Early Gains

It is better for the accumulator to experience lower stock market returns in the early years. He ends up with a larger balance later on.

Calculations

I used the Stock Returns Predictor to calculate annualized returns at a specified P/E10 level. I estimated the balance at Year 10 using the formula:

Final Balance = Initial Balance * (1+annualized return)^10

I estimated the P/E10 level at Year 10 using the formula:

Final P/E10 = Initial P/E10 * (1+annualized return)^10 / 1.068^10

This assumes that the long term return of the stock market is 6.8% after adjusting for inflation.

Starting with P/E10=17

If we start with $100000 and if we are Lucky during the first decade, it will grow to $204535 at Year 10. P/E10 will have risen to 18.0. Putting these values into the Stock Returns Predictor, the Most Likely balances at Years 20 and 30 will be $300300 and $500429, respectively.

If instead we are Unlucky during the first decade, our $100000 balance will grow only to $115119 at Year 10. P/E10 will have fallen to 10.1. Putting these values into the Stock Returns Predictor, the Most Likely balances at Years 20 and 30 will be $312186 and $675945, respectively.

Notice that we are better off if the lower returns occur early. This is because dividends are part of total return. Reinvested dividends buy more shares when prices are low. This pays off in later returns.

Starting with P/E10=10

Suppose that we use a delayed purchase or Valuation Informed Indexing. Suppose that we hold off until P/E10 falls to 10. This is still above the historical lows, which range between 5 and 8. But it gets us in at favorable valuations.

If we start with $100000 and if we are Lucky during the first decade, it will grow to $360957 at Year 10. P/E10 will have risen to 18.7. Putting these values into the Stock Returns Predictor, the Most Likely balances at Years 20 and 30 will be $514326 and $846540, respectively.

If instead we are Unlucky during the first decade, our $100000 balance will grow only to $209894 at Year 10. P/E10 will have risen only to 10.9. Putting these values into the Stock Returns Predictor, the Most Likely balances at Years 20 and 30 will be $518927 and $1079047, respectively.

Once again, we are better off if the lower returns occur early.

Further Remarks

The Unlucky and Lucky outcomes correspond to probabilities of 20% and 80%.

Seeing lower returns early is wonderful for an accumulator. It is just the opposite for the retiree, who makes withdrawals. The mathematics is different. He wants to retain higher stock prices as long as he can if he is selling stocks for income.

Using a delayed purchase or Valuation Informed Indexing pays off handsomely. The risks are that stock prices may not fall for a very long time and that the bottom may not be as low as it has been in the past.

Have fun.

John Walter Russell
August 15, 2009