Monte Carlo predictions ... any good ?

I was lying in bed thinking about how one predicts the future.
How one often looks at the past and assumes that the future is similar.
How one ...

>I thought you were giving up on financial stuff ... but anyway, what about it?
One popular method for predicting future stock prices is to look at historical returns, extract a Mean and Standard Deviation, assume some distribution (like normal of lognormal distribution, with that Mean and Volatility) then pick random returns from that distribution and apply them to our portfolio to see what'll happen.

>And do that a jillion times, right?
Yes. That's Monte Carlo simulation.
But it always seemed to me that extracting just two parameters from the past (Mean and Volatility) can't possibly be a good strategy.
Is the future really like the past? Can we really expect that the future Mean and Volatility will remain constant. Can we ...?

>So you want to extract more info from historical data?
No, not at all. In fact, one can just use the past returns, selected at random, to simulate some future stock evolution. That way you'll use all the info and you needn't assume a particular distribution. You use the actual data. That way ...

>And that's what you want to talk about?
Uh ... no. If you stop interrupting I'll tell you what I was thinking.

What I asked myself, while lying in bed, was:
"How close is the future to the past?" and, in particular,
"What should one use as Mean and Volatility?".

Remember that investment gurus often generate (somehow) a Mean and Volatility. Is there a "best" choice?

Anyway, here's what I thought:

  1. I'd pick some year, say 1965.
  2. I'd look at the Mean and Volatility of the weekly returns for that year.
  3. I'd then look at the Mean and Volatility of the weekly returns over the previous 1 year, 2 years, 3 years ... 10 years.
  4. I'd see which past is most like the future.

>Huh? You mean 1965 is the future?
Yes. I assume today is, say, Dec 31, 1964 and I use the past 1 year or 2 years etc. and see what's the best choice of Mean and Volatility for predicting the behaviour of a stock or the market for the following year.

>That's 1965, right? That's your "future", right?
Yes and...

>So what'd you get?

Here's that 1965 example, comparing to the Mean and Standard Deviation over the previous 1, 2, ... 10 years to the Mean and Standard Deviation for 1965 (which is shown in red).

That last chart, Mean - (1/2)(Standard Deviation)2, is an estimate of the weekly compound growth rate.

>Using the past 10 years ain't bad, eh?

Here's a few more:

However, if I use the Mean and Volatility for all 50 years I'd get this:

>That's good ... and I could have told you that!
Told me what? That more data, a more expansive history, all 50 years ... that that would have been good?
Let's look at the Mean weekly return for each year from 1954 to 2003 and compare it to the Mean weekly return for the entire 50 year span.
Here's what I get:

>Huh? An error of over 400%? You kidding?
That 400% means that the difference between the Mean return of 1974 and the Mean return for all 50 years - that difference was over four times the 50-year Mean. What I mean is, the 1974 Mean was -0.563% while the Mean over all 50 years was 0.165%
... and (-0.563-0.165)/0.165 = -4.41
... and that means 441%.

>I think you should have stayed in bed.