Revisiting P/E10

I did not start out assuming that P/E10 was a good measure of valuation. I checked a variety of measures and found that P/E10 was the best so far.

This time, I have examined variations on the number of years in the denominator. I looked at P/E1, P/E5, P/E10, P/E15, P/E20, P/E25 and P/E30.

Once again, P/E10 is best. One reason is my emphasis on Safe Withdrawal Rates.

I have found that you will know about the success of your retirement portfolio within 11 to 15 years. Either your portfolio will have grown substantially or it will be in trouble already. Seldom is there ambiguity at 11 to 15 years. It makes sense that retirement portfolio Safe Withdrawal Rates should be most sensitive to P/E10. Still, there are plausibility arguments for other time periods. They should not be ignored.

HSWR50 and HSWR80

I examined two portfolios, HSWR50 and HSWR80. They are identical except for the stock allocation. HSWR50 has 50% stocks (S&P500) and 50% commercial paper. HSWR80 has 80% stocks (S&P500) and 20% commercial paper. Expenses are 0.20% of the portfolio balance each year. I rebalanced both portfolios annually (at zero cost). I adjusted withdrawals to match inflation as measured by CPI-U.

I determined 30-Year Historical Surviving Withdrawal Rates for the years 1923-1980. I used Excel to determine regression equations and plot Historical Surviving Withdrawal Rates versus the Percentage Earnings Yield 100Ex/P for E1, E5, E10, E15, E20, E25 and E30.

I made visual estimates to determine confidence intervals. The level of confidence is in the neighborhood of 85% to 90%.

Previously, I had constructed tables of P/Ex using Professor Robert Shiller’s database, following his calculations except for the number of years of real earnings to average and then thinning the results to present only the January values.

HSWR50 Regression Equations

HSWR50 100E1/P = x.
Y = 0.3313x + 2.9768
R-squared = 0.6422.
Confidence interval = 1.4 to -1.4.

100E5/P = x.
Y = 0.3588x + 2.9102
R-squared = 0.5206.
Confidence interval = 1.8 to -1.2.

HSWR50 100E10/P = x.
Y = 0.4087x + 2.5821
R-squared = 0.7025.
Confidence interval = 1.0 to -1.0.

HSWR50 100E15/P = x.
Y = 0.3901x + 2.7899
R-squared = 0.6766.
Confidence interval = 1.0 to -1.2.

HSWR50 100E20/P = x.
Y = 0.3493x + 3.1309
R-squared = 0.6007.
Confidence interval = 1.4 to -1.2.

HSWR50 100E25/P = x.Y = 0.3267x + 3.3279
R-squared = 0.5519.
Confidence interval = 1.2 to -1.2.

HSWR50 100E30/P = x.
Y = 0.3062x + 3.5191
R-squared = 0.4797.
Confidence interval = 1.4 to -1.4.

HSWR50 Largest slope (the term multiplied by x): 0.4087 from 100E10/P.

Largest value of R-squared: 0.7025 from 100E10/P.

Smallest confidence interval: 2.0 (covering 1.0 to -1.0) from 100E10/P.

Smallest downside (negative portion of the confidence interval): -1.0 from 100E10/P and 100E15/P.

HSWR80 Regression Equations

HSWR80 100E1/P = x.
Y = 0.5283x + 2.433
R-squared = 0.612.
Confidence interval = 2.5 to -1.8.

HSWR80 100E5/P = x.
Y = 0.6409x + 1.8067
R-squared = 0.6228.
Confidence interval = 3.6 to -1.2.

HSWR80 100E10/P = x.
Y = 0.6892x + 1.5239
R-squared = 0.7491.
Confidence interval = 2.0 to -1.2.

HSWR80 100E15/P = x.
Y = 0.6579x + 1.8746
R-squared = 0.7214.
Confidence interval = 2.0 to -1.4.

HSWR80 100E20/P = x.
Y = 0.6094x + 2.3048
R-squared = 0.6853.
Confidence interval = 2.4 to -1.4.

HSWR80 100E25/P = x.Y = 0.59x + 2.5083
R-squared = 0.6746.
Confidence interval = 2.2 to -1.4.

HSWR80 100E30/P = x.
Y = 0.587x + 2.6192
R-squared = 0.6611.
Confidence interval = 2.2 to -1.6.

HSWR80 Largest slope (the term multiplied by x): 0.6892 from 100E10/P.

Largest value of R-squared: 0.7491 from 100E10/P.

Smallest confidence interval: 3.2 (covering 2.0 to -1.2) from 100E10/P.

Smallest downside (negative portion of the confidence interval): -1.2 from 100E5/P and 100E10/P.

Analysis

Once again P/E10 (or 100E10/P in the equations) turns out to be the best measure of value.

The percentage earnings yield 100E10/P (the inverse of P/E10 expressed as a percentage) has the biggest slope. This means that changes in 100E10/P cause the biggest changes overall.

The percentage earnings yield 100E10/P has the largest R-squared. It explains the greatest percentage of the variance (a measure of scatter).

The percentage earnings yield 100E10/P also has the smallest range (confidence interval).

This combination means that the variation in 100E10/P explains the largest percentage of the smallest amount of scatter. The remaining random (unexplained and/or otherwise undetermined) portion of data variation is smallest with 100E10/P.

The downside variation (negative portion of the confidence interval) was smallest with 100E10/P and either 100E5/P (for HSWR80) or 100E15/P (for HSWR50).

Conclusion

P/E10 remains the best measure of valuation that I have found so far.

Have fun.

John Walter Russell
April 22, 2006