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Texas oil and gas magnate Mr. T Boone Pickens, investor and philanthropist Mr. Warren Buffett, and billionaire "Robin Hood" Mr. Carl Icahn are 3 investment luminaries with sizeable portfolios.

Let's compare Mr. Pickens' and Mr. Icahn's portfolios with respect to diversification and optimization in the same way as we did Mr. Buffett's portfolio in my previous article: How Warren Buffett Manages Luck Skillfully

But before we proceed let me briefly explain what an optimizer is. An optimizer is a powerful tool that enables you to calculate portfolios that have the least volatility for a given expected return or equivalently, portfolios that have the highest expected return for a given level of volatility assuming the data that goes into their calculations are sufficient and they obey the important assumption of normality or near-normality.

When comparing the 3 luminaries above, we do not take into account the way they rebalance their portfolios which is a skill unto itself. We simply take a snapshot to see if their portfolio mix is diversified and optimal in a mathematical sense. At no time do we suggest that the optimized mix is the ultimate. It is simply used as a yardstick to make comparisons.

The Buffett portfolio has been reproduced at the bottom of this article for easy reference. For the Icahn and Pickens portfolios, we referred to this website.

THE ICAHN PORTFOLIO

The correlations between the 12 stocks of Mr. Icahn's portfolio are shown in the 3D graph on the right where the data that go into the correlation calculations are from 22nd August 2000 to 6 January 2011. Note that the diagonal denotes a stock's correlation with itself and therefore equals 1.

Icahn's holdings are shown below where the percentages have been adjusted to sum to 100%. We are interested in the proportions within the mix and not the actual mix itself. The Optimized Mix is constrained so that any stock will have a minimum weight of 0.5%. The optimization process calculates a portfolio with the highest expected annualized return but with a volatility that is approximately equal to the volatility of the Icahn Mix.

Stock Icahn Mix Optimized Mix
Amylin Pharmaceuticals (AMLN) 5.6% 6.5%
Commercial Metals Co (NYSE:CMC) 1.6% 0.5%
Dynegy Inc (NYSE:DYN) 2.6% 0.5%
Enzon Pharmaceuticals Inc (NASDAQ:ENZN) 1.4% 0.5%
Forest Laboratories (NYSE:FRX) 7.1% 16.0%
Lions Gate Entertainment Corp (NYSE:LGF) 6.8% 15.5%
Mentor Graphics Corp (NASDAQ:MENT) 4.8% 0.5%
Motorola Solutions (NYSE:MSI) 40.8% 0.5%
Oshkosh Corp (NYSE:OSK) 1.7% 22.7%
Take-Two Interactive Software (NASDAQ:TTWO) 2.6% 0.5%
The Clorox Co (NYSE:CLX) 19.5% 26.1%
The Hain Celestial Group (NASDAQ:HAIN) 5.5% 10.2%
* Motorola Mobility Holdings is excluded

THE PICKENS PORTFOLIO

The correlations between the 20 stocks in Mr. Picken's portfolio are shown in the 3D graph on the right where the data that go into the correlation calculations are from 7th November 2008 to 6th January 2012. Unlike the Buffett and Icahn portfolios, the Pickens portfolio is generally more positively correlated and none are negatively correlated over the period analyzed.

The holdings for the Pickens and Optimized portfolios are shown below. The optimized portfolio has a volatility that is approximately equal to the Pickens portfolio volatility.

Stock Pickens Mix Optimized Mix
Apache Corp (NYSE:APA) 5.67% 0.5%
Approach Resources (NASDAQ:AREX) 0.70% 9.2%
BP plc (NYSE:BP) 7.97% 0.5%
Canadian Natural Resources Ltd (NYSE:CNQ) 3.70% 21.8%
Chesapeake Energy Corp (NYSE:CHK) 9.48% 8.5%
Dawson Geophysical Co (NASDAQ:DWSN) 2.67% 0.5%
EOG Resources (NYSE:EOG) 6.23% 7.8%
Gastar Exploration Ltd (NYSEMKT:GST) 1.27% 0.5%
Halliburton Co (NYSE:HAL) 4.09% 0.5%
Hess Corp (NYSE:HES) 3.56% 0.5%
McMoRan Exploration Co (NYSE:MMR) 6.45% 0.5%
Murphy Oil Corp (NYSE:MUR) 3.67% 18.2%
National Oilwell Varco (NYSE:NOV) 5.02% 0.5%
Noble Corp (NYSE:NE) 8.19% 0.5%
Occidental Petroleum Corp (NYSE:OXY) 3.83% 0.5%
Plains Exploration & Production Co (NYSE:PXP) 6.89% 0.5%
SandRidge Energy (NYSE:SD) 6.45% 0.5%
Schlumberger Ltd (NYSE:SLB) 3.62% 0.5%
Suncor Energy (NYSE:SU) 4.16% 27.5%
Weatherford International (NYSE:WFT) 6.39% 0.5%

MIND THE GAP

The graph on the right shows the difference (or what our optimizer calls the Opportunity Cost) between the expected returns for the Icahn portfolio (yellow dot) and the optimized portfolio (green dot) with the same volatility. The difference between the two expected returns is 4.9%.

The graph on the left shows the difference between the expected returns for the Pickens portfolio and the optimized portfolio with the same volatility. The difference is 8.3%. In my article entitled Go Behind the Numbers, I explain how the expected returns should be viewed as anchors and not forecasts.

TIME DIVERSIFICATION

All other things remaining constant, the graphs below show how time further diversifies away volatility. Reading from left to right, the top row shows the Buffett portfolio, followed by the Icahn and Pickens portfolios. The bottom row displays the corresponding optimized time-diversification graphs for the 3 portfolios. As in my previous article, the right vertical axis measures the 68% confidence interval (denoted by the funnel) over a 10-year holding period. The left vertical axis measures the probability of a negative return (denoted by the blue bars) over the same holding period.

POUND FOR POUND

Allow me to borrow a phrase from the world of sports where "pound for pound" is a term to describe how things compare while bearing in mind their varying quantities:

Buffett Icahn Pickens
Proximity to Optimal

88% 85% 76%
Safety

83.8%

74.9% 78.0%
Return per Unit Volatility 0.99 0.67

0.77

Proximity to Optimal is defined here as the percentage of possible returns (annualized over the 10 years) that overlap, when taken across both the investor and optimal portfolios.

Safety is defined as the probability of the portfolio NOT incurring a negative return in the first investment year.

Return per unit volatility is the expected annualized return earned for each unit of volatility incurred by the portfolio.

AND THE WINNER IS...

Mr. Buffett's investment philosophy of not losing money, diversifying, and holding for the long term are fundamental tenets of his philosophy that contribute in no small part to his success. And this is reflected in all of the 3 scores above. Have a look again here at how Buffett's stocks are correlated in the negative direction.

It should be noted that in terms of absolute volatility, the Buffett Mix is more conservative at 17.3% volatility than Icahn and Pickens (both at about 30% volatility) so Icahn and Pickens may not be rewarded sufficiently for the volatility they are absorbing.

In terms of Safety, Warren's portfolio will have a less than 1% chance of incurring a negative annualized return (i.e. more than 99% chance of NOT incurring) over a 6-year holding period. Icahn's portfolio will achieve this over a 13-year holding period and Pickens a 10-year holding period.

For the Icahn universe of stocks, moving closer to its Optimal Mix might improve its Return per Unit Volatility a little. But it is the Pickens portfolio which seems to have a lot more potential if the weights were chosen differently, assuming the Optimized Mix is correct.

Again, the reader is reminded that the Optimized Mix is simply a yardstick based on historical results and assumes a normal distribution. An optimizer does not have the benefit of insight and skill that the 3 gentlemen will have going forward.

Appendix:

Buffet's portfolio from my previous article has been included here for easy reference:

Stock Buffett mix Optimized mix
Gannett Company (GCI) 0.07% 0.5%
USG Corp (USG) 0.64% 0.5%
American Express Company (AXP) 13.46% 0.5%
Wal-Mart Stores Inc (WMT) 4.67% 25.9%
ConocoPhillips (COP) 3.76% 14.8%
Costco Wholesale Corp (COST) 0.56% 0.5%
ExxonMobil Corp (XOM) 0.07% 9.4%
General Electric Company (GE) 0.31% 0.5%
GlaxoSmithKline (GSK) 0.12% 0.5%
Ingersoll Rand (IR) 0.43% 1.2%
Johnson & Johnson (JNJ) 3.36% 0.5%
Kraft Foods Inc (KFT) 6.95% 0.5%
M&T Bank Corp (MTB) 0.95% 5.7%
Moody's Corp (MCO) 1.97% 0.5%
Procter & Gamble Company (PG) 10.78% 0.5%
Sanofi-aventis (SNY) 0.32% 0.5%
The Bank of New York Mellon Corp (BK) 0.43% 0.5%
The Coca Cola Company (KO) 23.68% 10.3%
The Washington Post Company (WPO) 1.66% 0.5%
Torchmark Corp (TMK) 0.33% 0.5%
US Bancorp (USB) 3.85% 0.5%
United Parcel Services (UPS) 0.20% 0.5%
Wells Fargo & Company (WFC) 21.45% 24.7%
Source: Portfolio Optimization: Carl Icahn Vs. T Boone Pickens Vs. Warren Buffett