It has been raised now and then in various articles if Warren Buffett's success as an investor has been all due to skill or whether luck was involved. I like to think of Mr. Buffett as being able to manage luck skillfully. Let me illustrate what I mean.

According to warren-buffett-portfolio.com, these were Mr. Buffett's security holdings as at 4 January 2012:

American Express Company (NYSE:AXP), ConocoPhillips (NYSE:COP), Costco Wholesale Corp (NASDAQ:COST), Exxon Mobil Corp (NYSE:XOM), Gannett Company (NYSE:GCI), General Electric Company (NYSE:GE), GlaxoSmithKline (NYSE:GSK), Ingersoll Rand (NYSE:IR), Johnson & Johnson (NYSE:JNJ), Kraft Foods Inc (KFT), M&T Bank Corp (NYSE:MTB), Moody's Corp (NYSE:MCO), Procter & Gamble Company (NYSE:PG), Sanofi-aventis (NYSE:SNY), The Bank of New York Mellon Corp (NYSE:BK), The Coca Cola Company (NYSE:KO), The Washington Post Company (WPO), Torchmark Corp (NYSE:TMK), US Bancorp (NYSE:USB), USG Corp (NYSE:USG), United Parcel Service (NYSE:UPS), Wal-Mart Stores Inc (NYSE:WMT), Wells Fargo & Company (NYSE:WFC). Excluded from this list are Comdisco Holding Company and Wesco Financial Corp.

**Risks Diversified**

** **

The correlations between these 23 stocks are shown in the 3D graph on the right where the data that go into the correlation calculations are from 2nd July 2003 to 23rd December 2011. Read my article entitled "What You See May Not Be What You Get" for a discussion on the concept of correlation.

How correlated are Mr. Buffett's stocks to one another? It is visually clear that the correlations between any two stocks are not overly positive while some correlations are even negative. The more 2 stocks are not correlated in a positive way, the more the benefits of diversification. The diagonal shows a perfect correlation of 1 because a stock is perfectly positively correlated to itself.

The next graph on the right shows a slice of the 3D graph above for correlations between General Electric and the rest of the portfolio while the graph on the left shows the correlations for Wal-Mart Stores Inc. General Electric tends to be more highly positively correlated with the rest of the portfolio then Wal-Mart Stores Inc. but still offers some benefits of diversification.

In the next section, I would like to look at the actual percent that Mr. Buffett puts into these stocks and compare them against an optimized portfolio with the same volatility. An optimized portfolio is one that has the least volatility for a given expected return or the highest expected return for a given volatility. The optimized mix is constrained so that each stock has at least an allocation of 0.5%. This is so that no stock is excluded from the optimized portfolio.

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% |

The graph on the right shows the difference (or what our optimizer calls the Opportunity Cost) between the expected returns for his portfolio (yellow dot) and the optimized portfolio (green dot) with the same volatility. The difference between the two expected returns is a mere 2.2%. In my article entitled "Go Behind The Numbers", I talked about how one should view the expected returns as anchors and not forecasts.

**A Long Holding Period**

It is well known that Mr. Buffett believes the correct holding period is "forever". Let's look therefore at the difference in expected performance of the 2 portfolios over a period of 10 years. Mr. Buffett's portfolio is shown in the top half of the figure on the left.

The right vertical axis of the 2 graphs measures the 68% confidence interval after 10 years for Mr. Buffett's portfolio which is [11.6%, 22.6%] while that for the Optimized portfolio is [13.8%, 24.6%].

The 95% confidence interval (not shown) after 10 years is easily calculated to be [6.1%, 28.0%] for Mr. Buffett's portfolio while the Optimized portfolio has a confidence interval of [8.5%, 30.0%].

What is the percentage of overlap between the 2 portfolios? At the 95% confidence level, it is 82% and at the 98% confidence level there is an expected 88% overlap at the10th holding year between the confidence intervals of the 2 portfolios. In other words, when taken across both portfolios, 88% of the possible returns that may occur at that time would be the same.

**An Optimized Mind?**

Mr. Buffett's investment performance has been a subject of admiration, debate, jealousy, skepticism or all four sentiments combined. Sure, stocks he buys may rise, just because he buys them.

But I think Mr. Buffett's investment philosophy of choosing stocks that have a negative or low positive correlation to one another and then keeping them for the long haul are fundamental tenets of his philosophy that contribute in no small part to his success. So I would have been surprised if the risk-return profile of the Buffett portfolio had differed significantly from the optimized one since both use correlation to their advantage.

What is interesting is this.

There are an infinite number of possibilities when choosing a portfolio mix. A simple way would be to put equal weight in each stock. If Mr. Buffett had done that, the opportunity cost as calculated above would have been about twice as large. Mr. Buffett picked instead a portfolio mix that has a risk-return profile that is near mathematically optimal.

**Skill versus Luck**

Holdings that are greater than 1% in Buffett's portfolio are KO, WFC, AXP, PG, KFT, WMT, USB, COP, JNJ, MCO, WPO while those in the optimized portfolio are WMT, WFC, COP, KO, XOM, MTB and IR. While the risk-return profiles between the 2 portfolios are comparatively similar, differences in the actual mix would be attributable to Mr. Buffett's insight, investment knowledge, and skill.

When Mr. Buffett devises a portfolio mix that is nearly as efficient as an optimized one, you might see it as his way of managing the luck of the draw (i.e. reducing volatility). His skill, however, is determined by the weights in the mix he has chosen to go about to achieve this.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.