Another Look: High Risk at ?%

Research on Safe Withdrawal Rates

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JWR1945
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Another Look: High Risk at ?%

Post by JWR1945 » Mon Jun 28, 2004 6:33 am

In the previous post, I applied the New Tool using 6-year equations. That tells us something about how a retirement portfolio is progressing. This time, I apply the 14-year equations to give us an idea of what to expect.

The New Tool is most accurate at 14 years.

The New Tool calculates rates and confidence limits as a function of a portfolio's real, annualized return when there are no withdrawals (and with dividends reinvested and with 0.20% expenses). The New Tool does not directly incorporate valuations. This way, we can learn what is likely to happen even if stock valuations really have reached a permanent, higher plateau.

Refer to A New Tool from Wed Apr 28, 2004 at 4:41 pm CDT.
http://nofeeboards.com/boards/viewtopic.php?t=2427
and New Tool errata dated Tue, Jun 22, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2655

The equations for the straight lines that I produced have the form y = mx+b or return0 = slope*HDBR + intercept. Both return0 and HDBR are in percent. I have examined two portfolios, HDBR50 with a 50% stock allocation and HDBR80 with an 80% stock allocation. The Historical Database Rates are for 30 years. Expenses were 0.20% of the portfolio's current balance. Portfolios consisted of stocks and commercial paper with annual re-balancing.

50% Stocks

For a 50% stock portfolio, the relevant information is taken from the returns after 14 years. The equation is y = 2.1245x - 8.0652, where y = return0, which is the real, annualized total return with dividends reinvested, no withdrawals and with 0.20% expenses, and x = the Calculated Rate with 50% stocks. The standard deviation for x is 0.39% (or, more precisely, 0.391109%). The standard deviation for y is 0.83% (or, more precisely 0.830911%). The 90% confidence limits are plus and minus 1.64 times the standard deviation away from the Calculated Rates. For x, it is 0.64% (or, more precisely, 0.6414188%). The comparable limits surrounding the real, annualized total return, return0 = y, are plus and minus 1.4% (or, more precisely, 1.362694%).

Here are some Calculated Rates for various values of y = return0.
1) The equation is y = 2.1245x - 8.0652.
2) Solving for x: x = [y+8.0652] / [2.1245].
3) When y = 0, x = 3.80% (the Calculated rate for HDBR50).
4) When y = 2, x = 4.74%.
5) When y = 3, x = 5.21%.
6) When y = 4, x = 5.68%.
7) When y = 6, x = 6.62%.
8 ) When y = 8, x = 7.56%.

Since the confidence limits are plus and minus 0.64%, a withdrawal rate of 4.10% is safe when the 14-year real, annualized total return (return0) of the portfolio is 2%. A withdrawal rate of 5.04% is safe when the 14-year real, annualized total return (return0) of the portfolio is 4%.

If the real, annualized total return (return0) is flat (i.e., zero percent), 3.16% is safe, 3.80% has a 50-50 chance of success and 4.44% has very little chance of success.

We can look at this equation the other way. If the withdrawal rate is 4%, then the Calculated Rate of the real, annualized total return (return0) = y = 2.1245x - 8.0652 = 0.4328% with confidence limits of plus and minus 1.4%. Adding 1.4% to 0.4328%, we see that a real, annualized total return of 1.8% (or, more precisely, 1.8328%) at year 14 is sufficient to guarantee (a high level of) safety. Subtracting, we see that it takes a real, annualized loss of (1.0)% (or, more precisely, (0.9672)%) to be assured of failure.

80% Stocks

For an 80% stock portfolio, the relevant information is taken from the returns after 14 years. The equation is y = 1.8432x - 6.8875, where y = return0, which is the real, annualized total return with dividends reinvested, no withdrawals and with 0.20% expenses, and x = the Calculated Rate with 80% stocks. The standard deviation for x is 0.62% (or, more precisely, 0.620502%). The standard deviation for y is 1.14% (or, more precisely 1.143709%). The 90% confidence limits are plus and minus 1.64 times the standard deviation away from the Calculated Rates. For x, it is 1.02% (or, more precisely, 1.0176233%). The comparable limits surrounding the real, annualized total return, return0 = y, are plus and minus 1.9% (or, more precisely, 1.8756828%).

Here are some Calculated Rates for various values of y = return0.
1) The equation is y = 1.8432x - 6.8875.
2) Solving for x: x = [y+6.8875] / [1.8432].
3) When y = 0, x = 3.74% = the Calculated Rate for HDBR80.
4) When y = 2, x = 4.82%.
5) When y = 3, x = 5.36%.
6) When y = 4, x = 5.91%.
7) When y = 6, x = 6.99%.
8 ) When y = 8, x = 8.08%.

Since the confidence limits are plus and minus 1.02%, a withdrawal rate of 2.72% is safe when the 14-year real, annualized total return (return0) of the portfolio is flat (i.e., zero percent), 3.74% has a 50-50 chance of success and 4.76% has very little chance of success.

A withdrawal rate of 3.80% is safe when the 14-year real, annualized total return (return0) of the portfolio is 2%. A withdrawal rate of 4.89% is safe when the 14-year real, annualized total return (return0) of the portfolio is 4%.

We can look at this equation the other way. If the withdrawal rate is 4%, then the Calculated Rate of the real, annualized total return (return0) = y = 1.8432x - 6.8875 = 0.4853% with confidence limits of plus and minus 1.9%. Adding 1.9% to 0.4853%, we see that a real, annualized total return of 2.4% (or, more precisely, 2.3853%) at year 14 is sufficient to guarantee (a high level of) safety. Subtracting, we see that it takes a real, annualized loss of (1.4)% (or, more precisely, (1.4147)%) to be assured of failure.

If the withdrawal rate is 5%, then the Calculated Rate of the annualized total return (return0) = y = 1.8432x - 6.8875 = 2.3285% with confidence limits of plus and minus 1.9%. Adding 1.9% to 2.3285%, we see that a real, annualized total return of 4.2% (or, more precisely, 4.2285%) at year 14 would be required to guarantee (a high level of) safety. Subtracting, we find that it takes a real, annualized return no greater than 0.4% (or, more precisely, 0.4285%) to be assured of failure.

Multiple Compression

If P/E10 were to drop in half fourteen years from now, the annualized gain multiplier would be reduced to the 14th root of 0.5, which equals 0.9516952% and which is an annualized loss of (4.8 )% [since 100%*(0.952-1) = -4.8%]. If P/E10 were to drop to two thirds of its current level, the annualized gain multiplier would be reduced to the 14th root of 2/3, which equals 0.9714536 and which is an annualized loss of (2.9)% [since 100%*(0.971-1) = -2.9%].

P/E10 is currently around 27. If it were to drop in half, it would be 13.5, which is below its typical historical level but well above its lowest levels. If P/E10 were to drop to two thirds of its current value, it would be 18, which is still higher than normal, but not much so. It is reasonable to expect multiple compression to place a drag on the 14-year annualized real return of at least 2.9%. It could easily be a drag of 4.8%. It could even be worse.

You apply the multiple compression adjustment to the long-term annualized return of your portfolio. For a stock-only portfolio, this is 6.5% to 7.0%.

There will be a real danger if there is an overreaction on the downside with P/E10 falling all of the way to bargain levels. Such overreactions have occurred frequently in the past.

Have fun.

John R.

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