They say that stocks go down during the day and up at night.

Bruce Knuteson writes:

Prompted by your blog post this morning, I attach a plot from Figure 3 of They Still Haven’t Told You showing overnight and intraday returns to AIG (with logarithmic vertical scale, updated with data through the end of October).

If you invested $1 in AIG at the start of 1990 and received only intraday returns (from market open to market close), you would be left with one-twentieth of a penny, suffering a cumulative return of -99.95%. If you received only overnight returns (from market close to the next day’s market open), you would have $1,017, achieving a cumulative return of roughly +101,600%.

You can easily reproduce this plot yourself. Data are publicly available from Yahoo Finance.

AIG is just one of many stocks with a suspiciously divergent time series of overnight and intraday returns.

If you have a compelling innocuous explanation for these strikingly suspicious overnight and intraday returns that I have not already addressed, I would of course be keen to hear it.

Alternatively, if you can think of a historical example of a strikingly suspicious return pattern in a financial market that turned out to clearly be fine, I would be keen to hear it.

If neither, perhaps you can bring these strikingly suspicious return patterns to the attention of your readers.

What continues to stun me is how something can be clear and unambiguous, and it still takes years or even decades to resolve.

The linked article is fun to read, but I absolutely have no idea about this, so just sharing with you. Make of it what you will. You can also read this news article from 2018 by Matt Levine which briefly discusses Knuteson’s idea.

117 thoughts on “They say that stocks go down during the day and up at night.

    • I wonder if it has to do with the timing of news releases by firms. If firms announce news after the close, then overnight trading picks up the news and adds it to price and the next day is mean reversion. Then a firm that has consistently good news grows every night and reverts down the next day, so night returns are much larger. It’s also worth noting that most of the change appears to be from about 2009 when AIG was collapsing and being bailed out, so weird timing effects may of been really consistent. (Also, looks like a sharp drop in early 2020 so this make be volatility/crisis driven).

      There also seems to be an initial structural break in relative trend in 2001 which maybe help explain this pattern. I wonder if there were changes in how overnight trading/news announcements worked about that time.

  1. This is the first I’ve seen of this and it does seem like a mystery. I reproduced the AIG graphs and noticed the same thing as others with the September 2008 divergence – there was important negative news about AIG on the day the series diverge. Then I looked at AT&T stock – the picture is not quite as dramatic, but the two series diverge in February 2010. Before that time, intra day returns exceed inter day returns and after that time it switches.

    Just more evidence to add to what seems mysterious to me.

    • It seems like the AIG example also has more flips than initially described. (Dates approximate)
      – Pre 2001: Very similar with intraday advantage.
      – 2001-07: Big intraday under performance.
      – 2008-2011: Insane opposite performance favoring overnight.
      – 2012-2020: Intraday looks like its modestly over-performing.
      – 2020-prescent: Overnight over-performing.
      I can’t make up plots at work but I’m really curious to see the monthly gap in the two for a bunch of stocks to see how consistent these patterns are. It does appear that for periods some stocks consistently over or under perform based on time of day, but it does appear that relationship flips and has to do with big financial shocks. 2001 recession, financial crisis, and covid shock.

      • I looked at AT&T and EXON and both show the divergence, but less extreme than AIG. And the switch from intraday being more profitable than interday trading occurs at different points in time for each. But the crossing pattern in returns still shows up. I also looked at the buy and hold strategy and returns including splits/dividends and that strategy is better for EXON and slightly worse for AT&T, compared with the interday scheme. Knuteson’s paper shows a number of indices that all show similar patterns (for the intraday vs interday returns).

  2. This got a lot of attention about a year ago and the effect disappeared once it was published (presumably because lots of people started trading it). I haven’t checked whether the effect has reappeared or not.

  3. “Ref. [21] speaks values about the SEC’s ability to understand the cause of things.”
    Daannng! This is the snarkiest journal article that I have ever read. (In the SEC’s report (that this article shreds to bits), the SEC mistakenly uses the word “value” in place of “volume” several times.)

  4. Somewhat related – I was just wondering this morning, when I heard a report about futures prices (in Korea!), whether the direction of futures before the market opens (on average) is predictive of the outcomes of a broad scale stock index at the end of the day.

    I’m sure someone has investigated this and if it is significantly predictive someone is making money from that pattern, but just wondering if someone here knows.

    • “direction of futures before the market opens (on average) is predictive of the outcomes of a broad scale stock index at the end of the day.”

      No. No is the answer for every modern financial market that I know of. But if you’re not sure, just get on Robin Hood and put $10 on the prediction every day, see where you wind up after a year.

      Regarding the AIG question:

      After hours trading prices are highly volatile and liquidity is extremely low because very few people are trading. It’s essential to use limit orders in after hours trading. The quoted price is pretty much irrelevant. if you enter and order when the last trade was @$5.00 and don’t put in a limit, you could well actually pay $5.50, because the order will fill at any price. You have to go by the “ask”, and that often jumps unexpectedly. I’m not totally sure why but suppose the “ask” is $5.50 but the trader is only offering ten shares, which you can’t see. You put in a market order for $5.50 for 100 shares, boom, you pay whatever the trader wants for the other 90 – or maybe there are other limit sales lined up at $5.80, $6.00, and $6.50.

      In regular session trading, on the other hand, a market order for a widely available stock (like AIG) will execute within a few pennies of the last trade. That’s simply because of the much greater number of people trading, which forces traders to move sell prices up or down in much smaller increments.

      So whatever you say about after hours trading, it has to be said with these factors in mind. After hours is not at all comparable to regular session trading

      • Afterhours/premarket are low liquidity, but the highest liquidity is the first and last few minutes of regular trading (ie, 9:30 am and 4:00 pm ET).

        That is when all the big funds typically trade with each other.

      • > But if you’re not sure, just get on Robin Hood and put $10 on the prediction every day, see where you wind up after a year.

        ??? Of course I’m not sure, that’s why I asked.

        • I didn’t mean to be flippant. It would be an interesting thing to do. 20 years ago, it wasn’t possible to do with $10 but today with partial shares etc, it would be a cheap experiment. I don’t doubt the outcome but there’s much to be learned from the daily experience of it.

      • > Regarding the AIG question: After hours trading prices […] After hours is not at all comparable to regular session trading

        Note that the post has nothing to do with after hours trading.

  5. This is a somewhat well-known phenomenon and it extends to the broader market. For example, if you analyze the SPY (an S&P 500 tracking ETF) over the last three decades you will see that almost all of the return are generated overnight.

    There have been some papers looking at this pattern in the cross-section of stock returns and an explanation is based on investor clienteles, investor sentiment, and perhaps even private information.

    https://anderson-review.ucla.edu/wp-content/uploads/2021/03/Aboody-et-al_overnight_returns_and_firmspecific_investor_sentiment_JFQA2018.pdf

    However, the pattern at the market-level is harder to explain. But here is an attempt:

    https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr917.pdf

  6. “Overnight” in New York doesn’t mean overnight everywhere. There is stock activity somewhere in the world at all times. I wonder if someone has figured out how to take advantage of this potential arbitrage – more than likely, it’s well-known in the right circles.

    • Presumably they mean “after hours trading in US markets” – that’s the data that would be publicly available on Yahoo.

      I imagine for the person willing to put in the time there’s some possibility of arbitrage with stocks across international markets, but I can only think of a couple of ways that would work: first there might be some markets in which various stocks are thinly traded or have a limited number of shares, so that’s trading on liquidity limitations which may cause exploitable price variations – which is similar to trading in after hours markets in the US. the other way is of course currency arbitrage, but my guess is that’s easier to do directly with currency

  7. Questions for those of you who know more than I do (meaning most of you):
    Are dividends included in the daytime/nighttime returns calculations? If so, which do they show up in? All I can find is that dividends are paid when trading closes on the dividend day, but I don’t know if that would contribute to one measure or the other. Since dividends are a large part of the returns, this might have a big impact on that comparison.

    Also, looking at a number of the graphs for various stocks (individual stocks), the pictures are far less compelling. Some stocks show most of the gains occurring during the market-closed time and other the opposite. More show the overnight gains exceeding the intraday returns, but the pattern is far from uniform. At this point I am somewhat puzzled on why this is considered “suspicious.” I would add to my puzzlement the practical considerations raised by chipmunk in terms of the difficulty of actually completing those nighttime trades. One further point: if you actually bought at one day’s closing price and sold at the next days opening price, and did this over a long period of time, you would not receive the dividends (since you wouldn’t actually own the stock on the date required to earn the dividend).

    • I’m also not a Python programmer, but from Knuteson’s code, the returns calculations appear to be
      # Intraday returns are the returns from open to close.
      # returns_intraday[0] is the return from open on dates_datetime[0] to close on dates_datetime[0]
      returns_intraday = [price_close[i] / price_open[i] – 1 for i in range(n_days)]

      # Use adjusted prices to get close to close returns.
      # returns_close_to_close[1] is the return from close on dates_datetime[0] to close on dates_datetime[1]
      returns_close_to_close = [0.] + [price_close_adj[i] / price_close_adj[i-1] – 1 for i in range(1, n_days)]

      # Overnight returns are close to close returns sans intraday returns.
      # returns_overnight[1] is the return from close on dates_datetime[0] to open on dates_datetime[1]
      returns_overnight = [0.] + [(1 + returns_close_to_close[i]) / (1 + returns_intraday[i]) – 1
      # A big time gap (let’s say two weeks or more) means we are missing data.
      # We should not attribute the total return over this time gap to overnight.
      if dates_datetime[i] – dates_datetime[i-1] < timedelta(days=14) else 0
      for i in range(1, n_days)]
      If I am understanding this, it looks like the dividends are reflected in the overnight return calculation but excluded from the intraday calculation. If so, wouldn't that account for a substantial difference between the two (similarly for stock splits)?

  8. I was a financial pro in a previous life (Renaissance technologies)
    1. Dale Lehmann probably has it right. Of course dividends have to
    be included in a simulation
    2. But also notice that the “close” is an artificial price. You can’t actually
    trade at the closing price. A very careful simulation would trade at say
    the average price in the 5 minutes before the close. There may be some
    funny business (involving options perhaps) in which the closing price is
    artificially reduced. That would yield the observed effects.

    • But the problem is that the dividends appear to be included in the overnight return but not in the intraday return – do I have that right?
      (my read of the Python code is that the intraday return is calculated using opening and closing prices – which do not include dividends, splits, etc. – and this is then subtracted from the overall return, which includes dividends, to derive the overnight returns as the residual)

      • Dividends are awarded to shareholders of record on a given date. If you exclusively session trade – in at the beginning of a session, out at the end, regular or pre/post market, are you ever a shareholder of record? If you’re never a shareholder at the the close of business, my bet is that you’re never a shareholder of record. You’re using margin to trade, borrowing from the brokerage and returning to the brokerage at the end of the session.

        So my bet is that session traders don’t get any dividends.

      • Key word: “unpriced”. It’s guaranteed to receive an execution but not at a given price. It’s just a market order. Seems to me like it determines the closing price.

        • That’s the point!

          It doesn’t seem correct to say that “You can’t actually trade at the closing price.” because that’s what you get when you put a market-on-close order to be executed in the closing auction: a trade at at the closing price.

        • I think what he means is that you can’t specify a trade at the “closing price.” You enter the trade and get what you get. Perhaps you specified a certain amount, but you’re not guaranteed to get that amount unless someone wants to sell to you at that price.

          But yeah, you’re right, seems like someone got that price.

  9. AIG is not a good example given that it nearly blew up during the 2008 Downturn. Considered ‘too big to fail’, it was bailed out by Bush’s Treasury Secretary Henry Paulson working with Obama’s Timothy Geithner.

    Let’s have another illustrative stock that didn’t undergo such extreme unction.

    • I came to the same conclusion before reading the comments. It’s notable that while the stock lost nearly all of its value back then, AIG’s dividends didn’t change significantly. Good evidence for the dividend theory.

    • a bit odd to call Timothy Geithner “Obama’s” given that Geithner had been in his post at the NY Fed since 2003 and said bailout of AIG occurred 2 months prior to the 2008 Presidential Election

    • The data provided looks (to me) like it measures the returns differently for the two scenarios (intraday and overnight). If one measure includes dividends and the other does not, wouldn’t we expect to see the returns higher for the one that includes them? Isn’t the point of the “suspicious” finding that almost all of the returns are earned overnight and not during the day of trading?

      • Dale I want to emphasize again that it’s probably not possible to do what this person has illustrated with pre/after market trading because of liquidity.

        The way this calculation is done is as if Trader Bob started out with a $1 trade – a trade he could never make in pre/post market – then simply accumulated his fortune with “open” and “close” trades with his 1.2, then 1.7, then whatever weird amount of shares he’s trading as his net increases. But again it’s not possible to just pick your price and number of shares in pre/post market. Scaling up the starting amount doesn’t help – then down the road, Bob has 17K shares and he might get only 8K or 4K to trade at the open price and then has to trade at a higher price after that. As his number of shares gets larger, he has an increasingly difficult time matching the open and close prices in pre/post trading.

        Even during the regular session, if you had entered, say, a trade for 125 shr AMZN @ $2250 (before split), almost surely the trade would have executed in several different lots at slightly different prices – that’s in the regular session with a highly liquid stock.

        Anon says that the highest volumes pre/post market are at open and close, and that’s all well and good. but most days pre/post market has limited volume unless there is some immense news.

        • Your points are well taken but my concern is not with the practical feasibility of this trading. It is more about the (possibly) inconsistent measures being presented. If the basic picture is that nighttime is when almost all the returns are earned, that would be of interest – even if it is not feasible to trade and earn those returns. But I am questioning whether that fact is even true. If the nighttime returns include dividends and the intraday returns do not, then comparing them tells us nothing. Can you tell me if that is what is being presented? I think the Python code I attached above is sufficient to tell.

        • Dale, regarding if market gains are earned mostly at night, as a general rule I don’t think that’s the case.

          There is however one practice that affects this directly: the announcement of earnings in off hours. Many companies release earnings at market close and begin their quarterly conference calls shortly after. Stocks can gap dramatically (up or down) on earnings releases, as META did a few days ago, jumping nearly 20% overnight. (it also fell overnight in it’s previous 2 or 3 quarterly announcements). Lots of other companies release earnings during pre-market trading. Very few release at the opening bell.

          The effect is most pronounced for growth stocks. XOM or T would not experience much affect.

        • Anon says that the highest volumes pre/post market are at open and close, and that’s all well and good. but most days pre/post market has limited volume unless there is some immense news.

          I meant liquidity is highest at open/close during regular trading hours. Eg,

          https://www.cmegroup.com/education/articles-and-reports/assessing-liquidity.html

          Btw, I used to get tick and order book data from here:
          https://www.iexexchange.io/products/market-data-connectivity

          If it doesn’t turn out to be the dividend adjustment that might be a better source.

      • I don’t see anything about including dividends in the code you posted, it is just the open/close prices for the day. The charts are mislabeled because they do not actually show what you would make for multiple reasons. What could play an influence is different fees/commissions for regular vs extended trading. But I doubt that is the explanation.

        Most likely it has to do with funds hedging and rebalancing, but it would be interesting to figure out what exactly causes that pattern.

        • > What could play an influence is different fees/commissions for regular vs extended trading.

          Note that the post has nothing to do with extended trading.

        • I’m not a coder but almost everyone on this blog surpasses my abilities (I’d note a number of past conversations we’ve had about the importance of coding in the introductory statistics course, which I don’t agree with). But if you look at the code, the overall returns are calculated using the adjusted closing price (price_close_adj) which does include dividends, splits, etc., and the intraday returns are calculated using just the open/close prices for the day. That is what I am referring to when I say that the nighttime returns include dividends (since the nighttime returns are calculated as the residual from the overall returns after subtracting the intraday returns). Surely this interpretation is not beyond people’s ability to read the code enough to tell me if that is correct or not.

        • Here’s what ChatGPT says:
          Here is the code: # Intraday returns are the returns from open to close.
          # returns_intraday[0] is the return from open on dates_datetime[0] to close on dates_datetime[0]
          returns_intraday = [price_close[i] / price_open[i] – 1 for i in range(n_days)]

          # Use adjusted prices to get close to close returns.
          # returns_close_to_close[1] is the return from close on dates_datetime[0] to close on dates_datetime[1]
          returns_close_to_close = [0.] + [price_close_adj[i] / price_close_adj[i-1] – 1 for i in range(1, n_days)]

          # Overnight returns are close to close returns sans intraday returns.
          # returns_overnight[1] is the return from close on dates_datetime[0] to open on dates_datetime[1]
          returns_overnight = [0.] + [(1 + returns_close_to_close[i]) / (1 + returns_intraday[i]) – 1
          # A big time gap (let’s say two weeks or more) means we are missing data.
          # We should not attribute the total return over this time gap to overnight.
          if dates_datetime[i] – dates_datetime[i-1] < timedelta(days=14) else 0
          for i in range(1, n_days)]. My question is: does the measure of nighttime returns include dividends and the intraday returns does not?

          The code calculates the intraday returns, close-to-close returns, and overnight returns of stock prices. However, it does not appear to take into account dividends. The intraday returns are calculated as the difference between the close price and open price of a stock on a given day, divided by the open price. The close-to-close returns are calculated as the difference between the adjusted close price of a given day and the previous day's adjusted close price, divided by the previous day's adjusted close price. The overnight returns are calculated as the difference between the close-to-close returns and the intraday returns.

          In short, both the intraday and overnight returns do not appear to take dividends into account.
          [email protected]
          Don't adjusted closing prices include dividends?

          Yes, adjusted closing prices typically include dividends and other corporate actions such as stock splits. The adjusted closing price is the closing price of a stock that has been modified to accurately reflect the total return of the stock over a given period, including dividends and other corporate actions. By using adjusted closing prices in the calculation of close-to-close returns, the code aims to account for the effect of dividends and other corporate actions on the stock's total return.

          Notice that the initial response is wrong – since the word "dividends" does not appear in the code. But when prompted about the use of adjusted closing prices, I was able to get it to provide the answer I was looking for.

        • Please excuse the formatting – it isn’t clear to me how to format the ChatGPT exchange and paste it into this blog correctly.

        • and I missed the punchline:

          So, doesn’t that mean that the calculation of nighttime returns does include dividends as I was asking?

          Yes, that’s correct. The calculation of overnight returns in the code takes into account dividends and other corporate actions, since the close-to-close returns (which are used in the calculation of overnight returns) are based on adjusted closing prices that include dividends and other corporate actions.

        • > intraday returns are calculated using just the open/close prices for the day

          Because that’s the only thing relevant for intraday returns. You (could) buy at some price in the morning and sell at another price in the evening.

          Dividend are relevant for the overall returns though because if you buy at some date and sell at a later date the profit or loss is not just the difference in the price.

          That’s why adjusted prices are used to calculate returns over a long period where those adjustments could make a difference. (One could also define and adjusted open price but it wouldn’t change the daily open-to-close performance.)

        • Carlos
          The purpose of my continuing posts on this topic is to address the initial claim – about prices going down during the day and up at night. The paper claims to be comparing “receiving only intraday returns” with receiving “only overnight returns.” Neither of these involves holding a stock for extended periods of time (which I agree would require looking at adjusted prices). In other words, the “suspicious” finding that almost all of the returns are earned during overnight periods seems to me a largely artificial result of including dividends in one measure and not in the other.

        • My question is: does the measure of nighttime returns include dividends and the intraday returns does not?

          Sorry, I didn’t find the actual code at the links I clicked above so am just looking at your snippet. If adjusted returns refers to that column on the yahoo page, then yes.

          If a $0.08 cash dividend is distributed on Feb 19 (ex- date), and the Feb 18 closing price is $24.96, the pre-dividend data is multiplied by (1-0.08/24.96) = 0.9968.

          https://help.yahoo.com/kb/SLN28256.html

        • > The paper claims to be comparing “receiving only intraday returns” with receiving “only overnight returns.”

          You seem to strongly oppose the way that those returns are computed but are you sure that you have a more meaningful alternative?

          Consider this simple example to focus on the calculation – ignoring technicalities or why anyone would engage in such trading in the first place:

          There are two shares that give equal rights to a box with $100 in it which distributes $10 dollars among shareholders every Tuesday. A five-for-one split is scheduled for Monday.

          On Monday morning Alice buys a share for $50. On Monday evening Alice sells that share for $50. What’s Alice’s intraday return on Monday? (0%? Something else?)

          Bob bought that share for $50 on Monday evening. During the night, the exchange fairy reaches under Bob’s pillow and puts four additional shares next to the one he just bought – and also gives four additional shares to the other shareholder.

          On Tuesday morning Bob sells his five shares for $10 apiece. What’s Bob’s overnight return from Monday to Tuesday? (-80%? 0%? Something else?)

          Carol buys one of those $10 shares on Tuesday morning and in the evening she sells it for the same amount to Dave. What’s Carol’s intraday return on Tuesday? (0%? Something else?)

          During the night the exchange fairy puts a dollar bill next to the share under Dave’s pillow. (She does the same for the ten outstanding shares, taking the $10 from the box which has now only $90 in it.)

          On Wednesday morning Dave sells his share for $9 and keeps the $1 that the exchange fairy brought. What’s Dave’s overnight return from Tuesday to Wednesday? (-10%? 0%? Something else?)

        • Carlos
          What I computed for nighttime returns was buying at one day’s closing price and selling at the next day’s opening price. Doing that every day and comparing it to the intraday returns. The pictures are interesting but don’t seem to show the consistent pattern shown in the paper cited in the post. What I maintain is that the consistent pattern claimed in the post is due to a red herring – including dividends in one measure and comparing it to a measure that does not include dividends.

          The discussion that has ensued has convinced me that the practical realities would make this nighttime trading difficult, if not impossible to actually do. But that does not make it meaningful to compare returns with and without dividends and then claim that the difference is “suspicious” and results from things that happen when the market is closed. Also, I am not saying that those explanations are wrong – just that the data cited is polluted by including things not related to the phenomenon being discussed.

        • > What I maintain is that the consistent pattern claimed in the post is due to a red herring – including dividends in one measure and comparing it to a measure that does not include dividends.

          The point is that both measures – intraday and overnight – include the dividends received during the holding period (even though you may actually get the money a fee weeks later rather than finding it under the pillow).

          Did Dave experience negative returns from Tuesday close to Wednesday open? That’s the red herring – the fact is that he didn’t gain nor lose money. If you don’t take dividends into account you’re fabricating negative performance where none exists.

        • Carlos
          I believe you are wrong. Both measures do not include dividends. If you compute the intraday return as closing price – opening price, neither of those include dividends – that is why adjusted returns are different.

        • Carlos
          Here is the footnote from Yahoo finance describing the measures:
          “Close price adjusted for splits.**Adjusted close price adjusted for splits and dividend and/or capital gain distributions.”

          So, apparently splits are included, but dividends are not (in the close price rather than the adjusted close price).

        • > The point is that both measures – intraday and overnight – include the dividends ___received___during___the___holding___period___.

          When you include the dividends received by everyone while they hold the share (and also adjust for the split) the intraday returns for Alice and Carol are zero and the overnight returns for Bob and Dave are also zero.

          When you don’t include the dividends received by anyone nothing changes for Alice, Bob and Carol. However, there is an impact for Dave – who got a dollar bill. You may insist that we should just ignore that dollar and conclude that Dave lost one dollar (-10% return) in his overnight investment but that doesn’t seem reasonable.

          (I think that I mentioned before that you could also define an open.adjusted value and calculate the intraday gross return as close.adjusted/open.adjusted instead of close/open. The value will be the same, though, because there is nothing to adjust for during the day and the adjustment factor will be the same and will cancel out.)

        • Carlos
          I apologize if I just don’t understand what you are saying. Perhaps someone can help clarify. I don’t really follow your example – you put questions for the measured returns rather than your answers and I don’t really see the relevance of the toy example. I want to stay focused on the empirical evidence provided in the paper for the divergence between intraday and overnight returns. At least part of that divergence appears to be that the overnight return measure includes dividends and the intraday measure does not. I am questioning why that contribution to the divergence in measures is relevant to what the post is talking about – the “suspicious” finding that almost all of the gains occur overnight (and, again, I am not questioning whether that is true or not, but whether the evidence provided is appropriate for examining that question).

        • > I want to stay focused on the empirical evidence provided in the paper for the divergence between intraday and overnight returns.

          You’re not really focusing on their divergence – you are also questioning how they are calculated in the first place and that’s the thing I’m trying to clear up.

          The relevance of the toy problem is that apparently (I don’t know for sure – you didn’t answer the questions) you would say that the performance of the overnight holding for Dave is negative.

          I’ll put the question as simply as I can:

          You buy a share for $10. You sell it for $9. You get $1 in cash because you hold the stock during that time. What is the return on that investment?

        • For your question, I’d say your return is zero. More importantly, if it opens at $10 and closes at $9 and $1 cash is provided as a dividend during that day, Yahoo finance will report that as an opening price of $10, a closing price of $9, and an adjusted closing price of $10. So, the way Knuteson is calculating intraday returns will show a 10% loss. His overnight return measure will show 0%. In that case, the divergence has nothing to do with the speculations described in the paper, and only results from the way these are measured in Yahoo Finance.

        • > For your question, I’d say your return is zero.

          Good!

          > More importantly, if it opens at $10 and closes at $9 and $1 cash is provided as a dividend during that day, Yahoo finance will report that as an opening price of $10, a closing price of $9, and an adjusted closing price of $10.

          That’s not how dividends work.

          If the stock opens at $10 and closes at $9 the intraday return is -10%. That’s what you get if you buy at $10 and sell at $9. No dividend for you.

          Depending on what do you mean by “provided during that day” the $1 dividend goes to whoever had the stock yesterday night or tonight.

          If the relevant date was yesterday today it trades without the right to get the dividend. Let’s say it closed yesterday at $11. Someone who bought yesterday (close) at $11 and sold today (open) at $10 and gets $1 for holding the stock during that time didn’t really make a 9% loss (the return is zero – see above!). Yahoo finance will report that yesterday’s adjusted close is $10.

          If the relevant date is today whoever is holding the stock tonight gets the dividend. The stock will trade without the right to get the dividend tomorrow. Yahoo finance will report that today’s adjusted close is $8 (and apply the same factor 0.8888889 to the whole adjusted series).

        • I was trying to avoid the complications of timing – I can agree with what you write. But my point is that the dividends figuring into the nighttime return calculation but not the intraday calculation is a red herring as far as the phenomenon being discussed is concerned. The explanations for the divergence involve things like who makes trades when the market is closed, announcements, etc. – none of these are about dividends. If we want to compare the behavior of stock prices when markets are open and when they are closed, then I think it is wrong to include dividends when measuring stock price changes when they are closed, and not including them when they are open. When we look at all the graphs in the paper (showing intraday and nighttime returns), part of the difference is that one measure includes dividends and the other does not – doesn’t that obscure the paradox that is being discussed?

        • > If we want to compare the behavior of stock prices when markets are open and when they are closed, then I think it is wrong to include dividends when measuring stock price changes when they are closed, and not including them when they are open.

          I think that what is wrong is to say that if you buy for $10, sell for $9 and get $1 in cash your performance is -10%. I’m not sure that’s an improvement over including the dividends whenever they happen.

          In any case, ignoring dividends won’t change anything for the non-distributing stocks and I don’t quite see how the divergence may be “a largely artificial result of including dividends in one measure and not in the other” when the dividend yield in the S&P 500 is around 2% p.a. and those measures are 0% p.a. for intraday returns and 9% p.a. for overnight returns.

        • All I can say is that I’ve done the analysis (intraday, interday using adjusted closing prices, interday using day i closing price and day (i+1) opening price) for 3 stocks (AT&T, EXON, and AIG) and the pictures all look different. It may be that dividends are not that big of a deal, but why not use data appropriate for the question being asked? For some stocks, dividends are a big deal, for others they are not. But the pictures are all somewhat messy – I am not convinced that the suspicious finding is as consistent as it is being claimed (though the country index results look quite uniform compared with the individual stock pictures – I’m referring to the paper cited in the excerpt in Andrew’s post).

        • Here’s the quote from Seeking Alpha on dividends:

          “The dividend is payable on [some date] to stockholders of record or “unit holders of record” as of the close of business on [some date]”.

          IOW, if you don’t own the shares at close of business, you don’t get a dividend.

          Regarding extended hours:

          “The ex-dividend date includes extended hours trading both pre-market and after hours (7:00 a.m. ET to 8:00 p.m. ET). Pre-market trading occurs from 7:00 a.m. to 9:30 a.m. ”

          If you don’t own the shares at the close of either the regular or after-hours session the day before the ex-dividend date, you don’t receive a dividend payment. i.e., no dividends should be included in the returns of a stock that is theoretically traded at the close of every session.

          https://seekingalpha.com/article/765801-how-ex-dividend-dates-work

        • Dale, Carlos:

          I recognized something I misunderstood. I assumed that “overnight” meant “after hours” trading in this paper. It doesn’t. It means – I think as you stated above – from the close of the regular session on one day to the open of the regular session on the next day.

          So, then, according to the Seeking Alpha rules above, overnight holders **DO** get dividends, where as day session traders **DO NOT** get dividends.

          So the appropriate calculation includes dividends from “night” but none from “day”.

          Apologies, gentlefolks

    • Anon:

      stocks commonly gap down after dividend payments – the higher the div as a % of the stock price the bigger the gap. Lots of institutions trade into dividend stocks in the days or weeks before the record date then sell on the record date and move to the next stock. After all, once the $0.50 dividend is paid the stock is worth that much less

  10. In addition to the possible artifact of dividend and spilts, it appears that the shape of the graph is largely driven by the period around 2008–09: likely driven by a tiny number of “bad” days, or by a tiny number of “good” nights in that period. This is the general problem of visualizing a cumulative effect: another familiar example is how mutual funds often present their cumulative excessive returns, in which a significant positive cumulative return could be a result of an early day accidental luck. One alternative is to visualizing the daily return, or the histogram of daily returns, but they could be much nosier as well.

  11. I read OP’s linked SSRN paper and his correspondence with SEC, in which the claim is that such excess overnight return reveals the existence of a whale trader who has deployed a strategy to gain money via day trading manipulatively.

    I don’t know. It is one possible explanation of course. But I wonder if the evidences in the present paper have gone beyond reasonable doubts. Indeed, the author himself provides an alternate explanation in paragraph 1:

    > If you compare the distribution of overnight re- turns with the distribution of intraday returns (as we do in Figure 4 of Ref. [5]) for any of the individual stocks or indices in this article, you find the distribution of in- traday returns is wider than the distribution of overnight returns. Since returns are due to the bearing of risk and the intraday risk is greater than the overnight risk, you expect a larger intraday return than overnight return, on average.

    Well, if you have two random walk with equal mean, and one has 2 times bigger variance, then its expected cumulative return shall be smaller: that is simply Jensen’s inequality.

  12. I like Dale Lehman’s hypothesis. I e-mailed Bruce Knuteson where I pointed to the comments above and asked him if he was aware that dividends might be an issue. His response suggests he does not think dividends are an issue.

    • My final “contribution” to this post. Knuteson’s message to Andrew appeared to request alternative hypotheses from his readers, yet with our lengthy discussion regarding the treatment of dividends (as well as a number of practical realities of off-hours trading), he did not contribute anything above. It is good that you emailed him, and at least we have his opinion that dividends are not an issue. But that is fairly dissatisfying (to me, at least) as an explanation. One thing that this blog repeatedly is concerned with is the integrity of data analysis and the importance of measurement. In this case, however, Knuteson seems to have adopted the common position of ignoring or minimizing criticism – or even correcting comments that may be wrong.

      What I don’t get about this whole dividend issue is that it would be easy to measure nighttime returns using the closing price from one day compared with the opening price the next day. Then dividends would truly not be an issue for examining the behavior of stock prices (as opposed to true returns of holding the equities) intraday relative to nighttime – and I think that is the proper focus for examining the “suspicious” behavior that is being discussed. I say this because all of the explanations that Knuteson discusses involve issues of the nature of traders at different times or releases of information or other types of market imperfections. It was his use of adjusted closing prices that brings dividends into the picture, and that seems entirely unnecessary and undesirable to me. Dividends may turn out to be irrelevant indeed, but I don’t think there was any need for them to entire the calculations at all.

      • Agreed. It would have been more interesting if he had contributed to the discussion, given that he is the one who emailed Gelman and that the tone of his article is rather cocksure.

      • > it would be easy to measure nighttime returns using the closing price from one day compared with the opening price the next day.

        Of course that would be easy – even easier than bothering to take dividends into account.

        > Then dividends would truly not be an issue for examining the behavior of stock prices (as opposed to true returns of holding the equities) […] It was his use of adjusted closing prices that brings dividends into the picture, and that seems entirely unnecessary and undesirable to me.

        Someone examining the behaviour of prices, rather than returns, may soon discover that there is a factor affecting negatively the close-to-open price change in a quite systematic and predictable way. Dividends bring themselves into the picture!

        That someone may then decide to examine total returns instead – considering for example that when Microsoft closed on 12 Nov 2004 at $29.97 and opened the following trading day at $27.35 the -8.8% price change is less meaningful than the adjusted gain obtained if the $3 dividend received is not ignored.

        Toy model time! (the rest of the comment can be safely ignored – and probably should)

        We have a perpetual bond paying $1 every day. Let’s say that interest rates never change and every day is identical to every other day. The markets opens 12 hours per day, every day of the week. There are no taxes, no transaction costs, no heaven, no hell below us, etc.

        One can make the hypothesis that the investment returns are proportional to the holding time whether the markets are open or not. (A reasonable idea: unlike this toy bond real bonds pay coupons only from time to time and daily accruals are independent of weekends and holidays.)

        For simplicity let’s say the price of the bond opens every day at $100 ($10k would be a more reasonable price but let’s keep the maths simple) and let’s imagine that it closes every day at $100.5.

        Taking the $1 received into account we would say that intraday return is $0.50 and the overnight return is $0.50 (in percentage terms using yahoo-finance-like adjusted prices 0.50% and 0.502%).

        Looking at price changes we would say that intraday changes are $0.50 (+0.50%) and overnight changes are -$0.50 (-0.498%).

        The returns seems more relevant than the price changes in we want to check the hypothesis exposed above: the profitability of holding the bond overnight or intraday are similar as expected.

        I guess that the price changes could be more relevant if we were interested in price changes for some reason.

        • Can you explain how your toy example relates to this?

          “If you invested $1 in AIG at the start of 1990 and received only intraday returns (from market open to market close), you would be left with one-twentieth of a penny, suffering a cumulative return of -99.95%. If you received only overnight returns (from market close to the next day’s market open), you would have $1,017, achieving a cumulative return of roughly +101,600%.”

          And then more specifically how it relates to this:

          “The world’s stock markets display a decades-long pattern of overnight and intraday returns seem-
          ingly consistent with only one explanation: one or more large, long-lived quant firms tending to
          expand its portfolio early in the day (when its trading moves prices more) and contract its portfolio
          later in the day (when its trading moves prices less), losing money on its daily round-trip trades to
          create mark-to-market gains on its large existing book.”

          I’m not really questioning your claim that the returns including dividends are more important for assessing profitability (or lack thereof). But I still don’t see how they relate to the above story. After all, I can get dividends as a retail investor just by holding the stock – I have no need to be a “large, long-lived quant firm.”

        • Can you explain in what way reframing that example as follows is an improvement:

          “If you invested $1 in AIG at the start of 1990 and bought [assuming zero transaction costs] every day at market open and sold at market close you would be left with one-twentieth of a penny, suffering a cumulative return of -99.95%. If you bought at market close and sold at market open – and used all the dividends you got during that time to light the stove – you would have $630, achieving a cumulative return of roughly +629%.”

          The two things anyone would think upon reading that would be “$630 is much more than $0.0005” and “the overnight investment would have performed even better if I had not being burning all that money!” – not necessarily in that order.

          (That said there are many problems with that particular example but using total returns is not one of them.)

          Something that the toy example illustrates us that if we have an hypothesis about returns it’s appropriate to look at returns (and price changes can be misleading as they are depressed by dividends). The introduction to that paper says “To establish a baseline of normality relative to which the real world can be compared, let us think through what we expect a plot of a stock’s overnight and intraday returns to look like.” and while all that reasoning may be questionable it’s clear that the author does care about returns (the expectation of positive returns for bearing risk, etc.) and reducing artificially the “price returns” by throwing dividends away is hardly the right way to look at the issue.

          In the toy example one could also write that [assuming that fractional investments on the bond are possible] “If you invested $1 in the bond at the start of the year and bought every day at market open and sold at market close you would have $6.17 at the end of the year. If you bought at market close and sold at market open – and discarded the dividends – you would be left with 16 cents at the end of the year.” – obscuring the fact that the intraday and the overnight holders gain equally from their investment as expected.

        • I am willing to concede that ignoring dividends and using my nighttime trading pattern of buying at the closing price and selling at the next day’s opening price – is wrong – on those days that dividends are earned. But that is only 4 times per year. Indeed, that amounts to almost nothing in terms of the return over a long period of time. On the other hand, calculating the nighttime return as a residual: use adjusted returns (buy and hold over the whole time period) and then subtract the intraday returns to get nighttime returns – provides a very different picture. As it should, since the dividends are included in the latter approach but not in the former. The question is: which is the more appropriate way to look at the phenomenon of interest? I thought the “overnight anomaly” (as siddhartha refers to it below) was about price movements, and the supposed explanations have to do with a variety of things – none of which refer to dividends.

          So, my question is which way is a better way to measure the size of this anomaly – one based solely on price movements (and ignoring dividends) or one that reflects dividends in the nighttime strategy but not in the intraday strategy?

        • > Indeed, that amounts to almost nothing in terms of the return over a long period of time.

          Well, it was you who insisted in the importance of dividends since they are a large part of the returns (partly true) and everything was a largely artificial result of including dividends in one measure and not in the other (wrong).

          > The question is: which is the more appropriate way to look at the phenomenon of interest? I thought the “overnight anomaly” (as siddhartha refers to it below) was about price movements, and the supposed explanations have to do with a variety of things – none of which refer to dividends.

          I’m not sure I understand the question. Do you still think that the anomaly is about price changes or do you think now that it’s about returns?

          Doesn’t the answer to the previous question also give the answer to your question?

          In that toy example there is no (return) anomaly but looking at price changes as if they meant something we get a completely misleading picture.

        • > which way is a better way to measure the size of this anomaly – one based solely on price movements (and ignoring dividends) or one that reflects dividends in the nighttime strategy but not in the intraday strategy?

          You could rephrase that as “which way is a better way to measure the size of this anomaly – one based on the returns or one that ignores dividends in the nighttime strategy but not in the intraday strategy?”

        • You are correct – I did make a big deal out of dividends and was incorrect in my understanding of how ignoring them when looking at price changes gives misleading results. But I’m inclined to say we should be more interested in price changes than returns. Here is the way one of the papers siddhartha linked to puts it

          “the overnight effect – the propensity for stocks to deliver all their returns when the market is closed and no returns during the trading day”

          While it is referring to “returns” none of the discussion (virtually nothing in that reference) has anything to do with dividends (and their reinvestment). The discussion is all about price movements and who has the potential to create these movements or profit from them. It is true that if a large trader can profit from these nighttime movements, then part of those profits may come through dividends, but I believe that is not the point of this research (perhaps I’m wrong about that – this is not a literature I am familiar with, but I’m going on the fact that none of the work I’ve looked at is concerned about dividends at all). So, to focus on the asymmetry between price movements during the day vs. overnight, I think inclusion of dividends in the overnight returns artificially inflates that difference. “Artificially” may be a poor choice of words – the returns would be affected, but I don’t think there is anything anomalous about the fact that it is more profitable to earn dividends than not. Stock market returns are considerably higher if dividends are included and reinvested than if they are not – but why should we use that fact to measure the size of the nighttime anomaly?

        • > While it is referring to “returns” none of the discussion (virtually nothing in that reference) has anything to do with dividends (and their reinvestment).

          Because [exaggerating a bit throughout this comment] nobody other than you thinks that the anomaly has anything to do with dividends. Of course you take the dividend into account to calculate the returns. That’s how returns are calculated. Then the dividend gets out of the picture. Either the returns look fine or they don’t. You may want to explain where the anomaly comes from but whatever the reason it will not be that you calculated the returns using the dividends. That’s the correct way to calculate those returns. Doing differently would have distorted the returns and could make the anomaly look worse than it is, or not as bad, or create an artificial anomaly where none exists.

          > So, to focus on the asymmetry between price movements during the day vs. overnight, I think inclusion of dividends in the overnight returns artificially inflates that difference.

          To study the overnight return anomaly the focus should be on the asymmetry between returns during the day vs. overnight. Exclusion of dividends artificially lowers overnight returns and artificially depressing that difference (when overnight returns are much higher than intraday returns).

          > Stock market returns are considerably higher if dividends are included and reinvested than if they are not – but why should we use that fact to measure the size of the nighttime anomaly?

          The returns in the toy example are considerable higher when you include the $1 received every night – if you don’t the are in fact no returns and the intraday gain is offset by the overnight loss. The reason why you need to include dividends to measure the size of the nighttime anomaly is that if you don’t you will find an anomaly where none exists (everyone gains if you do the right calculation).

        • Carlos has the dividend issue exactly right.

          I will now give an example of a striking overnight anomaly involving a company that has never issued a dividend. I would have liked to cut and paste a graph from Excel similar to the graph for AIG but could not (anyone know a work around?). I’ll have to settle for giving numerical data only, but you can easily download the stock’s historical returns from Yahoo Finance and graph the results yourself.

          SNDL (Sundial) is a relative new cannabis company, listed since August 1, 2018. It has been a very bad buy-and-hold investment: a $1M stake at the open on 8/1/18 would now be worth roughly $17K, a -98.3% decline over 4.5 years.

          $1M invested only intraday would be a massively worse investment, worth less than $140 today. That’s a decline of -99.986% over 4.5 years.

          However, $1M invested only overnight would, in theory, be a stupendous investment worth about $124M today. That’s equivalent to an annualized return of 192%, i.e., nearly tripling every year.

          I say “in theory” because SNDL has a market cap of about $575M. To go all the way to $124M you’d have to be able to buy a full 20% of the company’s market cap at the close and unload that same 20% at the open, all without distorting the price against you. Impossible.

          You’d likely run into problems much sooner. SNDL only trades abut $50K-$500K at the open, so you’d likely get adverse impact trying to unload just $10-100K worth of SNDL stock at the open.

          This is similar to the problems Elon Musk encountered selling his TSLA shares in order to purchase Twitter. Tesla’s market cap is currently $600B and peaked above $1.2T in 11/21. Nevertheless, Musk depressed the Tesla stock price every time he unloaded a few $B worth of shares, even though each sale involved less than 1% of the company’s total market cap.

        • siddhartha:

          My first research job out of my undergrad math degree, back in the late 90’s was at Barra Inc, where I worked for the special projects group who developed their market-impact model. The model quantified statistically how much the market price would change if you attempted to trade a block of N shares, it estimated this function for all companies every day. At the time doing the data processing within the allotted time (ie. overnight) was a problem, as the model had to do a lot of calculation and computers were maybe around 100x slower at that time than they are now.

          In any case, I think this transaction cost is highly under-appreciated in most people’s models of basically everything. It’s also a problem for ideas about valuation of economic goods. For example, what’s the value of all the real estate in Los Angeles County? Well, you could take the prices that each lot would transact at today if sold / bought on its own as estimated by some good model, and add them up. But if you wanted to actually buy all of the lots in LA County, the price would move against you astronomically. If the sum of all the lots in LA County is say 1T dollars today, the cost to actually purchase them all might easily be 10T or more. After you’d bought up say 20% of them in a month, people would get wise to your desire to buy up everything, and start accepting only much higher prices than before.

          Anyway, thanks for bringing back some memories and for a very interesting discussion that gets away from some of the standard stuff we’ve seen on here recently.

        • siddhartha
          For my education, can you please tell me what I am doing wrong. I downloaded the SNDL data and computed intraday returns, buy and hold returns (using only the adjusted closing prices), and overnight returns calculated 2 ways. The first way is my (incorrect) method of buying every day at the closing price and selling the next morning at the opening price. The other method is the residual method used in Knuteson: calculate the overall return using adjusted closing prices (my buy and hold method) and subtract the intraday returns.

          I understand the practical issues you are raising about feasibility – I just want to understand what calculations are (in)correct. First, I verify your finding that $1 million invested on intraday results in ending up with $140. The buy and hold strategy, from my calculations, ends up with $25,943 – a terrible (but not as terrible) return. My incorrect overnight method gives me ending up with $8,096 and the residual method for overnight returns gives me $25,803.

          So, I am not getting the huge returns overnight that you are showing – clearly this must be due to my calculation of the buy and hold strategy. But all I did was take (adj close time t/adj close time (t-1))-1 and then put $1 million in on August 1, 2019 and let it stay in the stock until today. The other mystery to me is why my calculation of overnight returns (using the prior days closing price and the next morning’s opening price) is so different than the residual method. Since there are no dividends involved, this is a mystery to me.

          If you can clarify this, I’d appreciate that – it doesn’t look like rocket science to me, but perhaps it is worse (being finance).

        • Never Mind! My apologies. It may not be rocket science but I still managed to invert a formula. I can now confirm the same results as siddhartha for the SNDL stock. And, I accept the anomaly as real, though its practical significance is questionable.

          I also have a story similar to Daniel’s. A very early consulting project I had was to critique a zoning decision that was based on the “commercial value” of sand and gravel in a particular county. The number that had been estimated was huge – but was obtained by using the then-current market value of sand and gravel and applying it to the total sand and gravel at the sight in question. But that total amount was greater than the size of the potential market – so the then-current price was not relevant to what it could possibly sell for. Scale mattered.

  13. The dividend theory of the overnight market anomaly is a non-starter for many different reasons.

    Yes, it is true that if N owns a security only overnight and D only intraday, N will receive all of the dividends, and D none. Dividends are paid to whoever owns shares at the close before the ex-dividend date.

    However,

    1) The dividend theory cannot explain why many non-dividend stocks exhibit the overnight anomaly or why many dividend stocks fail to exhibit it.
    2) A single stock can exhibit the anomaly when it is not paying dividends and/or fail to exhibit the anomaly while paying dividends. AIG is an example of the latter phenomenon: it has paid quarterly dividends since at least the end of 1984, but its overnight anomaly does not begin until 2001 or so. The dividend theory fails to explain why the AIG overnight anomaly showed up when it did, and AIG is not alone in this respect.
    3) As pointed out by Carlos, typical dividend yields (about 2% per annum on average) are too paltry to explain the magnitude of the overnight anomaly in many cases.
    4) More generally, differences in dividend yield are useless for explaining differences in the size of the overnight anomaly.

    But more importantly than any of the above observations:

    5) If N buys a security at the close the evening prior to the ex-dividend date, she will see the next day’s opening price drop by the amount of the dividend. If N sells at the open, she will experience a temporary loss but will be made whole after a few weeks when the dividend is deposited in her brokerage account. If D buys at the open, he will buy at the newly discounted price and experience no dividend-related loss, temporary or otherwise.

    The dividend is paid to N precisely because it is deducted from her overnight return, and D receives no payment because the dividend is not deducted from his intraday return.

    Suppose your employer promises you a year-end bonus but subtracts the entire bonus amount from your November paycheck. Dividends are like that. A dividend is not a gift but the delayed repayment of sequestered capital gains.

    Example: BKE (The Buckle, Inc., an apparel retailer) paid a $3 dividend last month. The ex-dividend date was 1/12/23. BKE closed at $49.74 on 1/11/23 and opened at $46.85 on 1/12/23: it dropped $3 because of the dividend and gained 11¢ because of other factors. Absent the dividend and ceteris paribus, we would have expected an opening price of $49.85, an 11¢ profit per share.

    An overnight owner was down $2.89 per share temporarily but received the $3 dividend down the road, so her eventual overnight gain was eventually that same 11¢ per share.

    Accounting for dividends does not give N an unfair advantage over D; it merely compensates N for having dividend amounts subtracted from her returns. It would give D an unfair advantage NOT to do this. Admittedly, this unfair advantage is typically too small (~2% per annum) to undo any but the weakest positive overnight anomalies.

    A note on calculating intraday and nocturnal returns:

    Yahoo Finance supplies an unadjusted opening price O, an unadjusted closing price C, and an adjusted closing price aC.

    The close-to-close return = aC[t]/aC[t-1]. Adjusted prices are necessary since the dividend accrues to the overnight return.

    The intraday return = C[t]/O[t]. Adjusted prices are unnecessary since the dividend does not accrue to the intraday return.

    The overnight return = close-to-close/intraday = (aC[t]/aC[t-1])/(C[t]/O[t]). Adjustment for dividends is necessary and occurs in the numerator.

    This last formula is algebraically equivalent to (O[t]* aC[t]/C[t])/aC[t-1].

    The ratio aC[t]/C[t] is the adjustment factor that converts an unadjusted price to an adjusted one.

    O[t]* aC[t]/C[t] is therefore the adjusted opening price aO[t], which is not supplied directly by Yahoo but easily derived from their data (adjusted high and low prices can be similarly derived).

    The overnight return is therefore aO[t]/aC[t-1]. It’s the adjusted opening price divided by the prior adjusted closing price.

    Using adjusted prices does not change the intraday return, since aC[t]/aO[t] = aC[t]/(O[t]* aC[t]/C[t]) = C[t]/O[t].

    An alternative derivation (also outlined by Carlos):

    aC[t]/aO[t] = (C[t]* aC[t]/C[t]) / (O[t]* aC[t]/C[t]) = C[t]/O[t]. The final term results from cancelling out the adjustment factor present in both the numerator and the denominator.

    I am not convinced Bruce Knuteson’s evil hedge fund explanation for the overnight anomaly is correct. There is a plausible alternative theory involving the differing behaviors of institutional and retail investors. An academic account of this theory is available here:

    https://www.semanticscholar.org/paper/Paying-Attention%3A-Overnight-Returns-and-the-Hidden-Berkman-Koch/ff64bccbd678828e4a83fb0304e8e15148ef67a6

    And a more informal account here:

    https://www.advisorperspectives.com/articles/2022/06/24/night-moves-is-the-overnight-drift-the-grandmother-of-all-market-anomalies

    • Thank you for this – it helps overcome my lack of financial knowledge. I’m almost convinced – but it raises a question for me. I see how the next day’s opening price drops when the dividend is paid. So, when I calculate nighttime returns using the prior day’s closing price and the next day’s opening price (neither adjusted), then I would be underestimating the returns on those days – I’d see an “apparent” drop in price that just reflects the payment of the dividend. However, for the few stocks I looked at, calculating nighttime returns this way, and trading like that every day, ends up providing much higher returns than the intraday returns. So, even the incorrect method (if I understand you) of buying at the closing price and selling the next day’s opening price, results in much higher returns despite the fact that dividends will suppress the opening price. Of course, dividends are only paid periodically, so the fact that the return is so high must mean that the nighttime effect is that much stronger to overcome the underestimation due to the dividends.

      Am I just observing the phenomenon you are highlighting? And, while the nighttime return calculation will be wrong on those dividend days, is that fact just swamped by the nighttime effect on all the non-dividend days?

      • More or less yes. Dividends are paid a few times per year, so every day you do your calc is correct except those 4 days or so. The “overnight effect” swamps these few percent missing, and the error for not including dividends actually results in you calculating **too small** an excess return as you point out.

      • Daniel is correct. The overnight effect is frequently so large that leaving out the dividends makes little difference. Similarly, Usain Bolt would likely beat me in a 100 meter dash even if handicapped by a backpack full of rocks.

        Since the nocturnal investor gets the dividends, we might all well include the dividends in her returns. It makes little sense not to.

        Dividend payments reduce a few opening PRICES each year, but they have no effect on the intraday RETURNS and they depress overnight RETURNS only temporarily.

        If a stock is due to open at $10 and go up 5% intraday, it will close at $10.50. If a $1 dividend is paid, it will open at $9 and close at $9.45. The intraday investor makes the same 5% return in either case.

        If a stock closes at $10 and goes up 5% overnight, it will open at $10.50. If a $1 dividend is paid, it will open at $9.50. The overnight owner will see a temporary 5% loss that will convert to a 5% gain once the 10% dividend is deposited. The overnight investor makes the same 5% gain in either case, but in the dividend case the gain is not realized until the payment date, typically (and annoyingly) several weeks after the ex-dividend date.

        • If a stock is due to open at $10 and go up 5% intraday, it will close at $10.50. If a $1 dividend is paid, it will open at $9 and close at $9.45. The intraday investor makes the same 5% return in either case.

          Do you have evidence for this? It seems to assume people are not aware of the dividend beforehand, which of course they are.

          But also, the way yahoo adjusts for dividends may be chaining together multiple adjustments.

          https://help.yahoo.com/kb/SLN28256.html

          Perhaps someone wants to verify this but it looks like if Intel (INTC) closed at $27.85 on 11/04/2022 and payed a dividend of $0.365, then all previous close values are adjusted downward by a multiplier of 1- 0.365/28.20 = 0.9871.

          Then a dividend of $0.365 is payed on 02/06/2023 when the close price was $28.69, so the multiplier is 0.9873. This is then applied to all previous closing prices.

          So tracking 11/1/2022 close:

          Actual Close = $28.30
          Adjusted Close as of 11/04/2022 = $28.30*0.9871 = $27.93
          Adjusted Close as of 02/06/2022 = $27.93*0.9873 = $27.58

          Note there is also rounding going on. But I have not looked at the yahoo data myself to see if this is the procedure vs eg, only applying the multiplier to the previous dividend date, or something else.

          I’ve never cared about these adjusted close values, but it does seem like a procedure prone to producing artifacts.

    • siddhartha:

      Thanks for the refs. The pattern of spikes in the price of meme stocks at open is an interesting possible explanation. Meme stocks also trade more frequently at night. I’m sure if you compared the overnight volume of TSLA to UNP or CVS, the volume of TSLA would be proportionally far higher.

      I’m curious if you have any thoughts on overnight effects of other factors:

      1) the US regular “day” session is only 6.5hrs while “overnight” in the sense used in this paper is 17.5hrs

      2) the US regular day session (9:30a to 4p) is shorter than US business hours (8a-5p)

      3) the overnight period has three distinct segments: post-market, market closed, and pre-market. The day session is a single continuous session. The time during which the market is closed *should* occasionally generate news that could cause a substantial discrepancy between the closing price and the theoretical value, causing an open spike in pre-market trading.

      4) corporate news releases – which sometimes affect price – are almost always during pre/post-market

      5) Today with more global integration, government data releases occur ’round the clock, meaning price activity that they drive would be more likely to occur in the much longer overnight period.

      If the value of stocks is driven by news about companies and economies, it seems obvious that most of that news would be released outside the short regular US trading session – and on US markets that is actually done by design – so we should *expect* a significant overnight effect.

      • After-hours trading appears to be irrelevant to the overnight anomaly, which can be found in stocks that do not trade at all outside normal hours.

        The overnight interval is 2.7 times as long as the intraday session. In theory, overnight volatility should be √2.7 = 1.64 times as great as intraday volatility (volatility scales with the square root of time). In theory, stocks are exposed to 2.7 times as much news overnight compared to intraday.

        Increased exposure to news does not explain why so many stocks have an overnight bias. After all, news can be good or bad. One should therefore expect increased exposure exposure to news to increase overnight volatility rather than having a consistent directional effect on prices. In theory, overnight volatility should be √2.7 = 1.64 times as great as intraday volatility (volatility scales with the square root of time). In practice, overnight volatility is markedly less than intraday volatility. The overnight anomaly is a price and volatility anomaly.

        See https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2633476 (Night Trading: Lower Risk But Higher Returns?)

        In an earlier post I provided two persuasive articles that plausibly explain the overnight anomaly in terms of the differing behavior of institutional and retail investors.

        • “After all, news can be good or bad. ”

          Except that there is net positive economic growth. In equity markets specfically, crappy companies with consistent bad news shrink, their overall effect on the market is reduced, while as co’s like GOOG, META, TSLA, etc grow rapidly, the good news is obviously outpacing the bad.

          just something to consider. I find that in social sciences there is usually a lot going on that has to be ignored to make the problem analytically tractable, but unfortunately the compromise is often so great that it makes the outcome of the analysis irrelevant.

        • Reply to chipmunk below.

          (aside to all: why do some posts on this site have a reply button and others, like chipmunk’s below, do not?)

          The kind of news you’re taking about is consistent with the steady growth of successful companies, the gradual decline of poor companies, the upward trend of the market as a whole despite occasional recessions.

          However, if you sample stocks with outsize overnight returns you will find that most of these (as many as 75%) have negative intraday returns. A good number of these are not successful companies if judged by 24 hour returns, i.e., they are losing more money intraday than they are making at night. Nocturnal outperformers wit positive intraday returns typically have barely positive intraday returns. Only a few will have significantly positive intraday returns, and it is quite rare for a stick to simultaneously outperform both overnight and intraday.

          The sort of “news” that could account for such facts must be rather peculiar stuff: potent enough to cause a jump up in the opening price but with such a short-life that the price begins to fall very quickly intraday. From a paper on the overnight anomaly:

          “Excess overnight returns for [consistent overnight outperformers] disappear quickly after the open, but not instantaneously. They decline by 0.02% if sales are postponed by a few minutes after the open and disappear after 45 minutes.”

          Further, this “flash-in-a-pan” phenomenon needs to happen over and over again over months and years to explain prolonged and extreme overnight outperformance paired with prolonged and extreme intraday underperformance, as seen with AIG and SNDL.

          Ordinary economic news hardly seems a plausible explanation for such a repetitive and potent but short-lived phenomenon. Ordinary news may have a positive bias but tends to be intermittent and unpredictable with long-lasting impacts.

          I’ve provided two links to what I and many others think is a very plausible explanation of the overnight anomaly. Increased exposure to news during the much longer overnight session is not a part of that explanation. Why not give one or both of those articles a gander?

        • Sorry. I’m never quite sure where my replies will be inserted in the sequence of posts. I just replied to a post by chipmunk that has ended up above my reply and not, as I had erroneously expected, below it.

      • If the value of a stock is driven mostly by the financial results and outlook of the company does it seem obvious to you that we should expect a significant earnings-release effect?

        Significant as in “a large part of the long-term returns is concentrated in four predetermined days of the year”?

        Do you think that a portfolio containing GOOG and META will do much better if on earnings days you go all in the corresponding stock?

  14. To Anoneuoid:

    Consider a company with a $5B market cap composed of 100M outstanding shares with a share price of $50. If that company issues a $1 dividend, it will pay out $100M worth of dividends, thereby reducing its total market value to $49B and making $49 a fair share price, ceteris paribus. Concurrent factors may increase or decrease the share price above or below $49, but $49 and not $50 is the new fundamental starting point for any such changes.

    You are correct that rounding errors might eventually distort the accuracy of repeated retroactive dividend adjustments. One can avoid this problem by using a series of daily returns rather than prices. Returns only need adjustments on ex-dividend days, and no returns ever get readjusted. However, calculating cumulative growth is harder with returns: you have to multiply a series of returns. With prices, one merely divides the final price by the initial price. If the prices are unadjusted, you get the capital gain sans dividends. If the prices are adjusted, you get the capital gain with dividends reinvested. That’s why so many data providers provide retroactively adjusted prices: to make such cumulative growth calculations easy.

    • Consider a company with a $5B market cap composed of 100M outstanding shares with a share price of $50. If that company issues a $1 dividend, it will pay out $100M worth of dividends, thereby reducing its total market value to $49B and making $49 a fair share price, ceteris paribus.

      Yes, but we can be fairly confident Intel will issue another ~$0.365 dividend next quarter. Why is this not already priced in?

      • It is in some sense. Owning Intel is like owning a (pure) bond and a (pure) stock together. The bond gives you the right to receive the dividends, the stock gives you the right to a certain fraction of the liquidation value of the company’s assets, including the time-discounted value of future earnings. If a company never pays dividends then in some sense you’re just holding a fraction of its assets (including the future income and intellectual property and various intangible stuff such as consumer-goodwill as an asset)

        There are ETFs that buy mainly high-dividend yielding stocks. They are far less volatile and the ETF tends to move more like a bond than like a stock.

      • Why do you say that next quarter’s dividend isn’t priced at $49?

        Let’s say that today the stock starts trading ex-dividend, at $X, and prices every future cashflow in (discounted, because of their uncertainty and the time-value of money).

        What do you think that the right price was yesterday at the close if all the future cashflows had to be priced in?

        Hint: the future cashflows yesterday night were the same as today – just as uncertain as just as far in the future – plus a certain and immediate $1. (Absent relevant overnight information and ignoring taxes and other minor details.)

      • If I knew Intel was going to make a surprise announcement they will *not* issue a dividend next quarter, I would put everything into shorting INTC. It would be catastrophic for the stock price. Yet, according to your model, paying a dividend should reduce the price.

        I get that the company has slightly fewer assets, but this is already (usually) known beforehand and is swamped by much larger factors.

        • > Yet, according to your model, paying a dividend should reduce the price.

          Do you have a better model?

          Consider a stock that pays a $1 dividend tonight. If you can enter now either

          1) a (spot) trade to get it for $10 today or

          2) a (forward) trade to get it for $10 tomorrow

          do you have a preference for one choice over the other?

          (Hint: In both cases you pay $10. In one case you get the share and the dividend. In the other case you get only the share.)

        • Do you have a better model?

          Whatever model is supposed to account for the effect of dividends should definitely account for the volume dividend-only funds must now be forced to sell by some date. It should also account for the loss of confidence in the company, and that dropping dividends would probably coincidence with major stock buybacks or some other kind of announcement to blunt the effect.

        • Maybe we are talking about different things and we actually agree.

          The discussion was never about the effect of announcements or anything like that.

          It’s about a company that announces at some point that a $1 dividend will be paid on date D. Then the D-day arrives.

          With the information that you have at that time, what could make the expected fair price at the open of day D+1 diverge from the fair price at day D?

          Other than the fact that buying today you would hace exactly the same share tomorrow plus a dollar, of course.

          You didn’t answer the question in my precious comment. Would you pay the same or not? If not, why not?

        • Amazon announced in March 2020 that they would do a 20-for-1 split over the first weekend in June.

          The stock closed at $2447 on Friday 3rd and opened at $125 on Monday 6th. A 94.9% decline.

          Coincidence? I think not!

      • “Yes, but we can be fairly confident Intel will issue another ~$0.365 dividend next quarter. Why is this not already priced in?”

        Because you don’t get it unless you hold on through the ex date. If the dividend payments were made compounded and paid daily, then the div would be priced in all the time.

        But dividend “pricing in” isn’t as simple as it’s made out to be here. If you watch higher dividend stocks like INTC, VZ or T or others, you’ll see the price rises in the days before the ex date, as people trade into the stock to pick up the dividend. It would be interesting to see someone try to measure this effect. It’s probably proportional to the yield of the dividend and inversely proportional to the price risk of the stock. Anyway, for higher yielding stocks the dividend starts “pricing in” roughly speaking sometime in the two weeks previous to the ex date.

        • Many investors are irrationally attached to dividends. Absent frictions like taxes and commissions, a rational investor should be indifferent between receiving a dividend and selling the equivalent amount of shares. A famous 1961 paper by Miller and Modigliani (both Nobel laureates in economics) makes this case:

          https://www.jstor.org/stable/2351143

          For an easier read:

          https://en.wikipedia.org/wiki/Modigliani%E2%80%93Miller_theorem

          In decades past, high commissions made receiving dividends preferable to selling shares. That is no longer an issue.

          The dividend capture strategy consists of buying stocks just before their ex-dividend date and selling them just after, with the goal of harvesting as many dividends as possible. This should not be profitable, since the dividends will be cancelled out by the drops in the opening prices on the ex-dividend dates.

          See

          https://smartasset.com/investing/dividend-capture-strategy

          I found this to be the most telling line in the article:

          “If dividend capture was consistently profitable, computer-driven investment strategies would have already exploited this opportunity.”

          If there is a reliably irrational trend for investors to bid up the price before the ex-dividend date, the best strategy would be to buy the stocks even earlier and sell ino the run-up.

        • siddhartha:

          “If there is a reliably irrational trend for investors to bid up the price before the ex-dividend date, the best strategy would be to buy the stocks even earlier and sell ino the run-up.”

          See VZ for the last year. That’s one example, but I noticed it years ago and have long considered it normal behavior, so I’m sure I’ve seen it in dozens of stocks. It’s probably common in LPs, REITs, Oil Trusts and other hi yield units.

          If you buy the stock 2-3 weeks out before the dividend is priced in and sell on ex-date at the same price you paid, then you’re positive the dividend; or if you sell on the day before the ex-date you’re positive a gain approximately equal to the dividend. If you buy when the dividend is priced in, 2-3 days before the ex-date, then sell on the ex-date, you break even or possibly lose.

          Thanks for the references! great stuff!

          “If dividend capture was consistently profitable, computer-driven investment strategies would have already exploited this opportunity.”

          This is true but of course no trading strategy in the market is “consistently profitable” except cheating (e.g., front running). That’s what makes it hard. :))

      • If you buy my example company prior to the ex-dividend day, you get $1 for sure plus all future (and uncertain) dividends. If you buy ex-dividend, you only get the future dividends. The opening price must drop by $1 (ceteris paribus) to reflect that the $1 dividend is no longer in the stream of expected dividends.

        Expected dividends ARE priced in but are priced out once they have been paid.

  15. Maybe we are talking about different things and we actually agree.

    The discussion was never about the effect of announcements or anything like that.

    It’s about a company that announces at some point that a $1 dividend will be paid on date D. Then the D-day arrives.

    With the information that you have at that time, what could make the expected fair price at the open of day D+1 diverge from the fair price at day D?

    Other than the fact that buying today you would hace exactly the same share tomorrow plus a dollar, of course.

    You didn’t answer the question in my precious comment. Would you pay the same or not? If not, why not?

    I am not sure, you appear to be talking about a hypothetical “expected fair” price. I am talking about the actual price.

    1) a (spot) trade to get it for $10 today or

    2) a (forward) trade to get it for $10 tomorrow

    do you have a preference for one choice over the other?

    *If* that was the choice offered, obviously get share + dividend. But that has nothing to do with reality, since there are many much larger factors involved. Further, many of these factors tend to *increase* the price when dividends are issued.

    INTC has been issuing the $0.365 dividend since Feb 4th, 2022 (before that it was slightly lower at $0.347). Since that date the price has varied between $48 and $24. The dividend is smaller than a typical day-to-day fluctuation.

    Also, rather than multiply all previous values by ~0.99 (as done for these “adjusted closes”), why not simply add the dividend to the returns when it is paid?

    • > I am talking about the actual price.

      The actual price of a Microsoft share on the evening of Friday 12 November 2004 was $29.97.

      The actual price of a Microsoft share on the morning of Monday 15 November 2004 was $27.35.

      That’s the third largest close-to-open percentage decline for Microsoft since the dot-com crash (the largest one was a during a market-wide sell-off in March 2020 and the second largest on the night of the FY16 Q3 earnings release).

      Could the actual dividend of $3 that one got with Friday’s shares – but wouldn’t get with Monday’s shares – have anything to do with that price movement?

      Nah, that’s probably just my brain seeking patterns in coincidences.

      • This is what you are talking about: https://i.postimg.cc/J4vYVqj2/msft.png

        We see the stock immediately jumped from ~$28 to ~$30 after the announcement of the special $3.00 dividend on July 20th. Then it dropped down to ~$27.50 for two months, after which it rose back up to ~$30 just before the dividend payment. Finally it returned to where it was, followed by dropping all the way to ~$25.

        This is traders trying to cash in, it has little to do with “fair price” changing the date of the dividend.

        • Thanks for the chart. It illustrates well the point.

          Our primate brain sees that exceptional gap from close to open and tries to put in in relation with the $3 dividend distributed to shareholders that night – that just reduced the company assets by $32 billion.

          In fact the price drop was completely unpredictable and there was no reason to anticipate that Microsoft could lose tens of billions in market cap overnight.

          Another recent example:

          The actual price of a General Electric share on the evening of January 3rd was $84.98.

          The actual price of a General Electric share on the morning of January 4th was $68.41.

          We should once again resist the temptation to link the 20% overnight drop in the share price to the value of things distributed by the company to shareholders precisely at that time.

        • Our primate brain sees that exceptional gap from close to open and tries to put in in relation with the $3 dividend distributed to shareholders that night – that just reduced the company assets by $32 billion.

          The price rose in anticipation of the dividend because it triggered an increase in buying. Then when that was over, it went back down to where it was.

          Are you saying the “fair value” of MSFT *increased* that much just before the dividend date? I really don’t understand.

        • > Are you saying the “fair value” of MSFT *increased* that much just before the dividend date? I really don’t understand.

          Note that I’m only saying things about the period from Friday’s close to Monday’s open.

          Are you saying the overnight drop in price when the stock goes ex-dividend couldn’t be predicted? I really don’t understand.

          If you really think that giving thirty billions away doesn’t have an effect on the valuation of a company why don’t they all do it every week? Shareholders would be delighted if they could have their cakes and eat them too!

        • If you really think that giving thirty billions away doesn’t have an effect on the valuation of a company why don’t they all do it every week?

          This is a strawman. First, we are talking about the stock price, not the valuation. Second, as soon as this was announced (and probably before) there were many people trying to figure out the best scheme to profit from it. If anything the slow drop from ~$28 to ~$25 was the actual effect of the new valuation (which was announced back in July 2004).

          The notable event on the day of/after the dividend was people selling their stock who were waiting for it. Then it looks like the greater fools who bought up to $30 sold most back all the way down to $25 a few days later.

    • > INTC has been issuing the $0.365 dividend since Feb 4th, 2022 (before that it was slightly lower at $0.347).

      In the last four years the close-to-open returns of INTC have underperformed the market on each and every ex-dividend date (compared to 50% of the regular days).

      In the last 15 years it has underformed the market overnight in 92% of the ex-dividend days (compared to 50% of the regular days).

      The median overnight underperformance relative to SPY on ex-dividend days is on the 15th percentile of the distribution for regular days.

      Coincidences, coincidences everywhere!

    • Reply to Anoneuoid:

      I have frequently used the phrase “ceteris paribus” when stating that an opening price drops by the dividend on the ex-dividend date. This proviso acknowledges that other news might also move the price up or down simultaneously with the dividend drop, obscuring the purely dividend-related change.

      In theory, on a perfectly calm ex-dividend day (a day on which there was no other reason for the opening price to differ from last night’s closing price), one would see the price drop by exactly the amount of the dividend. In practice, one sees drops very close to the dividend amount when the dividend is large and the market is fairly calm without any firm-specific news of import. INTC is currently a poor choice for a demonstration of the dividend drop, since its typical dividend is smaller than its typical daily price movement.

      Carlos has provided some quick and dirty statistical evidence for the dividend drop. This could be done more mthodically as follows:

      1) Calculate the average daily price change over hundreds of thousands of non-dividend days.
      2) Calculate the average dividend-adjusted daily price change for all the ex-dividend days, i.e., add the dividends to the raw price changes, then take the average.

      Claim: the two averages will be equal. The average or expected price change on ex-dividend dates will equal the average or expected price change on other dates, minus the dividend.

      You wrote: “Also, rather than multiply all previous values by ~0.99 (as done for these “adjusted closes”), why not simply add the dividend to the returns when it is paid?”

      Stock databases typically provide only price and volume data: you have to calculate returns yourself. Yes, they could replace the Adjusted Close column by a Dividend column (zero on days other than ex-dividend dates), and the formula for a dividend-adjusted close to close return would be very simple: (C[t]+D[t])/C[t-1].

      As I explained in an earlier post, adjusted prices reduce the computation of total returns (= returns with dividends reinvested) to a single division: final adjusted price divided by initial adjusted price.

      Without a column of adjusted prices, one would have to calculate all the individual dividend-adjusted close-to-close returns and multiply then together. Far more laborious (especially before spreadsheets).

      • Follow-up to Aneunoid:

        I downloaded price data for IBM going back to 1985. IBM paid quarterly dividend throughout this period. The average annual dividend yield was 2.73%, for an average quarterly dividend of 0.6825%.

        The average raw (not adjusted) close to close price change was

        4.17 pips (= 0.0417%) on non-dividend days

        versus

        -66.45 pips (= -0.6645%) on ex-dividend days

        That implies an average “dividend drop” of 66.45 + 4.17 = 70.63 pips = 0.7063%.

        The calculated average dividend drop, 0.7063%, is remarkably close to the average dividend, 0.6825%.

        Not a coincidence.

        The result for IBM is very clean. Less clan results will occur if enough irrational investors pursue a dividend capture strategy, bidding up the price before the ex-dividend day and depressing the price afterwards, producing a distorted ex-dividend day drop bigger than the actual dividend. If this occurs, smart investors should sell into the run-up and buy back after the ex-dividend drop (missing the actual dividend of course, but pocketing a price difference that is larger than the missed dividend).

      • I wonder what percentage of this blog’s replies consist of folks patiently explaining things to Anoneuoid, arguing with Anoneuoid (seemingly once the patience has run out), or Anoneuoid reposting the same tired, refuted concepts that they’ve used on this blog or on other message boards under the pseudonym Nonbel.

        • Unanon: Good point!

          Anon: We appreciate your contributions, but please don’t overdo it on the replies to comments. We want to avoid the pointless back-and-forths that Phil refers to as “garbage time.” Thanks.

  16. There might be “painting the tape” at close and other trading practices. But there’s no liquidity at that price. NSPY is an ETF that seeks to take advantage of this night effect, and their returns are underperforming the S&P 500 index. https://finance.yahoo.com/chart/NSPY? -3.1% for the S&P 500 vs. -5.8% for the “night index”. Academics don’t know how to trade.

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