Price Drops

Valuations and prices are related, statistically.

Minimum Balances

I determined the minimum balances of the S&P500 with all dividends reinvested.

At first, I looked at nominal balances because that is what investors actually see. This was unsatisfactory. In Years 1 through 5, the minimum balances during the 1960s fell very little. Yet, these were the worst years for retirees. Inflation hid the true story.

Using real minimum balances (that is, adjusted for inflation), the problems of the 1970s showed up, but not those of the 1960s.

The best choice was to use the real minimum balances in Years 1 through 10. Initially, I eliminated the years which never showed a decrease. Later, I found that I could include those years as well. There was no need to develop a special procedure.

I determined the relationship between minimum balances (during Years 1 through 10) and both P/E10 and 100E10/P. P/E10 did slightly better.

I compared the relationship for both years 1921-1980 and 1921-1995. The shorter period produced a better curve fit. The longer period includes a few high valuation years from the beginning of the bubble.

I decided to use the 1921-1995 data.

Regression Equation

The regression equation for the minimum balance during Years 1 through 10, y, and P/E10, x, is:

y = -2609.8x + 136999 for an initial balance of $100000.

The confidence interval is plus and minus $30000.

The break even point, statistically, is P/E10=14.

Roughly speaking, one half of the time, minimum balances will stay above the calculated level. It will fall below the calculated level the rest of the time.

Solving for y=$70000, x=25.67. Only if P/E10 rises above P/E10=25.67 can we be assured that real balances will fall at some point within the following decade.

When P/E10=29.3, as it has been recently, the calculated minimum real balance in Years 1 through 10 is $60532. Starting from an initial balance of $100000, we can expect the actual, inflation adjusted balance of the S&P500 to lie between $30500 and $90500. The odds are about 80% that the minimum real balance will be above $45500. The odds are about 80% that the minimum real balance will be below $75500.

Conclusions

Today’s holder of the S&P500 index can expect his balance to fall to 60.5% of its current purchasing power within the next decade even with dividends reinvested. The likely range of outcomes is between 45.5% and 75.5%. The outer confidence limits are 30.5% and 90.5%.

Notice the significance of the minimum real balances throughout the entire decade as opposed to only a portion. This is entirely consistent with our investigations into Safe Withdrawal Rates.

Have fun.

John Walter Russell
May 17, 2007
Updated: May 24, 2007