Primary navigation:

QFINANCE Quick Links
QFINANCE Reference
Add the QFINANCE search widget to your website

Home > Asset Management Viewpoints > Bias-Free Investing Offers the Best Hope for Pension Funds

Asset Management Viewpoints

Bias-Free Investing Offers the Best Hope for Pension Funds

by Yves Choueifaty


Yves Choueifaty built TOBAM in 2006, when he was managing director, head of Lehman Brothers’s quantitative asset management business in Europe. He was also previously head of Lehman Brothers Asset Management France. Prior to joining Lehman Brothers, he was CEO of Credit Lyonnais Asset Management (CLAM), with assets under management of €70 billion. Mr Choueifaty graduated in 1992 from ENSAE in statistics, actuarial studies, finance, and artificial intelligence.

TOBAM, formerly part of the quantitative asset management group inside Lehman Brothers Asset Management Europe, specializes in a maximum diversification approach that attempts to avoid what you term “speculation.” How is this approach relevant to pension funds, for example, as they try to build returns to fund their future liabilities?

Let us define the word “speculation.” It comes from the Latin speculare, which means to be able to see. To speculate you need to take a view on the future and you need to build a portfolio that expresses that view. What we saw happening up to the global crash in 2008 (which I got to view first hand at Lehman Brothers) was a tremendous interest from pension funds in tracking cap-weighted benchmarks. By 2007 there had been a long-running bull market and cap-weighted benchmarks were very heavy bets on the sectors that had outperformed through the bull market years. Then came the crash and the benchmarks lost 30–40% of their value as the sectors that had been doing well, such as finance, failed. That experience created a great deal of interest in alternative approaches to cap-weighted benchmark-tracking portfolios. As a result, funds focused on building portfolios based on low-volatility stocks got a great deal of attention. Here, however, you need to be careful about definitions. If you are talking about low volatility, are you talking about a portfolio with a heavy bias to low-volatility stocks, or are you talking about a portfolio designed to have low volatility, but which does not express a view that market conditions will favor low volatility stocks?

TOBAM’s approach is to avoid all possible biases by building the most diversified portfolio possible. This brings us to the question, what exactly is diversification? It is one of the most used terms in investing. Everyone employs it, but it is not well defined. We have an approach to this at TOBAM which we have patented. A simple way of defining it is to say that if you have a universe of just two different, noncorrelated stocks, stock A and stock B, if you combine 80% of stock B with 20% of stock A, that will always result in a portfolio with volatility that is lower than 80% of the volatility of stock A plus 20% of the volatility of stock B. It is simply a mathematical fact that if you combine a set of noncorrelated assets in a proportionate way, the volatility will always be lower than if you combine the risks of the assets. If, with a larger universe, you go for the ratio of the weighted average of the volatilities divided by the volatility of the portfolio as a whole (TOBAM’s diversification ratio), you have a portfolio with some very interesting mathematical properties.

To make this clear, imagine again that there are only two stocks, A and B, and that A has a volatility of 30%, while B has a volatility of 15%. Let us say that there is a 60% correlation between them. Then if you work out the largest diversification ratio it will be one-third A combined with two-thirds B, and this will give you a diversified portfolio. The same is true if you have a universe of three stocks, A, B, and C, where A and B have a correlation of 95% (making them almost identical) and C has a correlation of just 5% with the other two (which means that events that impact A and B have very little impact on C). If you maximize the diversification ratio here you have a portfolio that consists of 26% A and 26% of B, with 48% of C. That represents a highly diversified portfolio of the universe of the three stocks, A, B, and C. At no point here are you making any speculative assumptions about the kinds of returns that you will get from A, B, or C.

It follows that this approach could not be more different from that of a value “buy and hold” manager, who would spend a lot of time getting to know the companies A, B, and C, and would try to form a view of their relative probabilities of success in the market based on their current product portfolio, their research and development pipeline, and their acquisition strategies, for example. When you have built the most diversified portfolio available to you, as a quantitative manager with a maximum diversification strategy your job is done. You have absolutely no way of extrapolating from that portfolio to make any kind of prediction about the potential relative success or failure of A, B, and C as companies. What you do have is a great deal of statistical evidence that shows that taken over a medium- to long-term period—which is precisely the kind of time frame that concerns pension funds—a maximally diversified portfolio delivers greater returns than portfolios with a built-in bias. There is, however, no “proof” that this fund will be the least volatile that you could construct. All we are saying is that it is the most diversified fund that you can construct.

Back to Table of contents

Further reading


  • Arnott, Robert D., Jason Hsu, and Philip Moore. “Fundamental indexation.” Financial Analysts Journal 61:2 (March/April 2005): 83–99. Online at:
  • Choueifaty, Yves, and Yves Coignard. “Toward maximum diversification.” Journal of Portfolio Management 35:1 (Fall 2008): 40–51. Online at:
  • Choueifaty, Yves, Tristan Froidure, and Julien Reynier. “Properties of the most diversified portfolio.” Working Paper. July 2011. Online at:
  • Haugen, Robert A., and Nardin L. Baker. “The efficient market inefficiency of capitalization-weighted stock portfolios.”  Journal of Portfolio Management 17:3 (Spring 1991): 35–40. Online at:
  • Markowitz, Harry. “Portfolio selection.” Journal of Finance 7:1 (March 1952): 77–91. Online at:
  • Sharpe, William F. “Capital asset prices with and without negative holdings.” Nobel Prize Lecture. December 7, 1990. Online at:


Back to top

Share this page

  • Facebook
  • Twitter
  • LinkedIn
  • Bookmark and Share