Gummy Slices

Overview

I have calculated Historical Surviving Withdrawal Rates for several portfolios built from Gummy’s database. (Gummy is the posting name of retired Professor Peter Ponzo.)

Gummy’s (Peter Ponzo's) Database

I have determined Calculated Rates, Safe Withdrawal Rates and High Risk Rates for each portfolio with and without rebalancing.

I found that the behavior of individual slices dominate the effect of composite portfolios.

I found that all of the portfolios behave in the same way with respect to rebalancing. Rebalancing is helpful during times of high valuations. Rebalancing is harmful during times of normal valuations. Rebalancing is very bad when valuations are low.

Portfolios

HSWR50GT and HSWR50GTn

HSWR50GT consists of 50% stocks and 50% T-Bills. It is rebalanced (between stocks and T-Bills) annually.

HSWR50GTn consists of 50% stocks and 50% T-Bills. It is NOT rebalanced (between stocks and T-Bills). Otherwise, it is identical to HSWR50GT.

The HSWR50GT and HSWR50GTn stock portfolios consist of the S&P500 with data taken from Gummy’s database.

HSWR50CT and HSWR50CTn

HSWR50CT consists of 50% stocks and 50% T-Bills. It is rebalanced (between stocks and T-Bills) annually.

HSWR50CTn consists of 50% stocks and 50% T-Bills. It is NOT rebalanced (between stocks and T-Bills). Otherwise, it is identical to HSWR50CT. (Elements within the stock portfolio are rebalanced internally. But the stock portfolio is not rebalanced with T-Bills.)

The HSWR50CT stock portfolio consists of 25% Large Capitalization Growth stocks, 25% Large Capitalization Value stocks, 25% Small Capitalization Growth stocks and 25% Small Capitalization Value stocks. All portfolio stock holdings are rebalanced internally, annually.

HSWR50VT and HSWR50VTn

HSWR50VT consists of 50% stocks and 50% T-Bills. It is rebalanced (between stocks and T-Bills) annually.

HSWR50VTn consists of 50% stocks and 50% T-Bills. It is NOT rebalanced (between stocks and T-Bills). Otherwise, it is identical to HSWR50VT. (Elements within the stock portfolio are rebalanced internally. But the stock portfolio is not rebalanced with T-Bills.)

The HSWR50VT and HSWR50VTn stock portfolios consist of 50% Large Capitalization Value stocks and 50% Small Capitalization Value stocks. Both portfolio stock holdings are rebalanced internally, annually.

Common Conditions

I used the Gummy 04A01 version of the Deluxe Calculator V1.1A08 dated January 28, 2005.

I set the expenses of all portfolios to 0.20%.

Withdrawal rates are percentages of the initial balance. I adjust withdrawal amounts to match inflation in accordance with the CPI.

I determined 30-year Historical Surviving Withdrawal Rates to a precision of 0.1%. That is, the balance at year 30 is positive at the 30-year Historical Surviving Withdrawal Rate. It is zero or negative when I increase the withdrawal rate by 0.1%.

I used Excel’s charting capability to calculate (linear) regression equations. The charts show 30-year Historical Surviving Withdrawal Rates versus the Percentage Earnings Yield 100E10/P, using Professor Robert Shiller’s P/E10 as the measure of valuation.

P/E10 is the current (real) price of the S&P500 divided by the average of the previous ten years of (real) earnings. Professor Robert Shiller has shown that P/E10 has intermediate term (10 years) predictive capability. He lists S&P500 data, including P/E10, at his web site.

Professor Shiller’s Web Site

The lines are Calculated Rates. Safe Withdrawal Rates are lower confidence limits (about the Calculated Rates). High Risk Rates are upper confidence limits (about the Calculated Rates).

Results

I have made my tables and charts available for public viewing in my Yahoo Briefcase. I have posted them as Microsoft Word documents.

Yahoo Briefcase

HSWR50GT and HSWR50GTn Results

These portfolios consist of 50% stocks and 50% T-Bills. The stock portfolio consists of the S&P500 with data from Gummy’s database.

HSWR50GT Historical Surviving Withdrawal Rates y versus x, the Percentage Earnings Yield 100E10/P equation:
1) y = 0.4554x+2.1602 plus and minus 0.8%
2) R-squared = 0.7174.

HSWR50GTn Historical Surviving Withdrawal Rates y versus x, the Percentage Earnings Yield 100E10/P equation:
1) y = 0.6442x+1.2462 plus 1.5% and minus 0.8%
2) R-squared = 0.7493.

HSWR50CT and HSWR50CTn Results

The HSWR50CT and HSWR50CTn stock portfolios consist of 25% Large Capitalization Growth stocks, 25% Large Capitalization Value stocks, 25% Small Capitalization Growth stocks and 25% Small Capitalization Value stocks.

HSWR50CT Historical Surviving Withdrawal Rates y versus x, the Percentage Earnings Yield 100E10/P equation:
1) y = 0.484x+2.9254 plus and minus 0.8%
2) R-squared = 0.8291.

HSWR50CTn Historical Surviving Withdrawal Rates y versus x, the Percentage Earnings Yield 100E10/P equation:
1) y = 0.757x+1.6591 plus 1.6% and minus 1.0%
2) R-squared = 0.8334.

HSWR50VT and HSWR50VTn Results

The HSWR50VT and HSWR50VTn stock portfolios consist of 50% Large Capitalization Value stocks and 50% Small Capitalization Value stocks.

HSWR50VT Historical Surviving Withdrawal Rates y versus x, the Percentage Earnings Yield 100E10/P equation:
1) y = 0.5428x+3.4165 plus and minus 0.8%
2) R-squared = 0.7673.

HSWR50VTn Historical Surviving Withdrawal Rates y versus x, the Percentage Earnings Yield 100E10/P equation:
1) y = 0.8572x+2.244 plus and minus 2.0% (for P/E10 of 17 and below)
2) R-squared = 0.7049.

Analysis

Rebalancing

The story about rebalancing depends very little on portfolio details.

Looking at the graphs, rebalancing and not rebalancing have similar low-side Historical Surviving Withdrawal Rates when the percentage earnings yield 100E10/P is around 6%. This corresponds to a P/E10 of 17.

At lower levels of earnings yield (and higher levels of P/E10), low-side Historical Surviving Withdrawal Rates favor rebalancing. High-side Historical Surviving Withdrawal Rates are neutral.

At higher levels of earnings yield (and lower levels of P/E10), low-side Historical Surviving Withdrawal Rates favor a decision not to rebalance. High-side Historical Surviving Withdrawal Rates strongly favor a decision not to rebalance.

Slices

The portfolios favor the two-component Value slices HSWR50VT, followed by the four-component composite HSWR50CT, followed by the single S&P500 component HSWR50GT. The slopes are similar (0.5428, 0.484 and 0.4554, respectively). The lines are almost parallel. The offsets show the difference (3.4165, 2.9254 and 2.1602, respectively).

It becomes apparent, upon reflection, that making slices alters the capitalization. That is, rebalancing among slices is not as significant as the change in the overall portfolio composition. When I separated the four components of HSWR50CT, I ended up favoring Small Capitalization stocks. Similarly, when I separated the two Value components of HSWR50VT, I emphasized Small Capitalization Value and eliminated Growth components. Of particular note, I eliminated the Small Capitalization Growth component, which drags performance down.

We have not learned about rebalancing slices. It is difficult to construct a meaningful portfolio without affecting capitalization weightings.

Conclusions

Our investigations using Gummy’s database support our previous conclusions regarding rebalancing. It helps a little bit during times of high valuations (P/E10 of 17 or higher). It takes away the upside during times of lower valuations. It can cause serious harm when stocks are cheap.

We have learned very little that is new about individual slices. We note that capitalization differences prevent us from making meaningful comparisons.

Have fun.

John Walter Russell
November 22, 2005