I got this e-mail from Mark H. which noted some strategy involving trailing 3-year market data in order to reorganize a portfolio for the coming year (or two or three or whatever). It got me thinking that ...

>Thinking? That was your first mistake.
Pay attention.
The question is:"Is three years meaningful? Should it be more? Less? What?

So I do the following ... similar to Part I:

1. Starting in Jan, 1950 I look at the Annualized Return over the previous N = 3 years.
2. I look at the return for the current year (namely 1950).
3. I repeat this (1) - (2) ritual for 1951, then 1952, then 1953, etc. etc.
4. With two sets of numbers (the trailing 3-year-returns and the current-year returns) I calculate the Pearson Correlation.
5. I repeat steps (1) - (4) with N = 1, 2 ... 15 years.

>I assume it depends upon your portfolio, eh? I mean ...
Yes, it depends upon the allocation between, for example, Large Cap Growth Stocks or maybe Small Cap Value Stocks and maybe some 5-year Treasuries and maybe some ...

>Okay, I get the idea. So you're looking for the best N. What did you find?
This:

 

>Negative correlation? You're kidding, right? You made a mistake, right?
Interesting, but (until I'm finished) you can play with my spreadsheet - which looks like this.

Just RIGHT-click here and "Save Target".

>But doesn't everybuddy use historical data to predict the future?
Well, that's a bit of an exaggeration, but ... uh, I've been known to ...

>Yes, yes. I know. You use your special patented technique. But, in Part I, we did the S&P 500. How about that?

Yes, here's 100% S&P >It's still got that up and down thing, right? Actually, it's down and up, but yes, it seems so: negative correlation in the short and long term. Funny, eh? If the near term past performance was good, then this year is likely to be not as good. It's curious, I know, but ... >Doesn't anything have POSITIVE correlation? Yes ... T-bills

>You used the Annualized return. What about the Average trailing return?
Same result. The charts change very little.

>So, is there a strategy there? I mean, can you take advantage ...?
I doubt it, but let me think on it ...

>If the trailing returns were positive, you'd expect the current year to have a negative return, so you reduce your holdings. How about that? A negative return? No. You'd expect a return which is not as good. For example, with a 4 x 25 slice & dice portfolio the relationship between 3-year trailing annualized return and the current year return is shown here: The beta is -2.8       (that's the slope: Δy/Δx) If the trailing return is x then you might expect the current year return to be y = -2.8 x + 0.3 so, if x = 0.08 (meaning an 8% trailing return), then you might expect y = -2.8 (0.08) + 0.3 = 0.076 or 7.6%     see the spot on the red regression line?

>But that could be negative, eh?
Yes, if the trailing return is REALLY large, you'd expect a negative return for the current year. Indeed, if the trailing return increases by, say Δx, then we'd expect the current return to change by Δy = -2.8 Δx.

>You'd "expect" a negative return? That's statistical mumbo jumbo. Does that really happen?
Sometimes ...

>So, do you still think it's a mathematical thing?
Yes. I can't believe this pseudo-periodicity is a consequence of market behaviour but rather a consequence of the moving window of trailing returns. For example, if I invent monthly returns which increase but with a random component - sort of like real, live stock market returns, graphically speaking - then I still get a pseudo-periodicity in the correlation, between current monthly return and the average of the previous N months.

>Invent? Did you say invent?
Yes, I "invent" stock prices (at month x) according to: 10 + 0.05{SIN(x) + e^x/10}(1+0.5 RAND)
and RAND is a random number between 0 and 1.

>Mamma mia! Where did that come from?
I told you. I invented it. Anyway, it gives this:

>Hey! I think I recognize the stock! Isn't it Microsoft? Yeah, because I notice that ...
No! It's pure invention. I play with a spreadsheet where, each time I press F9 to recalculate, I get a new pair of charts (like the above). The left chart looks much like an typical stock ... and the right chart almost always displays this periodicity.
>And do you ever get POSITIVE correlation, for short and long term trailing averages?
Sometimes.
>Yeah, so, what now?
I've already told you. I have to think on it ...