Year 15 Calculator Equations

I have placed Year 15 Calculator A into my Yahoo Briefcase.

Enter P/E10, your stock allocation, TIPS interest rate and final balance percentage for four portfolios. See how likely you will be of reaching your final balance percentage as a function of your withdrawal rate.

Portfolios

In general:

ZBR stands for Zero Balance Rate. CBR stands for Constant Balance Rate. ZBR20 and CBR20 have a 20% stock allocation. ZBR50 and CBR50 have a 50% stock allocation. ZBR80 and CBR80 have an 80% stock allocation. ZBR100T and CBR100T consist entirely (100%) of stocks. SwA stands for Switching Program A. SwB stands for Switching Program B. T1 stands for TIPS at a 1% interest rate. T2 stands for TIPS at a 2% interest rate. T3 stands for TIPS at a 3% interest rate.

All amounts include adjustments for inflation. All portfolio changes, including rebalancing, take place annually (in January). All portfolios are assessed 0.20% of the current balance in expenses. Withdrawal rates are percentages of the initial balance (plus inflation).

Specific portfolios: Zero Balances:

ZBR20T1 consists of 20% stocks (S&P500) and 80% TIPS at a 1% interest rate. It has a balance of zero at Year 15.

ZBR50T1 consists of 50% stocks (S&P500) and 50% TIPS at a 1% interest rate. It has a balance of zero at Year 15.

ZBR80T1 consists of 80% stocks (S&P500) and 20% TIPS at a 1% interest rate. It has a balance of zero at Year 15.

ZBR100T consists of 100% stocks (S&P500). It has a balance of zero at Year 15.

ZBSwAT1 consists of stocks (S&P500) and TIPS at a 1% interest rate. Its allocation varies with P/E10. It keeps both allocations between 25% and 75%. It allocates 75% to stocks when P/E10 is below 11. It allocates 40% to stocks when P/E10 is between 11 and 21. It allocates 25% to stocks when P/E10 is above 21. It has a balance of zero at Year 15.

ZBSwBT1 consists of stocks (S&P500) and TIPS at a 1% interest rate. Its allocation varies with P/E10. It allocates 100% to stocks when P/E10 is below 9. It allocates 50% to stocks when P/E10 is between 9 and 12. It allocates 30% to stocks when P/E10 is between 12 and 21. It allocates 20% to stocks when P/E10 is between 21 and 24. It allocates 0% to stocks when P/E10 is above 24. It has a balance of zero at Year 15.

ZBR20T2 is identical to ZBR20T1 except that its TIPS interest rate is 2%.

ZBR50T2 is identical to ZBR50T1 except that its TIPS interest rate is 2%.

ZBR80T2 is identical to ZBR80T1 except that its TIPS interest rate is 2%.

ZBSwAT2 is identical to ZBSwAT1 except that its TIPS interest rate is 2%.

ZBSwBT2 is identical to ZBSwBT1 except that its TIPS interest rate is 2%.

ZBR20T3 is identical to ZBR20T1 except that its TIPS interest rate is 3%.

ZBR50T3 is identical to ZBR50T1 except that its TIPS interest rate is 3%.

ZBR80T3 is identical to ZBR80T1 except that its TIPS interest rate is 3%.

ZBSwAT3 is identical to ZBSwAT1 except that its TIPS interest rate is 3%.

ZBSwBT3 is identical to ZBSwBT1 except that its TIPS interest rate is 3%.

Specific portfolios: Constant Balances:

CBR20T1 is identical to ZBR20T1 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR50T1 is identical to ZBR50T1 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR80T1 is identical to ZBR80T1 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR100T is identical to ZBR100T except that its balance at Year 15 equals its initial balance (plus inflation).

CBSwAT1 is identical to ZBSwAT1 except that its balance at Year 15 equals its initial balance (plus inflation).

CBSwBT1 is identical to ZBSwBT1 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR20T2 is identical to ZBR20T2 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR50T2 is identical to ZBR50T2 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR80T2 is identical to ZBR80T2 except that its balance at Year 15 equals its initial balance (plus inflation).

CBSwAT2 is identical to ZBSwAT2 except that its balance at Year 15 equals its initial balance (plus inflation).

CBSwBT2 is identical to ZBSwBT2 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR20T3 is identical to ZBR20T3 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR50T3 is identical to ZBR50T3 except that its balance at Year 15 equals its initial balance (plus inflation).

CBR80T3 is identical to ZBR80T3 except that its balance at Year 15 equals its initial balance (plus inflation).

CBSwAT1 is identical to ZBSwAT1 except that its balance at Year 15 equals its initial balance (plus inflation).

CBSwBT3 is identical to ZBSwBT3 except that its balance at Year 15 equals its initial balance (plus inflation).

Year 15 Equations

Year 15 Zero Balance Equations with 1% TIPS. x=100E10/P:

ZBR20T1=y. y=0.2146x+6.211 plus 0.8% and minus 0.6%. R-squared=0.5474.

ZBR50T1=y. y=0.5123x+5.0166 plus 1.8% and minus 1.6%. R-squared=0.58.

ZBR80T1=y. y=0.8326x+3.5472 plus 2.8% and minus 2.2%. R-squared=0.5593.

ZBR100T=y. y=1.0446x+2.5142 plus 4.0% and minus 2.6%. R-squared=0.5407.

ZBSwAT1=y. y=0.5528x+5.1141 plus 1.6% and minus 1.0%. R-squared=0.7547.

ZBSwBT1=y. y=0.5389x+5.2824 plus 1.0% and minus 1.0%. R-squared=0.8036.

Year 15 Constant Balance Equations with 1% TIPS. x=100E10/P:

CBR20T1=y. y=0.2859x-0.0652 plus 1.0% and minus 0.6%. R-squared=0.6043.

CBR50T1=y. y=0.7112x-2.5188 plus 2.4% and minus 1.4%. R-squared=0.6083.

CBR80T1=y. y=1.1227x-3.1532 plus 3.0% and minus 2.4%. R-squared=0.602.

CBR100T=y. y=1.4105x-4.5478 plus 5.0% and minus 3.0%. R-squared=0.5897.

CBSwAT1=y. y=0.6931x-0.7411 plus 1.6% and minus 1.6%. R-squared=0.7185.

CBSwBT1=y. y=0.6339x-0.1945 plus 2.0% and minus 1.4%. R-squared=0.7215.

Year 15 Zero Balance Equations with 2% TIPS. x=100E10/P:

ZBR20T2=y. y=0.2252x+6.5753 plus 1.0% and minus 0.6%. R-squared=0.5446.

ZBR50T2=y. y=0.5248x+5.2067 plus 1.4% and minus 1.4%. R-squared=0.5785.

ZBR80T2=y. y=0.8336x+3.6568 plus 2.5% and minus 2.4%. R-squared=0.5555.

ZBSwAT2=y. y=0.5504x+5.4472 plus 1.0% and minus 1.0%. R-squared=0.7331.

ZBSwBT2=y. y=0.5355x+5.6853 plus 1.0% and minus 0.8%. R-squared=0.7955.

Year 15 Constant Balance Equations with 2% TIPS. x=100E10/P:

CBR20T2=y. y=0.2894x+0.702 plus 1.0% and minus 0.6%. R-squared=0.6044.

CBR50T2=y. y=0.7155x-1.0686 plus 2.0% and minus 1.4%. R-squared=0.6137.

CBR80T2=y. y=1.1358x-3.078 plus 3.5% and minus 2.4%. R-squared=0.6018.

CBSwAT2=y. y=0.6864x-0.1774 plus 1.8% and minus 1.6%. R-squared=0.7176.

CBSwBT2=y. y=0.6315x+0.4181 plus 2.0% and minus 1.4%. R-squared=0.7371.

Year 15 Zero Balance Equations with 3% TIPS. x=100E10/P:

ZBR20T3=y. y=0.2337x+6.973 plus 0.8% and minus 0.6%. R-squared=0.5454.

ZBR50T3=y. y=0.5321x+5.4526 plus 1.2% and minus 1.2%. R-squared=0.5812.

ZBR80T3=y. y=0.842x+3.7173 plus 2.0% and minus 2.0%. R-squared=0.5555.

ZBSwAT3=y. y=0.5445x+5.8101 plus 1.0% and minus 1.0%. R-squared=0.7114.

ZBSwBT3=y. y=0.5262x+6.1136 plus 1.4% and minus 0.8%. R-squared=0.7764.

Year 15 Constant Balance Equations with 3% TIPS. x=100E10/P:

CBR20T3=y. y=0.2973x+1.4241 plus 1.0% and minus 0.7%. R-squared=0.6181.

CBR50T3=y. y=0.7196x-0.6193 plus 2.0% and minus 1.5%. R-squared=0.6157.

CBR80T3=y. y=1.1334x-2.8655 plus 3.5% and minus 2.4%. R-squared=0.6009.

CBSwAT3=y. y=0.6819x+0.3784 plus 1.8% and minus 1.4%. R-squared=0.7055.

CBSwBT3=y. y=0.6258x+1.0489 plus 2.0% and minus 1.5%. R-squared=0.745.

Other Equations

I interpolate for final balances between 0% and 100%. I showed that this is accurate in A Helpful Theorem. In fact, the theorem holds even with final balances greater than the initial balance.

The TIPS equations are in Equations for Design.

A Helpful Theorem
Equations for Design

Have fun.

John Walter Russell
August 21, 2006