More About Risky Alternatives

This extends my investigation into risky alternatives. I look at years 5 and 15.

Procedures

I have calculated the balances at years 5 and 15 of portfolios HSWR80T2, HSWR50T2 and HSWR20T2 for historical sequences beginning in 1923-1980. I used a withdrawal rate of 4.0% (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.

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

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

I used my Deluxe Calculator V1.1A08a as before. I used Excel plots to determine regression equations (i.e., linear curve fits) of balances versus the percentage earnings yield 100E10/P. I have solved the equations at today's earnings yield (of 3.5%, roughly) and at a favorable future earnings yield of 10.0% (P/E10=10). I have estimated confidence limits (visually) from the graphs.

Comparisons at Year 5

Equations

y = the (real) balance at year 5 starting from $100000.
x = the percentage earnings yield 100E10/P (i.e., 100/[P/E10]).

HSWR80T2, Withdrawal Rate = 4.0%, y = 10477x+35646 plus 60000 minus 40000. R-squared = 0.3935.

HSWR50T2, Withdrawal Rate = 4.0%, y = 6067.7x+58758 plus 30000 minus 20000. R-squared = 0.4028.

HSWR20T2, Withdrawal Rate = 4.0%, y = 2254.3x+77840 plus 10000 minus 10000. R-squared = 0.4152.

At today's earnings yield of 3.5%:

HSWR80T2, Withdrawal Rate = 4.0%, y = 72.3% of the initial balance (from 32.3% to 132.3%).

HSWR50T2, Withdrawal Rate = 4.0%, y = 80.0% of the initial balance (from 60.0% to 110.0%).

HSWR20T2, Withdrawal Rate = 4.0%, y = 85.7% of the initial balance (from 75.7% to 95.7%).

At a future earnings yield of 10.0%:

HSWR80T2, Withdrawal Rate = 4.0%, y = 140.4% of the initial balance (from 100.4% to 200.4%).

HSWR50T2, Withdrawal Rate = 4.0%, y = 119.4% of the initial balance (from 99.4% to 149.4%).

HSWR20T2, Withdrawal Rate = 4.0%, y = 100.4% of the initial balance (from 90.4% to 110.4%).

NOTE: The crossover point is an earnings yield of 5% (i.e., P/E10=20). When P/E10 is above 20, the averages favor low stock allocations. When P/E10 is below 20, the averages favor high stock allocations.

Comparisons at Year 15

Equations

y = the (real) balance at year 5 starting from $100000.
x = the percentage earnings yield 100E10/P (i.e., 100/[P/E10]).

HSWR80T2, Withdrawal Rate = 4.0%, y = 27803x-56419 plus 150000 minus 100000. R-squared = 0.5008.

HSWR50T2, Withdrawal Rate = 4.0%, y = 14815x+1806.8 plus 60000 minus 50000. R-squared = 0.5647.

HSWR20T2, Withdrawal Rate = 4.0%, y = 5095.1x+42334 plus 20000 minus 20000. R-squared = 0.6072.

At today's earnings yield of 3.5%:

HSWR80T2, Withdrawal Rate = 4.0%, y = 40.9% of the initial balance (from -59.1% to 190.9%).

HSWR50T2, Withdrawal Rate = 4.0%, y = 53.7% of the initial balance (from 3.7% to 113.7%).

HSWR20T2, Withdrawal Rate = 4.0%, y = 60.2% of the initial balance (from 40.2% to 80.2%).

At a future earnings yield of 10.0%:

HSWR80T2, Withdrawal Rate = 4.0%, y = 221.6% of the initial balance (from 121.6% to 371.6%).

HSWR50T2, Withdrawal Rate = 4.0%, y = 150.0% of the initial balance (from 100.0% to 210.0%).

HSWR20T2, Withdrawal Rate = 4.0%, y = 93.3% of the initial balance (from 73.3% to 113.3%).

NOTE: The crossover point is an earnings yield of 4.5% (i.e., P/E10=22). When P/E10 is above 22, the averages favor low stock allocations. When P/E10 is below 22, the averages favor high stock allocations.

Conclusions

These numbers let you know what is likely in the intermediate-term. Correlations are exceedingly strong: above 60% (R-squared above 0.36) at year 5 and above 70% (R-squared above 0.49) at year 15.

Starting from today's valuations, the most likely outcomes at years 5 and 15 favor low stock allocations. The best choice is to own no stocks at all.

You can learn quite a bit from looking at the confidence limits. When valuations are favorable (P/E10=10, earnings yield = 10.0%), it is hard to lose by adding stocks. Look at the lower confidence limits. When valuations are unfavorable (such as today, with a 3.5% earnings yield), you risk bankruptcy by owning stocks.

When valuations are favorable, the upside is huge.

Have fun.

John Walter Russell
February 11, 2006