Edited: Time Needed to Assure a Gain

We are assured that stocks will show a gain, eventually, even after adjusting for inflation.

How long do we have to wait? So far, the longest delay for the S&P500 has been 18 years. How about a confidence interval?

Data Collection

I brought up a table of S&P500 real returns for sequences lasting up to 60 years. I determined the final year with a loss for each sequence. About half of the time, there never was a loss.

I narrowed the sequences to those beginning in 1921-1980. This plot was well behaved. The equation for the number of years until the final lost y = 0.8935x-7.4279 plus 4 and minus 7, where x is P/E10. This equation and these confidence limits tell us what happens ON THE CONDITION that there is a loss.

The Effect of Valuations

When P/E10=8, valuations are attractive. Assuming that there is a loss, the number of years until the last loss is -0.3 plus 4 and minus 7. The negative numbers correspond to not having a loss.

When P/E10=14, which is slightly higher than usual, and assuming that there is a loss, the number of years until the last loss would be 5.1 years plus 4 and minus 7.

When P/E10=20, which defines the hazardous region, and assuming that there is a loss, the number of years until the last loss would be 10.4 plus 4 and minus 7.

When P/E10=28, as it has recently, and assuming that there is a loss, the number of years until the last loss would be 17.6 years plus 4 and minus 7.

At this point, we need to reconsider the probability that there is a loss.

Refinement for High P/E10

The number of sequences that begin with P/E10=20 and higher is 15 out of 110 from 1881-1990. The ratio is 13.6%. The number of sequences that begin with P/E10=20 and higher is 10 out of 60 from 1921-1980. The ratio is 16.7%.

The number of sequences that begin with P/E10=20 and higher and also avoid a loss is 1 out of 15. It is the 1901 sequence.

When P/E10 is 20 or above, the number of years until the last loss is 12.9 (on average). The observed range is between 5 and 18. Using the LINEST function, the standard deviation is 3.99 years and the confidence limits (90%, by formula, multiply by 1.64) are plus and minus 6.55 years about the mean. According to formula (without any adjustments), the confidence limits are 6.35 years to 19.45 years.

Today’s Outlook

In the original calculations, the probability of experiencing a loss at some point in the future was about 55%.

The original calculation showed that, assuming that there is a loss, the most likely waiting time before showing a profit (in real dollars) is 17.6 years. The worst case would be 21.6 years.

Using an alternative calculation that relies only on historical sequences with P/E10=20 and higher, assuming that there is a loss, the most likely waiting time until showing a profit (after adjusting for inflation) is 12.9 years, with possible delays ranging from 6.35 years to 19.45 years.

My Assessment

The probability of being blindsided is around 10% or 20% regardless of the quality of a study. I assign unlikely outcomes to this category.

Combining two approaches, I estimate that the last (real dollar) loss will occur at some point between 5 years and 20 years, most likely around 13 to 17 years.

Have fun.

John Walter Russell
December 14, 2006