Withdrawal Rates at Favorable Valuations

We can expect stocks to return to favorable valuations in the intermediate-term (approximately, ten years). I have already shown what this means for those who wait in a few cases. Here are some more cases.

I have calculated 30-year withdrawal rates for all of the portfolios in Equations for Design using P/E10 = 8, 10 and 12. Keep in mind that the final balances of portfolios SwOptT2, SwAT2, HSWR50T2 and HSWR80T2 are zero, but the final balances of CTVR50, CTVR80, HFWR50 and HFWR80 are not. The final balances of CTVR50 and CTVR80 equal their initial balances. The balances of HFWR50 and HFWR80 never fall below one-half of their initial balances.
Equations for Design

Portfolio Equations:

These equations are for portfolio lifetimes of 30 years. In every case, I set the annual expenses equal to 0.20% of the portfolio’s current balance. This is the approximate cost of an S&P500 index fund.

This is the equation for the Calculated Rate of portfolio SwOptT2.

The lower confidence limit is the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate. The term x is the percentage earnings yield 100/[P/E10].

y = 0.3276*x + 3.9729 plus 1.3% and minus 0.7%.

SwOptT2 consists of stocks (S&P500) and TIPS at a 2% interest rate. Allocations vary in accordance with P/E10. The P/E10 thresholds are 9-12-21-24. The stock allocations are 100%-50%-30%-20%-0%. This is the Optimized Switching portfolio with 2% TIPS.

This is the equation for the Calculated Rate of portfolio SwAT2.

The lower confidence limit is the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate. The term x is the percentage earnings yield 100/[P/E10].

y = 0.3776*x + 3.5222 plus 1.3% and minus 0.7%.

SwAT2 consists of stocks (S&P500) and TIPS at a 2% interest rate. Allocations vary in accordance with P/E10. The P/E10 thresholds are 11-21. The stock allocations are 75%-40-25%. This is the optimized Switching portfolio with 2% TIPS subject to constraint A. Constraint A limits stock and bond allocations to 25% to 75%.

This is the equation for the Calculated Rate of portfolio HSWR50T2.

The lower confidence limit is the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate. The term x is the percentage earnings yield 100/[P/E10].

y = 0.4031*x + 2.9478 plus 1.5% and minus 0.8%.

HSWR50T2 consists of stocks (S&P500) and TIPS at a 2% interest rate. I rebalance allocations annually. The stock allocation is 50%. The TIPS allocation is 50%.

This is the equation for the Calculated Rate of portfolio HSWR80T2.

The lower confidence limit is the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate. The term x is the percentage earnings yield 100/[P/E10].

y = 0.6758*x + 1.7538 plus 2.0% and minus 1.1%.

HSWR80T2 consists of stocks (S&P500) and TIPS at a 2% interest rate. I rebalance allocations annually. The stock allocation is 80%. The TIPS allocation is 20%.

This is the equation for the Calculated Rate of portfolio CTVR50.

The lower confidence limit is the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate. The term x is the percentage earnings yield 100/[P/E10].

y = 0.3279*x + 1.4254 plus 0.72% and minus 0.72%.

CTVR50 (Constant Terminal Value Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 50%. The commercial paper allocation is 50%. At the Calculated Rate, the final portfolio balance equals the initial balance.

This is the equation for the Calculated Rate of portfolio CTVR80.

The lower confidence limit is the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate. The term x is the percentage earnings yield 100/[P/E10].

y = 0.7033*x + 0.2133 plus 1.10% and minus 1.10%.

CTVR80 (Constant Terminal Value Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 80%. The commercial paper allocation is 20%. At the Calculated Rate, the final portfolio balance equals the initial balance.

This is the equation for the Calculated Rate of portfolio HFWR50.

The lower confidence limit is the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate. The term x is the percentage earnings yield 100/[P/E10].

y = 0.3408*x + 2.0804 plus 0.88% and minus 0.88%.

HFWR50 (Half Failure Withdrawal Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 50%. The commercial paper allocation is 50%. At the Calculated Rate, the lowest portfolio balance equals (or exceeds minimally) one-half of the initial balance in throughout the entire 30 years.

This is the equation for the Calculated Rate of portfolio HFWR80.

The lower confidence limit is the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate. The term x is the percentage earnings yield 100/[P/E10].

y = 0.6822*x + 0.5298 plus 1.864% and minus 1.864%.

HFWR80 (Half Failure Withdrawal Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 80%. The commercial paper allocation is 20%. At the Calculated Rate, the lowest portfolio balance equals (or exceeds minimally) one-half of the initial balance in throughout the entire 30 years.

Summary of the Equations:

This is the Calculated Rate of portfolio SwOptT2.
y = 0.3276*x + 3.9729 plus 1.3% and minus 0.7%.

This is the Calculated Rate of portfolio SwAT2.
y = 0.3776*x + 3.5222 plus 1.3% and minus 0.7%.

This is the Calculated Rate of portfolio HSWR50T2.
y = 0.4031*x + 2.9478 plus 1.5% and minus 0.8%.

This is the Calculated Rate of portfolio HSWR80T2.
y = 0.6758*x + 1.7538 plus 2.0% and minus 1.1%.

This is the Calculated Rate of portfolio CTVR50.
y = 0.3279*x + 1.4254 plus 0.72% and minus 0.72%.

This is the Calculated Rate of portfolio CTVR80.
y = 0.7033*x + 0.2133 plus 1.10% and minus 1.10%.

This is the Calculated Rate of portfolio HFWR50.
y = 0.3408*x + 2.0804 plus 0.88% and minus 0.88%.

This is the equation for the Calculated Rate of portfolio HFWR80.
y = 0.6822*x + 0.5298 plus 1.864% and minus 1.864%.

Calculated Rates:

When P/E10 = 8:

The Calculated Rate of portfolio SwOptT2 is 8.068.
The Calculated Rate of portfolio SwAT2 is 8.242.
The Calculated Rate of portfolio HSWR50T2 is 7.987.
The Calculated Rate of portfolio HSWR80T2 is 10.201.
The Calculated Rate of portfolio CTVR50 is 5.524.
The Calculated Rate of portfolio CTVR80 is 9.005.
The Calculated Rate of portfolio HFWR50 is 6.340.
The Calculated Rate of portfolio HFWR80 is 9.057.

When P/E10 = 10:

The Calculated Rate of portfolio SwOptT2 is 7.249.
The Calculated Rate of portfolio SwAT2 is 7.298.
The Calculated Rate of portfolio HSWR50T2 is 6.979.
The Calculated Rate of portfolio HSWR80T2 is 8.512.
The Calculated Rate of portfolio CTVR50 is 4.704.
The Calculated Rate of portfolio CTVR80 is 7.246.
The Calculated Rate of portfolio HFWR50 is 5.488.
The Calculated Rate of portfolio HFWR80 is 7.352.

When P/E10 = 12:

The Calculated Rate of portfolio SwOptT2 is 6.703.
The Calculated Rate of portfolio SwAT2 is 6.669.
The Calculated Rate of portfolio HSWR50T2 is 6.307.
The Calculated Rate of portfolio HSWR80T2 is 7.385.
The Calculated Rate of portfolio CTVR50 is 4.158.
The Calculated Rate of portfolio CTVR80 is 6.074.
The Calculated Rate of portfolio HFWR50 is 4.920.
The Calculated Rate of portfolio HFWR80 is 6.215.

Safe Withdrawal Rates:

Safe Withdrawal Rates are lower confidence limits relative to Calculated Rates.

When P/E10 = 8:

The Safe Withdrawal Rate of portfolio SwOptT2 is 7.4.
The Safe Withdrawal Rate of portfolio SwAT2 is 7.5.
The Safe Withdrawal Rate of portfolio HSWR50T2 is 7.2.
The Safe Withdrawal Rate of portfolio HSWR80T2 is 9.1.
The Safe Withdrawal Rate of portfolio CTVR50 is 4.8.
The Safe Withdrawal Rate of portfolio CTVR80 is 7.9.
The Safe Withdrawal Rate of portfolio HFWR50 is 5.5.
The Safe Withdrawal Rate of portfolio HFWR80 is 7.2.

When P/E10 = 10:

The Safe Withdrawal Rate of portfolio SwOptT2 is 6.5.
The Safe Withdrawal Rate of portfolio SwAT2 is 6.6.
The Safe Withdrawal Rate of portfolio HSWR50T2 is 6.2.
The Safe Withdrawal Rate of portfolio HSWR80T2 is 7.4.
The Safe Withdrawal Rate of portfolio CTVR50 is 4.0.
The Safe Withdrawal Rate of portfolio CTVR80 is 6.1.
The Safe Withdrawal Rate of portfolio HFWR50 is 4.6.
The Safe Withdrawal Rate of portfolio HFWR80 is 5.5.

When P/E10 = 12:

The Safe Withdrawal Rate of portfolio SwOptT2 is 6.0.
The Safe Withdrawal Rate of portfolio SwAT2 is 6.0.
The Safe Withdrawal Rate of portfolio HSWR50T2 is 5.5.
The Safe Withdrawal Rate of portfolio HSWR80T2 is 6.3.
The Safe Withdrawal Rate of portfolio CTVR50 is 3.4.
The Safe Withdrawal Rate of portfolio CTVR80 is 5.0.
The Safe Withdrawal Rate of portfolio HFWR50 is 4.0.
The Safe Withdrawal Rate of portfolio HFWR80 is 4.4.

High Risk Rates:

High Risk Rates are upper confidence limits relative to Calculated Rates.

When P/E10 = 8:

The High Risk Rate of portfolio SwOptT2 is 9.4.
The High Risk Rate of portfolio SwAT2 is 9.5.
The High Risk Rate of portfolio HSWR50T2 is 9.5.
The High Risk Rate of portfolio HSWR80T2 is 12.2.
The High Risk Rate of portfolio CTVR50 is 6.2.
The High Risk Rate of portfolio CTVR80 is 10.1.
The High Risk Rate of portfolio HFWR50 is 7.2.
The High Risk Rate of portfolio HFWR80 is 10.9.

When P/E10 = 10:

The High Risk Rate of portfolio SwOptT2 is 8.5.
The High Risk Rate of portfolio SwAT2 is 8.6.
The High Risk Rate of portfolio HSWR50T2 is 8.5.
The High Risk Rate of portfolio HSWR80T2 is 10.5.
The High Risk Rate of portfolio CTVR50 is 5.4.
The High Risk Rate of portfolio CTVR80 is 8.3.
The High Risk Rate of portfolio HFWR50 is 6.4.
The High Risk Rate of portfolio HFWR80 is 9.2.

When P/E10 = 12:

The High Risk Rate of portfolio SwOptT2 is 8.0.
The High Risk Rate of portfolio SwAT2 is 8.0.
The High Risk Rate of portfolio HSWR50T2 is 7.8.
The High Risk Rate of portfolio HSWR80T2 is 9.4.
The High Risk Rate of portfolio CTVR50 is 4.9.
The High Risk Rate of portfolio CTVR80 is 7.2.
The High Risk Rate of portfolio HFWR50 is 5.8.
The High Risk Rate of portfolio HFWR80 is 8.1.

Have fun.

John Walter Russell
September 20, 2005