My question is: suppose you take something like a stock index. Consider (A) the average price on all days in which the index has dropped for that particular day. Compare to (B) the average price on all days regardless of price direction on that day. Is A likely to be lower than B?
Superficially, one would think this has to be true. But offsetting that is the possibility that there is some correlation between price movement on one day and price movement on the prior and subsequent days.
The implication if this is correct would be that someone contemplating dollar cost averaging as an investment strategy would be better off skipping days on which the investment has increased and deferring that investment until the next time it decreases. (E.g. if you put $1,000 into the S&P on the first of every month, then you would skip the first of the month if the S&P is down for the day and instead put in $2,000 on the first of the next month, if it happens to be down on that day.)
The same question would apply to things like weather and any number of other sequential numbers subject to random movement. Though the answer may change based on the true randomness of movement for the given series.
If the numbers are perfectly random, then my intuition is that the average of dropped numbers ought to be lower. The reasoning being that you know nothing about the previous number, thus on average the previous number is the average. Therefore, the numbers you are averaging will be lower then average, on average.
Hope that makes sense.
I’m sure I could explore this more rigorously, but given the difficulty of writing out complex math on this board, I took a monte-carlo approach. I just wrote a python program that draws 10,000 normal distributed numbers (ave.: 0, std: 1), and took the average of the numbers that were less than the previous, which turned out to be -0.57 which is statistically significant. Running this many times gives very similar results every time.
Now, if the numbers aren’t perfectly random, but are correlated, then anything could happen depending on the correlations.
I know very little about stocks. But my (poor) understanding is that stocks do not have an average in the sense that the average of the past numbers will tell you anything about future behavior. (Obviously you can perform an average of previous performance, but my point is that this does nothing to predict future performance).
If I’m understanding correctly, I think the above does not follow, because there are also longer term trends to account for. Whether A or B is higher, it could be that there’s a trend that says the day X average, even once you account for A vs. B, tends to be lower than the day X+30 (or 60 or 90) days average, because of a historical upward trend in the market. You would then want to have bought your $1000 on day X, not day X+30, even if day X was not an A day, because while the down days were cheaper than the average day, both averages were rising over time.
As an extremely exaggerated example, I think you would take the opportunity to buy a stock 10 years ago if you could, even if the market was way up on the day you bought.
As a general rule for stocks, if you can find a simple pattern, then so can anyone else. And if everyone can spot a pattern, then they’ll invest accordingly, which will erase the pattern. Thus, there are no simple patterns in stocks.
What if you did the following instead: Keep a running total of those normally distributed numbers and, when the total decreases (the number you’re adding is negative), take the average of the previous total and new one. What do you get for the average of those numbers? This is closer to the scenario in the OP but I don’t know if it will make any difference in the final answer.
A common model for stock prices is that changes are lognormally distributed. So a more verisimilitudinous model might be to keep a running product of the exponentials of those normally distributed numbers.
There’s a whole field of stock analysis called ‘technical analysis’ that claims to be able to spot investable patterns in stock movements. Most or all of it is gambler’s fallacy logic.
If the market is efficient, then the current price of a stock represents all the information known publically about it. So if stocks were more likely to rise after a short fall, institutional investors and automated trading algoithms will already have priced that in by the time a solo investor sees the numbers.
It reminds me of casinos that encourage tracking the roulette wheel by giving out little notepads and pencils and having displays showing you the results of the last ten numbers.This gives the illusion that smart people can profit from deciphering the patterns.
If you see ‘black’ come up 5 times in a row, what should you do? Half the gamblers will tell you that black is ‘hot’ and you should bet black. The other half will tell you that white is ‘due’, and you should bet white. Neither half has a clue what will happen next.
If a stock falls one day, half of the investors might say that it’s due to return to its previous price because of regression to the mean , and the other half will say that a falling price means investors have discovered new information that’s negative, and it will fall some more. Technical analysts complicate this by assigning ‘breakthrough’ levels and price floors and all kinds of other signals and triggers they claim to glean from price movements.
The smart gamblers don’t bet roulette at all, because it’s a random walk with mo exploitable information and the house will take 5.26% of your money for trying. Likewise, individual investors who try to play the pattern game wind up giving all their money to the ‘house’ (brokers) who charge for the transactions, while gaining or losing nothing on the ‘trend’ because it’s just randomness.
For people without inside knowledge of the company or industry, or without the time and will to seriously pour over balance sheets and stuff, the best investing strategy is to buy mutual funds or other diversified investments in the right ratio to meet income, risk and growth needs, then hang onto them. Dollar cost averaging helps smooth the bumps and lowers risk a bit.
That’s a good point. It would depend on how much volatility there is on an average day vs the amount of long term trend.
This is a version of the “efficient market hypothesis”, but I think it’s overstated here.
The suggestion here is not that there’s a guarenteed way to make profit, but just that one investment strategy might be more efficient than another. So it would primarily be of interest to people who were otherwise contemplating the alternative strategy.
The only way to lock in profits if the OP’s thesis is correct would be to buy on down days and sell (or sell short) on all other days. Besides for the uncertainty involved in how much to invest on all days vs down days, ISTM that the execution costs of such a strategy would make it impractical.
Even assuming that it’s true that the average price on days when the stock has dropped is lower than the overall average price, I don’t think that this strategy is necessarily going to work.
By not investing on a specific day when the price didn’t drop, you don’t get to invest on an average day when the price dropped, you get to invest at some future day when the price dropped, and during the intervening days, you’re making (presumably) a lower return because you’re keeping your investment in cash (or whatever).