Year 10 Choices

This extends our investigation of intermediate-term timing. I have added to the choices in my Risky Alternatives article. I contrast today’s actions, starting from today’s valuations, to those of the not-too-distant future, when valuations will be much more favorable.

Risky Alternatives

Procedure

I have calculated the balances at year 10 of portfolios HSWR80T2, HSWR80T2n, HSWR50T2, HSWR50T2n, HSWR20T2 and HSWR20T2n for historical sequences beginning in 1923-1980. I used withdrawal rates of 3.0% (plus inflation), 4.0% (plus inflation) and 5.0% (plus inflation).

HSWR80T2 consists of 80% stocks (i.e., S&P500) and 20% TIPS at a 2% interest rate. It is rebalanced annually. Expenses are 0.20% of the portfolio's current balance.

HSWR80T2n is the same as HSWR80T2 except that it is not rebalanced. Withdrawals are taken from stocks and TIPS in proportion of their respective balances.

HSWR50T2 is the same as HSWR80T2 except that it has 50% stocks and 50% TIPS.

HSWR50T2n is the same as HSWR50T2 except that it is not rebalanced. Withdrawals are taken from stocks and TIPS in proportion of their respective balances.

HSWR20T2 is the same as HSWR80T2 except that it has 20% stocks and 80% TIPS.

HSWR20T2n is the same as HSWR20T2 except that it is not rebalanced. Withdrawals are taken from stocks and TIPS in proportion of their respective balances.

I used my Deluxe Calculator V1.1A08a. I used Excel plots to determine regression equations (i.e., linear curve fits) of balances versus the percentage earnings yield 100E10/P. I estimated confidence limits (visually) from the graphs.

I have solved the equations at today's earnings yield (of 3.5%, roughly), which is exceedingly high, and at an earnings yield of 10% (P/E10=10.0), which is favorable, but well within the historical range.

Equations

y = the (real) balance at year 10 after starting with $100000 initially.
x = the percentage earnings yield 100E10/P (i.e., 100/[P/E10]).

HSWR80T2, Withdrawal Rate = 3.0%, y = 15561x+25195 plus 100000 minus 70000. R-squared = 0.3614.

HSWR80T2, Withdrawal Rate = 4.0%, y = 15090x+15235 plus 100000 minus 70000. R-squared = 0.3682.

HSWR80T2, Withdrawal Rate = 5.0%, y = 14620x+5273.9 plus 100000 minus 70000. R-squared = 0.3749.

HSWR50T2, Withdrawal Rate = 3.0%, y = 8917.1x+52924 plus 60000 minus 40000. R-squared = 0.3973.

HSWR50T2, Withdrawal Rate = 4.0%, y = 8661.5x+42379 plus 60000 minus 40000. R-squared = 0.4065.

HSWR50T2, Withdrawal Rate = 5.0%, y = 8405.9x+31834 plus 50000 minus 40000. R-squared = 0.4158.

HSWR20T2, Withdrawal Rate = 3.0%, y = 3287.6x+74822 plus 15000 minus 15000. R-squared = 0.4304.

HSWR20T2, Withdrawal Rate = 4.0%, y = 3221.5x+63849 plus 15000 minus 10000. R-squared = 0.4425.

HSWR20T2, Withdrawal Rate = 5.0%, y = 3155.3x+52876 plus 15000 minus 10000. R-squared = 0.4535.

HSWR80T2n, Withdrawal Rate = 3.0%, y = 16333x+20810 plus 120000 minus 70000. R-squared = 0.3362.

HSWR80T2n, Withdrawal Rate = 4.0%, y = 15812x+11160 plus 120000 minus 70000.R-squared = 0.3422.

HSWR80T2n, Withdrawal Rate = 5.0%, y = 15291x+1508.7 plus 120000 and minus 70000. R-squared = 0.3483.

HSWR50T2n, Withdrawal Rate = 3.0%, y = 10183x+45643 plus 80000 minus 40000.R-squared = 0.3404.

HSWR50T2n, Withdrawal Rate = 4.0%, y = 9849x+35555 plus 80000 minus 40000.R-squared = 0.3482.

HSWR50T2n, Withdrawal Rate = 5.0%, y = 9514.9x+25467 plus 80000 minus 40000.R-squared = 0.3563.

HSWR20T2n, Withdrawal Rate = 3.0%, y = 4125x+69962 plus 30000 minus 20000. R-squared = 0.3507.

HSWR20T2n, Withdrawal Rate = 4.0%, y = 4008.6x+59264 plus 30000 minus 20000.R-squared = 0.3621.

HSWR20T2n, Withdrawal Rate = 5.0%, y = 3892.1x+48567 plus 25000 minus 20000.R-squared = 0.3736.

Comparisons at Year 10

Today's earnings yield is 3.5%.

HSWR80T2, Withdrawal Rate = 3.0%, y = 79.7% of the initial balance (from 9.7% to 179.7%).

HSWR80T2n, Withdrawal Rate = 3.0%, y = 78.0% of the initial balance (from 8.0% to 198.0%).

HSWR50T2, Withdrawal Rate = 3.0%, y = 84.1% of the initial balance (from 44.1% to 144.1%).

HSWR50T2n, Withdrawal Rate = 3.0%, y = 81.3% of the initial balance (from 41.3% to 161.3%).

HSWR20T2, Withdrawal Rate = 3.0%, y = 86.3% of the initial balance (from 71.3% to 101.3%).

HSWR20T2n, Withdrawal Rate = 3.0%, y = 84.4% of the initial balance (from 64.4% to 114.4%).

HSWR80T2, Withdrawal Rate = 4.0%, y = 68.1% of the initial balance (from -1.9% to 168.1%).

HSWR80T2n, Withdrawal Rate = 4.0%, y = 66.5% of the initial balance (from -3.5% to 186.5%).

HSWR50T2, Withdrawal Rate = 4.0%, y = 72.7% of the initial balance (from 32.7% to 132.7%).

HSWR50T2n, Withdrawal Rate = 4.0%, y = 70.0% of the initial balance (from 30.0% to 150.0%).

HSWR20T2, Withdrawal Rate = 4.0%, y = 75.1% of the initial balance (from 65.1% to 90.1%).

HSWR20T2n, Withdrawal Rate = 4.0%, y = 73.3% of the initial balance (from 53.3% to 103.3%).

HSWR80T2, Withdrawal Rate = 5.0%, y = 56.4% of the initial balance (from -13.6% to 156.4%).

HSWR80T2n, Withdrawal Rate = 5.0%, y = 55.0% of the initial balance (from -15.0% to 175.0%).

HSWR50T2, Withdrawal Rate = 5.0%, y = 61.3% of the initial balance (from 21.3% to 111.3%).

HSWR50T2n, Withdrawal Rate = 5.0%, y = 58.8% of the initial balance (from 18.8% to 138.8%).

HSWR20T2, Withdrawal Rate = 5.0%, y = 63.9% of the initial balance (from 53.9% to 78.9%).

HSWR20T2n, Withdrawal Rate = 5.0%, y = 62.2% of the initial balance (from 42.2% to 87.2%).

At a future favorable valuation, the earnings yield might be 10.0% (P/E10=10.0).

HSWR80T2, Withdrawal Rate = 3.0%, y = 180.8% of the initial balance (from 110.8% to 280.8%).

HSWR80T2n, Withdrawal Rate = 3.0%, y = 184.1% of the initial balance (from 114.1% to 304.1%).

HSWR50T2, Withdrawal Rate = 3.0%, y = 142.1% of the initial balance (from 102.1% to 202.1%).

HSWR50T2n, Withdrawal Rate = 3.0%, y = 147.5% of the initial balance (from 107.5% to 227.5%).

HSWR20T2, Withdrawal Rate = 3.0%, y = 107.7% of the initial balance (from 92.7% to 122.7%).

HSWR20T2n, Withdrawal Rate = 3.0%, y = 111.2% of the initial balance (from 91.2% to 141.2%).

HSWR80T2, Withdrawal Rate = 4.0%, y = 166.1% of the initial balance (from 96.1% to 266.1%).

HSWR80T2n, Withdrawal Rate = 4.0%, y = 169.3% of the initial balance (from 99.3% to 289.3%).

HSWR50T2, Withdrawal Rate = 4.0%, y = 129.0% of the initial balance (from 89.0% to 189.0%).

HSWR50T2n, Withdrawal Rate = 4.0%, y = 134.0% of the initial balance (from 94.0% to 214.0%).

HSWR20T2, Withdrawal Rate = 4.0%, y = 96.1% of the initial balance (from 86.1% to 111.1%).

HSWR20T2n, Withdrawal Rate = 4.0%, y = 99.4% of the initial balance (from 79.4% to 129.4%).

HSWR80T2, Withdrawal Rate = 5.0%, y = 151.5% of the initial balance (from 81.5% to 251.5%).

HSWR80T2n, Withdrawal Rate = 5.0%, y = 154.4% of the initial balance (from 84.4% to 274.4%).

HSWR50T2, Withdrawal Rate = 5.0%, y = 115.9% of the initial balance (from 75.9% to 165.9%).

HSWR50T2n, Withdrawal Rate = 5.0%, y = 120.6% of the initial balance (from 80.6% to 200.6%).

HSWR20T2, Withdrawal Rate = 5.0%, y = y = 84.4% of the initial balance (from 74.4% to 99.4%).

HSWR20T2n, Withdrawal Rate = 5.0%, y = 87.5% of the initial balance (from 67.5% to 112.5%).

Analysis

Different withdrawal rates affect offsets, but not the slopes.

The amount that a portfolio balance varies with valuations depends upon the portfolio allocation, but not the withdrawal rate. The primary influence of valuations is to change the overall return of the stocks.

[In Gummy’s Safe Withdrawal Rate equation, the portfolio’s balance at year 10/the portfolio’s initial balance = (gain product term)*(1 – withdrawal rate/the 10-year historical surviving withdrawal rate of a sequence). The (gain product term) equals the portfolio’s final balance (i.e., at year 10) when there are no withdrawals and no deposits. It does not depend upon the order of returns. The 10-year historical surviving withdrawal rate DOES depend upon the order of returns. The 10-year historical surviving withdrawal rate of a sequence is 1/Gummy’s Magic Sum at year 10.)]

There is very little difference between rebalancing versus not rebalancing.

Rebalancing is better when valuations are high (e.g., today’s earnings yield of 3.5%). Not rebalancing is better when valuations are low (e.g., at a future earnings yield of 10.0%).

Look at the effect of rebalancing versus not rebalancing at a 3.5% earnings yield and a 4.0% withdrawal rate with 50% stocks (i.e., HSWR50T2 and HSWR50T2n).

HSWR50T2, Withdrawal Rate = 4.0%, y = 72.7% of the initial balance (from 32.7% to 132.7%).

HSWR50T2n, Withdrawal Rate = 4.0%, y = 70.0% of the initial balance (from 30.0% to 150.0%).

Look at the effect of rebalancing versus not rebalancing at a 10.0% earnings yield and a 4.0% withdrawal rate with 50% stocks (i.e., HSWR50T2 and HSWR50T2n).

HSWR50T2, Withdrawal Rate = 4.0%, y = 129.0% of the initial balance (from 89.0% to 189.0%).

HSWR50T2n, Withdrawal Rate = 4.0%, y = 134.0% of the initial balance (from 94.0% to 214.0%).

Valuations affect the best allocation.

Here are the comparisons at today’s valuations, with rebalancing at a 4.0% withdrawal rate. The earnings yield 100E10/P is 3.5%. The best choice is 20% stocks as opposed to 50% or 80%.

HSWR80T2, Withdrawal Rate = 4.0%, y = 68.1% of the initial balance (from -1.9% to 168.1%).

HSWR50T2, Withdrawal Rate = 4.0%, y = 72.7% of the initial balance (from 32.7% to 132.7%).

HSWR20T2, Withdrawal Rate = 4.0%, y = 75.1% of the initial balance (from 65.1% to 90.1%).

Similarly, here are the comparisons at today’s valuations, without rebalancing at a 4.0% withdrawal rate. The earnings yield 100E10/P is 3.5%. The best choice is 20% stocks as opposed to 50% or 80%.

HSWR80T2n, Withdrawal Rate = 4.0%, y = 66.5% of the initial balance (from -3.5% to 186.5%).

HSWR50T2n, Withdrawal Rate = 4.0%, y = 70.0% of the initial balance (from 30.0% to 150.0%).

HSWR20T2n, Withdrawal Rate = 4.0%, y = 73.3% of the initial balance (from 53.3% to 103.3%).

At today’s valuations, the best choice overall is 20% stocks (as opposed to 50% or 80%) with rebalancing.

Here are the comparisons at a favorable, future valuation, with rebalancing at a 4.0% withdrawal rate. The earnings yield 100E10/P is 10.0%. The best choice is 80% stocks as opposed to 20% or 50%.

HSWR80T2, Withdrawal Rate = 4.0%, y = 166.1% of the initial balance (from 96.1% to 266.1%).

HSWR50T2, Withdrawal Rate = 4.0%, y = 129.0% of the initial balance (from 89.0% to 189.0%).

HSWR20T2, Withdrawal Rate = 4.0%, y = 96.1% of the initial balance (from 86.1% to 111.1%).

Similarly, here are the comparisons at a favorable, future valuation, without rebalancing at a 4.0% withdrawal rate. The earnings yield 100E10/P is 10.0%. The best choice is 80% stocks as opposed to 20% or 50%.

HSWR80T2n, Withdrawal Rate = 4.0%, y = 169.3% of the initial balance (from 99.3% to 289.3%).

HSWR50T2n, Withdrawal Rate = 4.0%, y = 134.0% of the initial balance (from 94.0% to 214.0%).

HSWR20T2n, Withdrawal Rate = 4.0%, y = 99.4% of the initial balance (from 79.4% to 129.4%).

At a favorable, future valuation, the best choice overall is 80% stocks (as opposed to 20% or 50%) without rebalancing.

Summary

At today’s valuations, the best choice overall is 20% stocks (as opposed to 50% or 80%) with rebalancing.

At a favorable, future valuation, the best choice overall is 80% stocks (as opposed to 20% or 50%) without rebalancing.

Valuations dominate everything: all choices, all effects.

NOTE: I have based my choices strictly on expected (average, mean) returns. I have not included the effect of scatter.

Have fun.

John Walter Russell
February 8, 2006