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If someone believed that the US stock market is 40% overvalued compared
to its long term average valuation, then would it be prudent to sell
most of your US stocks, and wait for a better entry point?
Even if that entry point might be 5-10 years away?

Yes and no.

I believe that the broad US equity market is very overvalued.
But I don't own the broad US market.

If the only thing you could buy were SPY, you'd be right; I'd sit on
cash and wait for a great entry point. But there are always some securities
which are attractively valued, so I own only those to the best of my ability.
The central expected return for cheap firms purchased now can be
quite good even if the broad market is overvalued, and of course this avoids
the problem taht over/undervaluation cycle can last a very long time
and broad valuation levels are therefore crummy predictors in the short run.

But if one were to try this "wait for a good entry point", how do you know
when to get back in? At is happens, a guy in late 1962 was asked
to design a method to identify a good time to enter the market for
the purposes of a long term hold and came up with a simple trigger.
It has worked amazingly well since then. It's called a Coppock signal.
On the surface it looks like purely technical analysis mumbo jumbo, but it's
really just looking for the first upturn after the first really big bear market.
Phrased that way it seems pretty simple and sensible.
There have been only 12 signals since it was invented, most recently
the end of May 2009 when the S&P was at 919.
On average the 2 years following a signal returns about 13.4%/year in real total
return following such a signal versus 7.9%/year for the rest of the two year intervals.
So, I'd buy on the first Coppock signal following the next time the S&P is in triple digits.

Here's a nice figure for you regarding broad valuation levels.
Let's posit that there is some sort of a trend for growth in real
earnings for the S&P. Earnings might grow a little more quickly some
decades than others, but they long run trend rises a maximum of only so much per year.
You will get different trend lines depending on your start and end dates.
The most optimistic possible (steepest) slope is the trend line starting 1985-11-08 and ending today.
That trend line suggests on-trend earnings today for the S&P of $66.60 in today's money.
The average observed earnings yield since 1936 can be considered a
good definition of a "normal" valuation level, being about 7.20%.
So, by this line of reasoning the most optimistic (highest) possible
fair value of the S&P today is 66.6/.072 = 925 for the S&P.
That assumes that earnings will continue to grow at a record breaking pace indefinitely.
With the S&P at 1460 this line of reasoning suggests that the S&P is at least 57% overvalued.
Any other choice of trend line dates will give greater levels of overvaluation.
If you like you could add 20% to that 925 figure for any possible holes
in the reasoning (it's different this time?), but you still get the same general result.

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