesterday's after hours.
Lastly, "whole" refers to day close divided by previous day close, so today's 4:00 PM price divided by yesterday's 4:00 PM price.
I then combined all returns in one data-frame, and call it both (I know, I should probably work on my naming skills).
Just to show how the returns have been distributed throughout time.
Here we can see that during crashes there are huge movements in both after hours/premarket and day returns such as 2001, 2008 and 2020.
Then to see the cumulative returns of after hours/premarket returns, every day from 1993 to 2021, it would just be a product of all the "night Returns". Since if you were to buy at market close and sell at market open you would only get the after hours/premarket returns and all the after hours/premarket returns must be multiplied to reflect the compounding from 1993 to 2021. Same thing if you were going to buy at market open and sell at market close (the day returns).
So cumulative returns of after hours/premarket is 975%.
While cumulative return of day return is actually negative 9.6%. So you would actually lose money if you bought at open and sold at close every day, from 1993 to 2021.
There seems to be no real explanation with this huge difference, theory range from institution knows of this difference, and so they buy at close and sell at open or earnings always drops outside of trading hours, so most gain are from after hours or as simple to there are more hours at night than during the day (hahaha). This data suggests that buy and hold to be a better strategy than trading during the day. There is a whole academic paper that is written about how this behaviour is present from individual stocks to futures. Here we can confirm that we got the same results as what was given in the paper.
To continue with this analysis, I wanted to answer whether it was statistically significant that the mean of the day returns were smaller than the after hours/premarket returns.
So first I did a T-test:
Null hypothesis: Mean of Day Returns = Mean of after hours/premarket returns
Alternative Hypothesis : Mean of Day Returns < mean of after hours/premarket returns
From the T-test we can see that since the significance level is lower than 0.05, so we reject the Null hypothesis. From the given data we can support the alternative hypothesis. Here we can see that the mean of the day returns is + 0.0033% while the after hours/premarket returns is +0.034%, which make sense given our previous statement saying that the cumulative night returns are much larger than day returns.
But I realized that this data wasn't normally distributed, since if the market was actually normally distributed it would be practically impossible to have a + or - 10% in a single day. Which renders the T-test kind of useless for more analysis, since the T-test assumes the data are normally distributed.
As we can see from the QQplot both the night and day returns are far from being normally distributed. If they were, then all the points would have to be distributed on the line, here we can see that both after hours/premarket and day returns has fat tails, so it is not a normal distribution.
Since we can't use the mean to compare day and night return, we can however, use the median. In our case of "If you saw the premarket to be up, when the market opens, do you expect the market to keep going up and close higher?" it actually makes more sense to use the median rather than the mean, since you should be wondering whether most of the time if the premarket returns is up would the market keep going up?
Here I first selected all the data that has after hours/premarket return greater than 1 and called it above1. Because to answer the question "If you saw the premarket to be up, when the market opens, do you expect the market to keep going up and close higher?", I have only selected the times when the after hours/premarket is up along with the corresponding day returns.
Then I used an R-package made by my professor Ken Butler. In this package one can use the sign test instead of the T test, since the sign test doesn't assume the data to be normally distributed.
Null Hypothesis: Median of Day Returns = 1
Alternative Hypothesis: Median of Day Returns > 1 (I made this 1 because if you think the market is going to keep going up because the after hours/premarket was up, then day return should be greater than 1)
To use this test, we first find "upper" in the table, and get the p-value. We can see that this p-value is very small, much smaller than 0.05, so we can reject the Null hypothesis. And conclude that the median night returns are larger than the median day returns.
So to answer our question "If you saw the after hours/premarket to be up, when the market opens, do you expect the market to keep going up and close higher?", the answer should be a yes. Since the median value of day returns is larger than 1, when the premarket/after hours is up. In a laymen example, if the market closed yesterday at $10, and opened at $15 the market is going to close most of the time higher than $15.
However, from the previous point that most gains coming from after hours/premarket and not from day, we can confirm that the median after hours/premarket gains are greater than median day gains.
Here Null Hypothesis: Median of Day Returns = Median after hours/premarket Returns
Alternative Hypothesis: Median of Day Returns < Median after hours/premarket Returns
Here looking at the "lower" alternative the significance level is below 0.05, so we can reject the Null hypothesis, and we can conclude that the median day returns are smaller than the median after hours/premarket returns. Which means that even though the market keeps going up after seeing the after hours/premarket gains, most of the gain has already been taken during the after hours/premarket. Buy and hold investors should be happy reading this.
Now you might be wondering "If you saw the premarket to be down, when the market opens, do you expect the market to keep going down and close lower?"
Here I did the same thing as above, the only change we have to do is having different hypothesis.
Null Hypothesis: Median of Day Returns = 1
Alternative Hypothesis: Median of Day Returns > 1
Here instead of using "lower" we use "upper", here we can see that the p-value is very small, much smaller than 0.05. So we reject the Null Hypothesis. So we accept that the median day returns are positive when the premarket/after hours is down.
To answer the question "If you saw the premarket to be down, when the market opens, do you expect the market to keep going down and close lower?", the answer is no. This means that if the premarket is down, the market has already dropped and is on the way back up. In a laymen example, this means that if yesterday the market closed at $10 and opened at $5, the market will close higher than $5.
However, similar to how the premarket/after hours take most of the gains, it takes most of the losses too.
Here we use "whole", which is the return of "day close divided by previous day close". We use this because we want to find out whether the market will close lower today than it did yesterday, when after hours/premarket is down.
Here is the null hypothesis: Median return of whole = 1
Alternative hypothesis: Median return of whole < 1
From the data, since we want to see if it's lower than 1, we use "lower", and here we see that the significance level for the null hypothesis is much smaller than 0.05, so we reject the null hypothesis, and accept the alternative. This means that even though the median day return is positive, the median whole day return isn't. Combining with our previous finding, an example would be, if the market closed yesterday at $10, and opened today at $5, the market will close today higher than $5 but lower than $10. This could mean that during the after hours/premarket, they tend to overreact to bad news and push it lower than it needs to be, but the premarket gets the direction correct, and the present day closing price will still be lower than yesterday's closing price.
From this exercise we can conclude,
This shouldn't be a suggestion to actually buy at close and sell at market open every day, since I didn't facotor in will be taxes and transaction fees, but it is nonetheless interesting to see the dynamic of the market. Also note that this analysis is just using the price data of SPY from 1993 to 2021, and might not reflect the true nature of every other stock and ETF across different regions and time period. The academic paper that I linked above went into more details exploring this phenomenon.