Dollar Cost Averaging Today

Rob Bennett has identified the need to integrate 10-year findings and 30-year findings. When it comes to investing strategies, no one is going make it to year 30 if he becomes overly discouraged at year 10.

Dollar cost averaging is a time-tested, successful strategy. In most cases, but not all cases, dollar cost averaging reduces the average cost of the shares that you purchase. Exceptions occur in the presence of a strong trend.

But what about today? What about today’s valuations? How about alternatives? What happens ten years from now?

Conditions Examined

I started with an investment of $1000 and added $1000 (plus inflation) every year thereafter using my Deluxe Calculator Version V1.1A08a. I invested into an all-stock (S&P500) portfolio. I used historical sequences of S&P500 stock returns (with dividends reinvested) starting from 1923-1980. I set expenses at 0.20% of the portfolio’s current balance. I selected the CPI as my measure of inflation.

I determined the real balances at years 5, 10, 15, 20, 25 and 30.

I plotted the balances versus the percentage earnings yield 100E10/P of the S&P500 at the beginning of each historical sequence. I used Excel to determine regression equations (i.e., straight-line, linear curve fits). I estimated confidence limits visually.

[The percentage earnings yield is 100E10/P or 100%/[P/E10], where P/E10 is Professor Robert Shiller’s measure of valuation. It is the current (real) price divided by the average (real) earnings of the previous decade. Professor Shiller’s P/E10 for the S&P500 is an extension of what Benjamin Graham advised for individual stocks: average 5 to 10 years of earnings.]

Equations (1923-1980 sequences)

At Year 5:

y = 417.58x + 4310.2 plus $4000 and minus $3000.
R-squared = 0.2396.
When x = 3.5%, y = $5772 (from $2.8K to $9.8K).
Five lowest balances: $4066, $4499, $4668, $4751 and $5006.

At Year 10:

y = 851.52x + 9805.5 plus $10000 and minus $8000.
R-squared = 0.1828.
When x = 3.5%, y = $12786 (from $4.8K to $22.8K).
Five lowest balances: $7466, $8974, $9569, $9689 and $10108.

At Year 15:

y = 2321.6x + 11810 plus $20000 and minus $12000.
R-squared = 0.2618.
When x = 3.5%, y = $19936 (from $8K to $40K).
Five lowest balances: $12466, $13773, $14120, $14447 and $14611.

At Year 20:

y = 4257.8x + 18348 plus $40000 and minus $20000.
R-squared = 0.2127.
When x = 3.5%, y = $33250 (from $13K to $73K).
Five lowest balances: $19332, $20774, $20892, $20984 and $21058.

At Year 25:

y = 2645.4x + 58871 plus $70000 and minus $40000.
R-squared = 0.0317.
When x = 3.5%, y = $68130 (from $28K to $138K).
Five lowest balances: $26828, $31381, $32254, $32708 and $33994.
NOTE: The plot included the sequences beginning in year 1980, which was incomplete. It includes dummy data with heavy losses during the final year.

At Year 30:

y = -3851.9x + 138942 plus $100000 and minus $70000.
R-squared = 0.0321.
When x = 3.5%, y = $125460 (from $55K to $225K).
Five lowest balances (among completed sequences): $43508, $49274, $50373, $51151 and $52897.
NOTE: The plot included sequences beginning in years 1975-1980, which were incomplete. They include dummy data with heavy losses during the final years.

Baseline for comparisons

I used TIPS with a 2% interest rate as a baseline.

Since the balance is $1000 in year zero (i.e., at the very start), the formula for the investment total uses N+1, where N is the number of years.

y = [annual deposit]*[(1+interest)^(N+1)-1]/interest.

Annual deposit = $1000 and interest = 2%.

Observations and Comparisons

Breaking Even

Observe that it is possible to lose money when dollar cost averaging. The total amount invested at year 5 is $6000 (in real dollars) since the balance is $1000 at the very start. At year 10, the total amount invested is $11000 (in real dollars). At year 15, it is $16000 (in real dollars). At year 20, it is $21000 (in real dollars).

At years 5, 10 and 15, the five lowest balances are ALL less than the amount invested. At year 20, the four lowest balances are less than the amount invested.

At year 25, the total amount invested is $26000 (in real dollars). All of the balances at year 25 exceeded this.

Similarly, at year 30, the total amount invested is $31000 (in real dollars). All of the balances at year 30 exceeded this.

Compared with 2% TIPS

These are the balances when investing in 2% TIPS:

N = 5 years, y = $6308.
N = 10 years, y = $12169.
N = 15 years, y = $18639.
N = 20 years, y = $25783.
N = 25 years, y = $33671.
N = 30 years, y = $42379.

These are the balances from stocks, using today’s 3.5% earnings yield in dollar cost averaging the equations:

N = 5 years: when x = 3.5%, y = $5772 (from $2.8K to $9.8K).
N = 10 years: when x = 3.5%, y = $12786 (from $4.8K to $22.8K).
N = 15 years: when x = 3.5%, y = $19936 (from $8K to $40K).
N = 20 years: when x = 3.5%, y = $33250 (from $13K to $73K).
N = 25 years, when x = 3.5%, y = $68130 (from $28K to $138K).
N = 30 years: when x = 3.5%, y = $125460 (from $55K to $225K).

Today’s Odds

For an investor who is buying stocks today, the odds are that he will be behind 2% TIPS at year 5 and only slightly ahead at year 10.

Looking at the lower confidence limits: it takes about 25 years before an investor who starts out buying stocks today can be assured of being better off than someone else who simply buys 2% TIPS.

To a decent but coarse approximation, the odds are 20% that an actual outcome will be more than one-half of the way between the calculated value and its confidence limit. At year 10, the odds are about 20% that the stock market investor’s balance will be below $8.8K (with $11K contributed). At year 15, the odds are about 20% that the stock market investor’s balance will be below $14K (with $16K contributed). At year 20, the odds are about 20% that the stock market investor’s balance will be below $23K (with $21K contributed).

Starting at today’s valuations, it takes about 20 years before a stock market investor can be reasonably confident (80%+) of achieving a gain (after inflation) even though he uses dollar cost averaging.

Transition Region

The upside potential may be attractive enough by year 15 to attract a stock market investor. He has about a 20% chance of reaching a balance of $30K (plus inflation) at year 15. He has (slightly) better than 50%-50% odds of beating 2% TIPS.

Alternative Approaches

We have mentioned alternatives before. Buy TIPS now. Switch over to stocks when they become attractive. Our numbers favor 100% TIPS today.

History has validated Benjamin Graham’s alternative: keep stock and bond allocations between 25% and 75%. Vary allocations in accordance with relative attractiveness (i.e., valuations). This translates into 75% TIPS today with 25% stocks.

Benjamin Graham’s advice is credited with minimizing regret.

Have fun.

John Walter Russell
February 3, 2006