Sleep ... as an investment strategy
motivated by a discussion on Bogleheads

I've always been fascinated (and amused) by statements like:

It took 25 years for the DOW to regain its level before the 1929 crash.
>You mean it's not true?
Of course it's true. Check out the chart:

>Then what's so amusing?
Well, maybe that's a poor choice of word since 1929 was, after all, a disastrous year.
It's just that one looks at the ridulously high DOW immediately before the crash and considers an investor who just happened to invest at that temporary high.
On the other hand, an investor who had invested in the DOW five years before the crash, then fell asleep until five years after ... she'd have made money.
That suggests that SLEEP is a good investment strategy.

Indeed, if the DOW grows exponentially, like:
DOW = A er t
then log(DOW) would grow linearly, like so:
log(DOW) = log(A) + r t

So if we plot log(DOW) instead of DOW, then ...

>We'd get a straight line!
Uh ... only if DOW grew exponentially ... which it don't ... not exactly.
Nevertheless, it'd look like this:

There have been two crashes in the last hundred years. The second was in October, 1987 when the DOW dropped 23% on the 19th.
That second crash don't look too bad on that log scale, eh?

Had you invested at the end of December, 1986 and ...

>And fallen asleep, you'd make money, right?
Only if you slept long enough.

It would have taken about two years for the DOW to recover to its pre-October19 high.

>So how long would I have to sleep ... in other time periods?
Good question. Here's what we'll do:

• We browse djindexes for the weekly DOW values from October 1, 1900.
• We consider the N-year periods ... well, actually 52N weeks ... starting each week from Oct 1, 1900.
• We see how often the DOW had a positive return over that 52N week period.
• Then we vary N from N = 1 to N = 10.
• Then we ...
>N = 1 to N = 10 means 1 to 10 years, right?
If there are 52 data points per year in the weekly index values from djindexes.
Anyway, here's the chart:

>Hmmm ... interesting. So what are you suggesting?
That you go to sleep.