Tuesday, September 04, 2007

An Apocryphal Tale: The Ten Best/Worst Days In Ten Years

There's an old aphorism with which I am acquainted that goes something like this:

"In any ten year period, if you miss the ten best days of the S&P, you'll lose half (or some similar value) of the return during the period."

To some extent, while the concept seems reasonable, I have treated it somewhat apocryphally.

Until now.

Last week, in the midst of the recent market turmoils, with various pundits calling for, demanding, expecting, etc., a Fed rate cut later this month, I thought it propitious to revisit this old tale.

Here's what I did. Using a daily adjusted S&P500 price series from Yahoo, I created a ten year series, from which I calculated daily total returns.

I then sorted the total return series by returns, in descending order.

For the ten years beginning August 29, 1997, the S&P500 statistics are:

6.5% average annual return

.03% average daily return

.05% median daily return

1.14% standard deviation of daily returns

+5.73% best daily return

-6.87% worst daily return

So far, so good. We see that the past ten years have, largely due to 2001-02, provided an average annual S&P500 return which is slightly more than half of the long term annual average return of 11%. The median daily return is above the mean daily return, informing us that the distribution of daily S&P returns is skewed positively. This is despite the worst daily return being lower, in absolute value terms, than the best daily return. The standard deviation of the daily returns, at 1.14%, is far greater than the mean or median daily return, indicating a very volatile daily value.

But, what about the aphorism that led to this ad hoc research? What are the returns of the ten best (and worst) days of the S&P over this ten year period?

+48.4% summed return of the ten best days of the S&P during the period

-48.% summed return of the ten worst days of the S&P during the period

This gives us:

65.2% summed actual daily returns for the S&P over the ten year period

16.8% summed daily returns for the S&P over the ten year period, without the ten best days

113.2% summed daily returns for the S&P over the ten year period, without the ten worst days

Each group of 10 days, best and worst, comprise approximately 74% of the ten years' summed total returns of the S&P. If we compare these two 'ten day' returns to the long run average annual S&P return of 11%, they comprise only +/- 44% of the total return of an average ten year period.

So, if we took a number of samples of ten year periods of the S&P, we might very well find that the aphorism is true. Something approaching half of the value of the S&P returns over a ten year period may be accounted for by just the ten best, or worst, days of the S&P over the period.

So what?

Well, it demonstrates how good your 'market timing' had better be, if you are a market timer. Miss a few days, either way, and you have an entirely different return than the market, even if you are only invested in the S&P500.

Frankly, it is simply stunning. At least to me. I can think of no other word.

To learn that missing only 10 out of some 2,500 days of S&P daily returns can remove between 50% and 75% of the total return of the ten year period confirms my belief that market timing is folly. Or making daily market calls, like Jim Cramer did this morning, on CNBC.

My own equity investment strategy approach distinguishes between markets in which we should be long, and those in which we should be short. Long term. Period. No attempts to predict daily, weekly, or monthly market moves.

Our equity strategy typically mirrors large daily moves in the S&P, but with larger magnitudes.

Now that our major focus is applying the equity strategy via long-dated, out of the money call options, this is doubly true. Although, relative to comparable S&P500 calls, it's not yet clear if this behavior extends to options.

Nonetheless, the validating of this little apocryphal tale heavily reinforces my belief in remaining invested, long or short, continuously, and abstaining from going to cash, unless very briefly, amidst noisy long term market signals.

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