lack_ey wrote: Let us assume that we think processes A, B, C, and D all each have positive mean (at a significant level), that the expected value is positive*. Also, they have roughly the same standard deviations and distributions that aren't basket cases. So you're saying that a combination 0.25*(A + B + C + D) won't have positive expected value? How? Or even any weighted combination of the four? Does this even require another statistical test?
OK, I don't know what "distributions that aren't basket cases" means, so I cannot respond to that part.
As for the rest, the problem is you are making a couple of assumptions that basically determine the reliability of the expectation. I keep bringing up LTCM because they did exactly this. They had a set of bets, I think it is often described as 4 general categories, but it seems there were many individual bets within these. Each of these categories of bets was expected to have a positive return. The fund blew up because these 4, or whatever, bets that they thought were not highly correlated turned out to all go bad in response to the same event. By design, the managers thought, these factors were not highly correlated, and one event should not have trashed the portfolio.
I don't know whether they assumed the bets were independent, or they assumed correlations among them. In either case, they assumed they knew what the correlations were. But they were wrong.
If you mix several variables together, the outcome depends on how the variables covary. The simplest case is that the correlations are zero and the variables are independent. But in the case of financial markets and extreme events, you don't know whether the correlations are zero. You might have observed that the correlations were close to zero over certain periods of time. But what does that tell you about their behavior when something extreme happens? Apparently, not much. Remember, you can model the likelihood of any particular event as extremely low, but collectively unlikely things happen all the time.
To believe that your portfolio has controlled its risk through betting on a variety of factors, you have to believe that you know the entire variance covariance matrix of the bets. You have to believe that you know it from "normal times" based on a look back at available data. But you also have to believe that you know what these covariances do in the extreme. You don't know what these extreme events will be, how many there are that can affect your portfolio, or how your investments will behave when one of these extreme events happens.
That is why I think it will take a long time- perhaps decades, to find out what extreme events could affect this mix of bets. Of course, if you change the mix of bets, then you change the sensitivity to particular extreme events, making some less important and others more important.
These problems apply just as much to a 3-fund portfolio. But with a 3FP there are plenty of data, decades, from after people started investing that way. They are 3 extremely liquid markets and by having only 3 bets, you have a far smaller matrix to estimate. As you add bets, your covariance estimation task gets much more complex, it is harder to check the accuracy of so many predictions against actual data. Because there will be many extreme events that might affect any particular relationship, you then have to decide how much attention to pay to errors you detect. Was this some insignificant, once in a lifetime, coincidence that did not really challenge the reliability of your estimate? Was it proof that you were fundamentally wrong in your analysis? Was it somewhere in between? For the 3 fund portfolio you have a simpler job and a lot of data. That by no means exhausts the universe of possible extreme events, but it gives you much more information about extreme events than AQR has for QSPIX or the managers of LTCM had for their strategy.
And all of the above ignores that that the LTCM and QSPIX were paid for running the fund. So they had/have ever reason to paint a rosy picture of how things were expected to turn out. Assume no dishonesty, but through simple human nature, it would be easy to conclude that errors that turn up are insignificant, and to pick data ranges, sources and analysis methods that would encourage people to invest.
Remember, it seemed like a great idea, and it worked spectacularly for a while. It worked right up to an extreme event. Then it did not work so well.
We don't know how to beat the market on a risk-adjusted basis, and we don't know anyone that does know either |
We assume that markets are efficient, that prices are right |