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**A New Tool**from Wed Apr 28, 2004 at 4:41 pm CDT.

http://nofeeboards.com/boards/viewtopic.php?t=2427

I have looked at two standard portfolios, HDBR50 and HDBR80, over 30-year lifetimes. HDBR50 consists of 50% stocks and 50% commercial paper. HDBR80 consists of 80% stocks and 20% commercial paper. Stocks are represented by the S&P500 index. The expense ratio is 0.20% for both. Withdrawal amounts are adjusted to match inflation (according to CPI-U). Any dividend amount not needed for withdrawals is reinvested.

I have summarized Calculated Rates (previously referred to as the Zero Balance Rates) and Safe Withdrawal Rates for both portfolios when the real, annualized returns (with no withdrawals but with 0.20% expenses and with dividends reinvested) are 0%, 2%, 4%, 6% and 8% at 6, 10 and 14 years. [I refer to these annualized returns as return0.]

Calculated Rates are the best estimate and they correspond roughly to a 50%-50% chance of portfolio survival.

Each Safe Withdrawal Rate is at the lower 90% confidence limit relative to its Calculated Rate. This provides a 95% chance of survival since the 10% chance of something's being outside of the 90% confidence limits includes 5% on the High Risk side and 5% on the low risk, Safe Withdrawal side. All of the table entries are conditional upon having the annualized real return exactly as specified.

It is important to remember that a low conditional Safe Withdrawal Rate does not necessarily reflect anything worse than the uncertainty at a specified number of years. This is especially true with the 6-year data. For example, it takes very high returns during the first six years to guarantee that a 4% withdrawal rate will be successful (while allowing only a 5% chance of error).

HDBR50 versus return0 at 6 years

Code:

All SWRs and Calculated Rates are conditional:

If the return is 0%, the SWR is 1.65%. [The Calculated Rate is 3.69%.]

If the return is 2%, the SWR is 2.41%. [The Calculated Rate is 4.45%.]

If the return is 4%, the SWR is 3.17%. [The Calculated Rate is 5.21%.]

If the return is 6%, the SWR is 3.92%. [The Calculated Rate is 5.96%.]

If the return is 8%, the SWR is 4.68%. [The Calculated Rate is 6.72%.]

HDBR50 versus return0 at 10 years

Code:

All SWRs and Calculated Rates are conditional:

If the return is 0%, the SWR is 2.79%. [The Calculated Rate is 3.95%.]

If the return is 2%, the SWR is 3.63%. [The Calculated Rate is 4.80%.]

If the return is 4%, the SWR is 4.50%. [The Calculated Rate is 5.66%.]

If the return is 6%, the SWR is 5.35%. [The Calculated Rate is 6.51%.]

If the return is 8%, the SWR is 6.21%. [The Calculated Rate is 7.37%.]

HDBR50 versus return0 at 14 years

Code:

All SWRs and Calculated Rates are conditional:

If the return is 0%, the SWR is 3.16%. [The Calculated Rate is 3.80%.]

If the return is 2%, the SWR is 4.10%. [The Calculated Rate is 4.74%.]

If the return is 4%, the SWR is 5.04%. [The Calculated Rate is 5.68%.]

If the return is 6%, the SWR is 5.98%. [The Calculated Rate is 6.62%.]

If the return is 8%, the SWR is 6.92%. [The Calculated Rate is 7.56%.]

HDBR80 versus return0 at 6 years

Code:

All SWRs and Calculated Rates are conditional:

If the return is 0%, the SWR is 1.22%. [The Calculated Rate is 4.19%.]

If the return is 2%, the SWR is 2.10%. [The Calculated Rate is 5.07%.]

If the return is 4%, the SWR is 2.97%. [The Calculated Rate is 5.94%.]

If the return is 6%, the SWR is 3.85%. [The Calculated Rate is 6.82%.]

If the return is 8%, the SWR is 4.73%. [The Calculated Rate is 7.70%.]

HDBR80 versus return0 at 10 years

Code:

All SWRs and Calculated Rates are conditional:

If the return is 0%, the SWR is 2.14%. [The Calculated Rate is 3.92%.]

If the return is 2%, the SWR is 3.16%. [The Calculated Rate is 4.94%.]

If the return is 4%, the SWR is 4.18%. [The Calculated Rate is 5.96%.]

If the return is 6%, the SWR is 5.21%. [The Calculated Rate is 6.99%.]

If the return is 8%, the SWR is 6.23%. [The Calculated Rate is 8.01%.]

HDBR80 versus return0 at 14 years

Code:

All SWRs and Calculated Rates are conditional:

If the return is 0%, the SWR is 2.64%. [The Calculated Rate is 3.74%.]

If the return is 2%, the SWR is 3.72%. [The Calculated Rate is 4.82%.]

If the return is 4%, the SWR is 4.81%. [The Calculated Rate is 5.91%.]

If the return is 6%, the SWR is 5.89%. [The Calculated Rate is 6.99%.]

If the return is 8%, the SWR is 6.98%. [The Calculated Rate is 8.08%.]

For the most part, the conditional Calculated Rates with 80% stocks are higher than for 50% stocks. But the conditional Safe Withdrawal Rates are lower with 80% stocks than for 50% stocks. That is the result of volatility.

There is an important caveat. The returns are for the portfolio that is being examined, not for the stock market. When stock returns are higher than those of commercial paper, the overall return of a higher stock portfolio (80% stocks) will be higher than that of a lower stock portfolio (50% stocks).

Commercial paper generally returns at least a small, positive real return (but it is not doing so today). If that continues, the overall return of a 50% stock portfolio will be greater than that with 80% stocks if the stock market has a flat (0%) real return over the next 6, 10 or 14 years, as applicable.

For the optimist

For someone who expects 7% real returns in the 10-year time frames, the conditional Safe Withdrawal Rates are around 5.35% to 6.21% (with 6% and 8%, respectively, and 50% stocks) and 5.21% and 6.23% (with 6% and 8%, respectively, and 80% stocks.

For someone who expects 7% real returns in the 14-year time frames, the conditional Safe Withdrawal Rates are around 5.98% to 6.92% (with 6% and 8%, respectively, and 50% stocks) and 5.89% and 6.98% (with 6% and 8%, respectively, and 80% stocks.

We can summarize this by saying that 7% real returns at year 10 result in Safe Withdrawal Rates between 5.21% and 6.23%. At year 14, they result in Safe Withdrawal Rates between 5.89% and 6.98%.

For the pessimist (realist?)

For someone who expects a 1% real return in the 10-year time frames, the conditional Safe Withdrawal Rates are around 2.79% to 3.63% (with 0% and 2%, respectively, and 50% stocks) and 2.14% and 3.16% (with 0% and 2%, respectively, and 80% stocks).

For someone who expects a 1% real return in the 14-year time frames, the conditional Safe Withdrawal Rates are around 3.16% to 4.10% (with 0% and 2%, respectively, and 50% stocks) and 2.64% and 3.72% (with 0% and 2%, respectively, and 80% stocks.

We can summarize this by saying that a 1% real return at 10 years results in Safe Withdrawal Rates between 2.14% and 3.63%. At year 14, they result in Safe Withdrawal Rates between 2.64% and 4.10%.

Keep in mind that a cash equivalent with a zero percent real interest rate (i.e., the matches inflation exactly) would provide a 3.33% withdrawal rate for thirty years (and end with a balance of zero).

Applying the New Tool

Technically, the New Tool requires an exact time period. As a practical matter, we can relax this restriction to an approximate interval provided that return0 dwells close to a selected value throughout much of the interval. We might select a typical value of return0 for the years 8 through 12 and use it with the 10-year formulas. What is not allowed is selecting a value when return0 only hits it momentarily. For example, if return0 briefly hit 0% twice between 8 and 12 years but typically stayed around 3%, it would be improper to use the formulas for 0%. You would have to use the formulas for 3%.

Have fun.

John R.