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This question claims that stock prices are considered "memoryless". Informally it is defined in the question to say that "past performance isn't an indicator of future performance". Technically memorylessness is a property of random variables, and again informally is used about probabilities: i.e. the fact that a coin came up tails last time it was thrown doesn't mean it is more likely to come up heads this time.

The trouble with this is that stock market prices are not random variables. However imperfectly, they represent the value placed on a company, and that valuation is going to be largely controlled by real world events. If a company's circumstances don't change, then a drop in its share price is going to be followed by a rise later. The prices can of course change when the company's circumstances change, but they aren't "memoryless" either. A company's future state is influenced by its past.

So: are share prices really described as "memoryless"? Is there a technical meaning of the term? What does it really mean?

EDIT:The other question now includes a link to this article which seems to equate the "memoryless" hypothesis with the "efficient market" hypothesis.

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As you say, a string of random numbers has no memory or state. A stock price is very different, in that it is full of state -- I.E., a past market belief that the stock will outperform is by nature embedded in the current price. Good question. –  NickC Nov 28 '11 at 17:18
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This seems like more of a speech disguised as a question. –  JohnFx Nov 28 '11 at 21:02
    
The questions is in the last paragraph but one. It was the last paragraph until I added the edit. –  DJClayworth Nov 28 '11 at 21:09
    
@DJClayworth If you want more search terms that might help when searching for information like this, look up the notion that stock prices follow a random walk or exhibit characteristics of a Markov process, since those are mostly just synonyms for memoryless random variables. Another answer referred to Markov models, but random walks are important as well. –  John Bensin Apr 4 '13 at 21:14

6 Answers 6

up vote 3 down vote accepted

It reminds me of the Efficient Market Hypothesis, except that just states in its weakest form that the current market price accounts for all information embedded in previous market prices. In other words, people buying today at 42 know it was selling for 40 yesterday, and the patterns and such.

To say that stock is memoryless strikes me as not quite right -- to the extent that stocks are valued based on earnings, much of what we infer about future earnings relies on past and present earnings.

One obvious counterexample to this "memoryless" claim is bankruptcy. If a stock files bankruptcy, and there isn't enough money to pay senior debt, your shares are worth 0 in perpetuity.

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I added a link backing this up. –  DJClayworth Nov 28 '11 at 20:20
    
I'm accepting this because it appears to be the most widely accepted description of the term. However there do appear to be conflicting uses. –  DJClayworth Jan 2 '12 at 17:48

I think that "memoryless" in this context of a given stock's performance is not a term of art. IMO, it's an anecdotal concept or cliche used to make a point about holding a stock.

Sometimes people get stuck... they buy a stock or fund at 50, it goes down to 30, then hold onto it so they can "get back to even". By holding the loser stock for emotional reasons, the person potentially misses out on gains elsewhere.

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This is an interesting question that may actually be better suited to Quant.SE.

First of all, stock prices are random variables, or, to be more precise, stochastic processes (a time-ordered string of random variables). The alternative to being stochastic is being deterministic, and I doubt you believe that stock prices are deterministic (meaning, they are fully knowable in advance). The fact that real world events drive the randomness has no bearing on whether or not it is random. So, to start, I think you have confused the technical definition of random with a colloquial concept.

Now, the heart of the question is whether stock prices are memoryless. Ultimately, this is an empirical question that has been addressed in many academic studies. The conclusion of most of this research is that stock prices are "almost" memoryless, in the sense that the distribution of future stock prices displays very little dependence upon past realizations, although a few persistent anomalies remain. One of the most robust deviations from memorylessness is the increase in the volatility of a stock following large declines. Another is persistence in volatility. In general, in fact, the volatility is far more predictable than the mean of stock price changes. Hence "memorylessness" is a far stronger assumption than the efficient markets hypothesis.

The bottom line, however, is that the deviations from memorylessness are relatively small. As such, despite its limitations, it is a decent working assumption in some contexts.

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I am unconvinced by the argument that everything is either random or "fully known in advance". If you have a particular definition of "random" in mind, could you give it, please? Some references would also help. –  DJClayworth Nov 30 '11 at 15:33
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By that definition a stock that is 99% likely to go up and 1% to go down is classed as "random". A good technical definition but not necessarily useful. –  DJClayworth Nov 30 '11 at 17:22
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Your question is meaningless without a definition of random. Definitions are useful so people can be sure they are talking about the same thing rather than talking past each other based on hidden assumptions. –  Tal Fishman Nov 30 '11 at 18:44
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@DaveBall strictly speaking, you are correct, but only cranks still take chaos to be a reasonable assumption for real world stock prices. They're clearly random. –  Tal Fishman Jan 1 '12 at 1:03
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@DaveBall It's difficult to demonstrate a negative. It's more an impression I have from the fact that, to my knowledge, there haven't been any papers in major finance journals that assume stock prices are deterministic but chaotic. See this quant.SE question, and in particular see the comments. Also, I changed "known" to "knowable" in light of your comments. Even chaotic processes are "knowable", just not very easy to figure out. –  Tal Fishman Jan 1 '12 at 16:45

With my current, limited knowledge (see end), I understand it the following way:

Are share prices really described as "memoryless"?

Yes.

Is there a technical meaning of the term? What does it really mean?

The meaning comes from Markov Models: Think of the behavior of the stock market over time as a Markov Chain, i.e. a probabilistic model with states and probabilistic transitions. A state is the current price of all stocks of the market, a transition is a step in time. Memoryless means that transitions that the stock market might make can be modelled by a relation from one state to another, i.e. it only depends on the current state. The model is a Markov Chain, as opposed to a more general Stochastic Process where the next state depends on more than the current state. So in a Markov Chain, all the history of one stock is "encoded" already in its current price (more precisely in all stock's prices).

The memorylessness of stocks is the main statement of the Efficient Market Theory (EMT).

If a company's circumstances don't change, then a drop in its share price is going to be followed by a rise later.

So if the EMT holds, your statement above is not necessarily true. I personally belief the EMT is a good approximation - only large corporations (e.g. Renaissance Technologies) have enough ressources (hundreds of mathematicians, billions of $) to be able to leverage tiny non-random movements that stem from a not completely random, mostly chaotic market.

The prices can of course change when the company's circumstances change, but they aren't "memoryless" either. A company's future state is influenced by its past.

In the EMT, a stock's future state is only influenced by its past as much as is encoded in its current price (more precisely, the complete market's current state). Whether that price was reached by a drop or a rise makes no difference.


The above is my believe, but I'm by far no finance expert. I am working professionally with probabilistic models, but have only read one book on finance: Kommer's "Souverän investieren mit Indexfonds und ETFs". It's supposed to contain many statements of Malkiel's "A Random Walk Down Wall Street".

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@jidugger mostly got it right. It basically mean that past performance of a stock, or a basket of stocks, are not at all useful when trying to predict its future. There is no proven correlation between past and future performance.

If there was such a correlation, that was "proven" or known, then investors would quickly exploit this correlation by buying or selling this stock, thus nullifying the prediction.

It doesn't mean the specific individuals cannot predict the future stock market - hell, if I set up 2^100 different robots, where every robots gives a different series of answers to the 100 questions "how will stock X do Y days from now" (for 1<=Y<=100), then one of those robots would be perfectly correct. The problem is that an outside observer has no way of knowing which of the predictor robots is right.

To say that stock is memoryless strikes me as not quite right -- to the extent that stocks are valued based on earnings, much of what we infer about future earnings relies on past and present earnings.

To put it another way - you have $1000 now, and need to decide whether to invest in a particular stock, or a stock index. The "memoryless" property means that no matter how many earning reports you view ... by the time you see them, the stock price already accounts for them, so they're not useful to you. If the earning reports are positive, the stock is already "too high" because people bought it before you did. So on average, you can't use this information to predict the stock's future performance, and are better off investing in an index fund (unless you desire extra risk that doesn't come with more profitability).

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It means price movements in the past do not affect price movements in the future.

Think of the situation of a coin, if you flip it once, and then you flip it a second time, the results are independent of each other. If the first time, you flipped a HEAD, it does not mean that the coin will remember it, and produce a TAIL the second time. This is the meaning of "memoryless".


FYI, stock markets are clearly not memoryless. It is just an assumption for academic purposes.

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Thank you for repeating the explanation of "memoryless" that I gave in the question. –  DJClayworth Jan 2 '12 at 17:46

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