More Gummy Slices

Overview

I have come across a wonderful web site. It presents the mathematics of Modern Portfolio Theory clearly. I recommend it highly to those with the appropriate background. It is John Norstad's Finance Page.

John Norstad's Finance Page

Ironically, I ascribe special significance to Gummy Slices and this extension, More Gummy Slices, because of what John Norstad has written.

Our data clearly show that the capitalization weighted Total Stock Market (using the S&P500 as an adequate surrogate) has been a consistently inferior stock holding (as compared to slices of the S&P500).

In view of John Norstad’s mathematical proofs, we should reject ALL THREE of these leading academic theories:

1) The Efficient Market Hypothesis.
2) The Capital Asset Pricing Model.
3) The Fama-French Three Factor Model.

However, I cannot reject these leading academic theories directly, not on their own terms. I can and do reject them, but on my terms: the optimization criterion is hopelessly flawed.

My graphs show that the minimum balances with slices are equal to or better than the balances of the (capitalization weighted) S&P500 index. The S&P500 returns are clustered tightly about inferior numbers. The slices are (almost) always better, but they have a lot of scatter. Sometimes, their returns are a little bit better. Sometimes, their returns are a whole lot better. Always (well, almost always), their returns are better.

If the stock market behaves itself over a period of interest (and, often, it does not), you can leverage a small positive return with narrow scatter into a large return with a tolerable amount of scatter. This assumes, of course, that you are able to leverage your holdings at zero cost, that you are able to satisfy all margin calls and that you do not change your approach.

The Slices

I looked at two sets of data. The first consisted of portfolios with 50% stocks and 50% T-Bills, rebalanced annually. The second set used the same stock portfolios, but by themselves.

HSWR50CT and HSWR100C

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

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.

HSWR100C has the same stock holdings as HSWR50CT. It is made up entirely of stocks.

HSWR50GT and HSWR100G

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

The HSWR50GT stock holding is the S&P500 index (using Gummy’s database).

HSWR100G has the same stock holdings as HSWR50GT. It is made up entirely of stocks.

HSWR50VT and HSWR100V

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

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

HSWR100V has the same stock holdings as HSWR50VT. It is made up entirely of stocks.

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 zero.

I set the withdrawal rate equal to zero.

I selected the CPI for inflation adjustments.

I set the initial balance to $10000. I determined portfolio balances (and total returns) at years 10, 20 and 30.

I used Excel's charting capability to calculate (linear) regression equations. The charts show balances 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

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

HSWR50CT, HSWR50GT and HSWR50VT

HSWR50CT consists of 50% of the Gummy COMPONENTS and 50% T-Bills.
HSWR50GT consists of 50% of the Gummy S&P500 composite and 50% T-Bills.
HSWR50VT consists of 50% of the Gummy VALUE Components and 50% T-Bills.

In all cases:
1) The highest line is HSWR50VT.
2) The middle line is HSWR50CT.
3) The lowest line is HSWR50GT.

10-Year Balances:

HSWR50CT: y = 1100.6x+8905.4 plus and minus $5000. R-squared is 0.3822.
HSWR50GT: y = 1071.2x+6869.8 plus and minus $5000. R-squared is 0.3054.
HSWR50VT: y = 1341.1x+9271.8 plus and minus $6000. R-squared is 0.4553.

20-Year Balances:

HSWR50CT: y = 3282.8x+5231.4 plus and minus $10000. R-squared is 0.7532.
HSWR50GT: y = 3273.5x-485 plus and minus $10000. R-squared is 0.6516.
HSWR50VT: y = 3772.2x+9652 plus and minus $10000. R-squared is 0.7189.

30-Year Balances:

HSWR50CT: y = 1121.9x+37464 plus and minus $15000. R-squared is 0.0686.
HSWR50GT: y = 1098.5x+24767 plus $15000 and minus $10000. R-squared is 0.1815.
HSWR50VT: y = 1831.4x+52734 plus and minus $25000. R-squared is 0.0948.

HSWR100C, HSWR100G and HSWR100V

HSWR100C consists of 100% of the Gummy COMPONENTS.
HSWR100G consists of 100% of the Gummy S&P500 composite.
HSWR100V consists of 100% of the Gummy VALUE Components.

In all cases:
1) The highest line is HSWR100V.
2) The middle line is HSWR100C.
3) The lowest line is HSWR100G.

10-Year Balances:

HSWR100C: y = 3492.6x+913.56 plus $15000 and minus $10000. R-squared is 0.4991.
HSWR100G: y = 3064.9x-1104.4 plus and minus $15000. R-squared is 0.3653.
HSWR100V: y = 4484.3x+191.5 plus and minus $17000. R-squared is 0.4612.

20-Year Balances:

HSWR100C: y = 14616x-34707 plus $50000 and minus $30000. R-squared is 0.6452.
HSWR100G: y = 11781x-35630 plus and minus $30000. R-squared is 0.6364.
HSWR100V: y = 19835x-35418 plus $80000 and minus $50000. R-squared is 0.5636.

30-Year Balances:

HSWR100C: y = 14523x+42299 plus $200000 and minus $100000. R-squared is 0.0997.
HSWR100G: y = 7262.5x+28773 plus $80000 and minus $50000. R-squared is 0.1331.
HSWR100V: y = 25644x+94765 plus $400000 and minus $250000. R-squared is 0.1051.

Analysis

Once again, we find that the Value portfolio is best, the four-component Composite is second and the capitalization weighted S&P500 (from Gummy’s database) is worst.

Rarely is the return of either the Value portfolio or Composite portfolio as low as that of the (capitalization weighted) S&P500. But both have tremendous upside potentials, which widens their spreads.

As before, expected returns are always greater when starting from a lower valuation (i.e., high percentage earnings yield, 100E10/P, and low P/E10).

As before, the predictive effect of P/E10 is high in the intermediate-term as we see in years 10 and 20. Its importance diminishes by year 30 (during accumulation, with dividends reinvested and without withdrawals).

Have fun.

John Walter Russell
November 27, 2005