martincmartin wrote: ↑Wed Aug 10, 2022 7:25 am
alex_686 wrote: ↑Tue Aug 09, 2022 10:28 pm
Yes, I am confident [that the stock market is a random walk]. This is adjacent to my day job. Lots of theory and empirical analysis on this.
Yes, and the theory and empirical analysis says it holds in some ways, at some times, approximately. All the theory has hypotheses that are only approximately met in practice. For example,
Wikipedia says:
> Many decades of empirical research on return predictability has found mixed evidence.
The
criticism section is long and as a lot of good information. It's far from settled among economists.
With mean reversion you are implying a larger mathematical structure that underlies stock movements, that past performance affects future performance.
Or that there's some underlying variable other than current price that affects future performance. Like future profits, and future interest rates. Or the "fighting the last war" nature of human beings.
Let say the S&P was at 4,000. It then crashes to 3,000. If the system was reverting to the mean then the market would not be a random walk. Rather there would be a strong bias for upwards movement.
Or a weak bias for upwards movement. Like, say, valuations.
There is no inherent reasons why long term rates should be 2% or 5%.
The Fed is trying to keep long term rates at 2%. When expected future rates are less, they lower the benchmark rate or even do quantitative easing. When higher, they raise the benchmark rate. They hope that they can cool expectations without causing a recession, but if faced with a choice between allowing persistent inflation or causing a recession, they'll cause a recession.
I think we have to agree to disagree. If belief in the EMH requires one to believe there is no inherent reason why long term rates should be 2% or 5%, and you believe this with all your experience from this being adjacent to your day job, I don't think I'm going to convince you. And I don't think you're going to convince me, or the markets, that 5% is as likely as 2% for long term rates.
But from time to the relationships change and we enter into a new secular period where we have new and different relationships. ... It is also why the longer the time frame the less mean reversion there is. You are moving from one secular period with one underlying structure to a different secular period with a different underlying structure.
Perhaps we mean different things by "mean reversion." If the different secular periods have different means, then that seems like it's not a random walk to me. And my point is: a secular period with a low mean is unlikely to be followed by another secular period with another low mean. For example, the 1970s had stagflation. The Fed was following a Keynesian model, saying "inflation isn't our problem, government needs to raise taxes and/or lower spending to fix it." After a decade of trying the same thing and it not working, eventually Paul Volker came around an very publicly raised interest rates to the point where it caused a recession. Since then, central banks have targeted inflation.
So the 1970s were a different secular period than 1982+. But the point is, people learned from what wasn't working, and tried something else. This behavior, of people trying new things when old things don't work then "fighting the last war," means a decade of low returns are unlikely to be followed by another decade of low returns.
hmmm. Let me try to put a finer point on some of my points.
A system that has a random walk does not mean the system is random. There can still be a underling principles that drive the system. What a Random Walk specifically means the amount of memory that system has. Or to put it another way, the amount of forecasting we can do with prior information.
Consider a dust mote and Brownian Motion. You have 2 forces acting of the dust mote, gravity and the random bombardment or air molecules. The overall motion of the dust mote is down - gravity is a harsh mistress. But you also have Brownian Motion knocking the dust mote left, right, up, and down. For simplicity sake lets just say left and right. 40% of the time the dust mote is going to jog right, 40% it is going to jog left, 10% down, and 10% chance up. You notice that the dust mote makes 10 up jogs. What is the chance that the next movement would be up? If it is a independent system, a random walk which Brownian Motion is, then the answer is 10%.
Here is the critical bit. If the system is mean reverting then the chance of a upwards motion would be something lower than 10%. The system would have a memory of the 10 up movements and would mean revert to some down movements.
So let us tie this back to your point on interest rates.
That rates are 2% or 5% are not a random event. There is a reason why they are where there are. We can create models to figure out those reasons and with reasonable confidence make a logical estimate of what they will be in the future.
We can look backwards at current rates and we can assume that future rates will be similar in the secular period. i.e., there is a modest amount of mean reversion. There are economic forces that drive rates within a band that makes rational sense. To bring this back to the dust mote, there is gravity that affects the system.
Now, onto the Random Walk, mean reversion, and what historical data tells us. You suggested that "low mean is unlikely to be followed by another secular period with another low mean", giving the 70s as a anecdotal example. This is not true. Tha would imply the system has a memory and will mean revert to its natural correct state. It does not. Humans are pattern recognition machines, and we are engineered to find patters even when there are none. I have worked with lots of data from lots of markets from lots of time periods. A low period is just as likely to follow a low period as a high period. There is no mean reversion.
Now, back to tie this back to what the OP is saying and why I think it is a false statement, and a rather optimism statement.
First, the critical point. If we have a crash in year 1 what is the chance that we will have a crash in year 2? Lets say we have had 10 years of bull markets, what is the chance of crash in year 11? The answer is that the chance is the same. i.e., crashes are random walk events, unseen in the prior data, a priori.
Second, I will grant this is kind of hard to see. See the point that humans are pattern recognition machines. But the OP is also working with a very small data set. That it has taken 20 years to recover in this data set does not statistical imply that is the natural maximum recovery period. The error bands are huge.
Third, the underlying economic forces that are in play are dynamic. Whatever caused a 10 or 20 year recovery period is not in operating now. Economic forces and relationships have changed. To put this is a specific case, I will refer back to the example where the market fell from 4,000 to 3,000. If the economic forces where constant then the system would be mean reverting. The correct inherent value of the market would be 4,000 and we should see movement back there. We don't. In my example interest rates have changed. The new correct value of the market is 3,000.
To wrap this all up.
People like to say that since the market has on average returned 10% a year for the past 100 years then it should continue to return 10% a year. i.e., that there is a mean reversion to 10%. Or that since the historical P/E ratio of the S&P has been 15 then the market will mean revert to a P/# of 15. Statically tests show this is not true.
Does the length of the current secular region tell us how long until the next
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.