Balances with TIPS Calculators

I have placed several Balances with TIPS calculators in my Yahoo Briefcase. They are in my Lucky 7 Calculators folder.

Yahoo Briefcase

Here are the conditions and equations.

Calculator

I used Deluxe Calculator V1.1A08a. It includes a data update (through mid-2004).

I set the initial balance equal to $100000. I set expenses at 0.20% of the current balance. I rebalanced the portfolios annually. I adjusted withdrawals to match inflation in accordance with CPI-U.

The stocks were the S&P500 index. The data source is Professor Robert Shiller’s database. The percentage earnings yield 100E10/P is 100%/[P/E10]. Professor Shiller’s measure of value P/E10 is the current real price divided by the average of the most recent decade of real earnings.

Professor Shiller’s Web Site

I simulated TIPS by providing a constant real interest rate without any capital gains or losses.

Otherwise, I used default values. Data are January values.

I used Excel’s capabilities to plot Balances at Years 10, 20 and 30 versus the percentage earnings yield 100E10/P. I used Excel’s capabilities to calculate regression equations (straight-line, linear curve fits). I estimated confidence limits visually. The inner confidence levels are half way between the regression equations (i.e., the straight lines) and the regular confidence limits.

Using the standard Gaussian (bell shaped curve, normal) approximation, the inner confidence limits correspond to confidence levels close to 20% and 80%. The regular, outer confidence limits correspond to confidence levels in the neighborhood of 5% and 95%. (I am unwilling to assign a confidence level greater than 90% (two-sided, 95% one-sided) to the Gaussian approximation.)

Conditions

HSWR20T0 consists of 20% stocks and 80% TIPS with an interest rate of 0%.
HSWR50T0 consists of 50% stocks and 50% TIPS with an interest rate of 0%.
HSWR80T0 consists of 80% stocks and 20% TIPS with an interest rate of 0%.

HSWR20T1 consists of 20% stocks and 80% TIPS with an interest rate of 1%.
HSWR50T1 consists of 50% stocks and 50% TIPS with an interest rate of 1%.
HSWR80T1 consists of 80% stocks and 20% TIPS with an interest rate of 1%.

HSWR20T2 consists of 20% stocks and 80% TIPS with an interest rate of 2%.
HSWR50T2 consists of 50% stocks and 50% TIPS with an interest rate of 2%.
HSWR80T2 consists of 80% stocks and 20% TIPS with an interest rate of 2%.

Year 10 Balances with 0% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T0: y = 2859x + 61342 plus 20000 and minus 20000 and R-squared = 0.4343.
HSWR50T0: y = 8181.3x + 45938 plus 40000 and minus 30000 and R-squared = 0.3994.
HSWR80T0: y = 15070x + 22967 plus 100000 and minus 60000 and R-squared = 0.3629.

Withdrawal Rate = 4.0%

HSWR20T0: y = 2799.9x + 51209 plus 15000 and minus 15000 and R-squared = 0.4471.
HSWR50T0: y = 7940.3x + 35906 plus 40000 and minus 30000 and R-squared = 0.409.
HSWR80T0: y = 14609x + 13212 plus 100000 and minus 50000 and R-squared = 0.3697.

Withdrawal Rate = 5.0%

HSWR20T0: y = 2740.9x + 41076 plus 15000 and minus 15000 and R-squared = 0.4585.
HSWR50T0: y = 7699.3x + 25874 plus 40000 and minus 40000 and R-squared = 0.4186.
HSWR80T0: y = 14148x + 3456.8 plus 100000 and minus 60000 and R-squared = 0.3766.

Year 20 Balances with 0% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T0: y = 4898x + 26688 plus 20000 and minus 20000 and R-squared = 0.6535.
HSWR50T0: y = 17658x - 12613 plus 60000 and minus 60000 and R-squared = 0.6339.
HSWR80T0: y = 40985x - 101396 plus 160000 and minus 140000 and R-squared = 0.5789.

Withdrawal Rate = 4.0%

HSWR20T0: y = 4503.4x + 9998.1 plus 20000 and minus 20000 and R-squared = 0.6278.
HSWR50T0: y = 16629x - 34521 plus 50000 and minus 50000 and R-squared = 0.6516.
HSWR80T0: y = 38600x - 122723 plus 160000 and minus 120000 and R-squared = 0.597.

Withdrawal Rate = 5.0%

HSWR20T0: y = 4421.1x - 15614 plus 20000 and minus 20000 and R-squared = 0.6209.
HSWR50T0: y = 15600x - 56430 plus 60000 and minus 50000 and R-squared = 0.6578.
HSWR80T0: y = 36305x - 144051 plus 160000 and minus 120000 and R-squared = 0.6094.

Year 30 Balances with 0% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T0: y = 4381.7x + 6539.5 plus 20000 and minus 10000 and R-squared = 0.6558.
HSWR50T0: y = 16843x - 3731.2 plus 60000 and minus 40000 and R-squared = 0.5557.
HSWR80T0: y = 42647x - 54215 plus 200000 and minus 120000 and R-squared = 0.4634.

Withdrawal Rate = 4.0%

HSWR20T0: y = 4950.2x - 34533 plus 20000 and minus 10000 and R-squared = 0.6668.
HSWR50T0: y = 18345x - 68852 plus 60000 and minus 40000 and R-squared = 0.6974.
HSWR80T0: y = 45628x - 156098 plus 180000 and minus 100000 and R-squared = 0.5975.

Withdrawal Rate = 5.0%

HSWR20T0: y = 5573x - 76239 plus 20000 and minus 20000 and R-squared = 0.591.
HSWR50T0: y = 19914x - 134619 plus 50000 and minus 50000 and R-squared = 0.7509.
HSWR80T0: y = 48693x - 258752 plus 180000 and minus 100000 and R-squared = 0.6978.

Year 10 Balances with 1% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T1: y = 3070.7x + 67794 plus 20000 and minus 20000 and R-squared = 0.4329.
HSWR50T1: y = 8555.1x + 49252 plus 50000 and minus 40000 and R-squared = 0.399.
HSWR80T1: y = 15339x + 23888 plus 120000 and minus 70000 and R-squared = 0.3629.

Withdrawal Rate = 4.0%

HSWR20T1: y = 3007.9x + 57252 plus 20000 and minus 20000 and R-squared = 0.4453.
HSWR50T1: y = 8306.3x + 38971 plus 40000 and minus 40000 and R-squared = 0.4085.
HSWR80T1: y = 14872x + 14038 plus 120000 and minus 60000 and R-squared = 0.3697.

Withdrawal Rate = 5.0%

HSWR20T1: y = 2945.1x + 46710 plus 20000 and minus 20000 and R-squared = 0.4565.
HSWR50T1: y = 8057.5x + 28690 plus 40000 and minus 40000 and R-squared = 0.4179.
HSWR80T1: y = 14406x + 4187.1 plus 100000 and minus 50000 and R-squared = 0.3765.

Year 20 Balances with 1% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T1: y = 5705.8x + 37137 plus 20000 and minus 20000 and R-squared = 0.6537.
HSWR50T1: y = 19422x - 9731.1 plus 60000 and minus 40000 and R-squared = 0.6324.
HSWR80T1: y = 42456x - 103378 plus 180000 and minus 120000 and R-squared = 0.5785.

Withdrawal Rate = 4.0%

HSWR20T1: y = 5435.5x + 14240 plus 30000 and minus 30000 and R-squared = 0.6539.
HSWR50T1: y = 18317x - 32717 plus 60000 and minus 60000 and R-squared = 0.651.
HSWR80T1: y = 40096x - 125090 plus 160000 and minus 100000 and R-squared = 0.5967.

Withdrawal Rate = 5.0%

HSWR20T1: y = 5165.1x - 8655.8 plus 30000 and minus 30000 and R-squared = 0.6342.
HSWR50T1: y = 17213x - 55703 plus 60000 and minus 60000 and R-squared = 0.6595.
HSWR80T1: y = 37736x - 146802 plus 140000 and minus 120000 and R-squared = 0.6096.

Year 30 Balances with 1% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T1: y = 5234.5x + 24840 plus 20000 and minus 20000 and R-squared = 0.6286.
HSWR50T1: y = 18954x + 10264 plus 60000 and minus 60000 and R-squared = 0.5279.
HSWR80T1: y = 44768x - 49176 plus 200000 and minus 200000 and R-squared = 0.4548.

Withdrawal Rate = 4.0%

HSWR20T1: y = 5850.2x - 21597 plus 30000 and minus 30000 and R-squared = 0.6818.
HSWR50T1: y = 20540x - 60287 plus 80000 and minus 60000 and R-squared = 0.6738.
HSWR80T1: y = 47817x - 154456 plus 200000 and minus 200000 and R-squared = 0.5873.

Withdrawal Rate = 5.0%

HSWR20T1: y = 6512.9x - 68511 plus 30000 and minus 30000 and R-squared = 0.6312.
HSWR50T1: y = 22169x - 131237 plus 60000 and minus 40000 and R-squared = 0.7476.
HSWR80T1: y = 50936x - 260377 plus 180000 and minus 180000 and R-squared = 0.6906.

Year 10 Balances with 2% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T2: y = 3296.2x + 74762 plus 20000 and minus 20000 and R-squared = 0.4316.
HSWR50T2: y = 8943.8x + 52737 plus 50000 and minus 40000 and R-squared = 0.3987.
HSWR80T2: y = 15613x + 24830 plus 100000 and minus 60000 and R-squared = 0.363.

Withdrawal Rate = 4.0%

HSWR20T2: y = 3229.5x + 63793 plus 10000 and minus 10000 and R-squared = 0.4436.
HSWR50T2: y = 8687x + 42200 plus 50000 and minus 40000 and R-squared = 0.4079.
HSWR80T2: y = 15140x + 14883 plus 100000 and minus 60000 and R-squared = 0.3697.

Withdrawal Rate = 5.0%

HSWR20T2: y = 3162.8x + 52824 plus 20000 and minus 20000 and R-squared = 0.4546.
HSWR50T2: y = 8430.2x + 31664 plus 40000 and minus 40000 and R-squared = 0.4173.
HSWR80T2: y = 14668x + 4936.6 plus 100000 and minus 60000 and R-squared = 0.3765.

Year 20 Balances with 2% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T2: y = 6638.4x + 49618 plus 20000 and minus 20000 and R-squared = 0.6531.
HSWR50T2: y = 21349x - 6392.3 plus 80000 and minus 40000 and R-squared = 0.6309.
HSWR80T2: y = 44073x - 105393 plus 180000 and minus 100000 and R-squared = 0.5782.

Withdrawal Rate = 4.0%

HSWR20T2: y = 6332.2x + 24797 plus 30000 and minus 30000 and R-squared = 0.6573.
HSWR50T2: y = 20163x - 30522 plus 60000 and minus 40000 and R-squared = 0.6501.
HSWR80T2: y = 41646x - 127499 plus 160000 and minus 80000 and R-squared = 0.5964.

Withdrawal Rate = 5.0%

HSWR20T2: y = 6026x - 23.467 plus 30000 and minus 30000 and R-squared = 0.6444.
HSWR50T2: y = 18978x - 54652 plus 60000 and minus 60000 and R-squared = 0.6607.
HSWR80T2: y = 39220x - 149605 plus 160000 and minus 60000 and R-squared = 0.6097.

Year 30 Balances with 2% TIPS

x = the percentage earnings yield 100/[P/E10].
y = the balance at the year indicated.

Withdrawal Rate = 3.0%

HSWR20T2: y = 6273.1x + 49313 plus 20000 and minus 20000 and R-squared = 0.5933.
HSWR50T2: y = 21346x+ 27252 plus 180000 and minus 100000 and R-squared = 0.5015.
HSWR80T2: y = 46998x - 43637 plus 200000 and minus 200000 and R-squared = 0.683.

Withdrawal Rate = 4.0%

HSWR20T2: y = 6948.8x - 3448.5 plus 30000 and minus 20000 and R-squared = 0.6813.
HSWR50T2: y = 23023x - 49273 plus 80000 and minus 40000 and R-squared = 0.648.
HSWR80T2: y = 50118x - 152446 plus 200000 and minus 100000 and R-squared = 0.5772.

Withdrawal Rate = 5.0%

HSWR20T2: y = 7641.5x - 56375 plus 30000 and minus 30000 and R-squared = 0.6625.
HSWR50T2: y = 24719x - 125981 plus 80000 and minus 40000 and R-squared = 0.7383.
HSWR80T2: y = 53293x - 261770 plus 200000 and minus 100000 and R-squared = 0.683.

Have fun.

John Walter Russell
March 10, 2006