# From Markowitz to ODIAM

In the classical investment theory, built in the fifties, the two key concepts were the expected return and the accepted risk. These two attributes were linked to portfolio (a weighted combination of financial instruments), and the key question was: “How to build an optimal portfolio, i.e. how to find a set of optimal weights when building a portfolio from a set of available instruments?”

Markowitz provided the most complete and elegant solution in the “Efficient frontier” theory. This theory provides a simple and practical answer to the above question, suggesting maximizing the return/risk ratio, a goal that may be easily described in mathematical terms.

The Markowitz model has been intensively used in the last decades, and it is still considered as the best way to build a portfolio allocation. However it may be discussed on two points.

The first relates to the expected returns. The key question is how to define expected returns. The simplest way is to use the results of market regressions (linear regression linking instrument prices to market prices). The alpha values found in the regression allow identifying “growth instruments”, i.e. instruments with an expected growth even when that market shows a neutral behavior. But then the next question is the link between past alpha values – as derived from regression – and future alpha values, to be used as critical part of the expected returns1. Actually this link is thin, and no systematic over-performance has ever been generated by assuming such persistent link. And then what would be the essence of the expected returns of instruments? We consider that such expected returns is not public, objective information, but rather the expression of the individual, private perception of an analyst studying the instruments attributes: current price, growth potential, strengths and weaknesses, and any relevant fundamental information. So the expected return is basically nothing else than a translation of subjective opinions on instruments.

The second relates to the accepted risk. Should we consider that an investor always wants to minimize his risk level? This implies a long discussion. The key questions of this discussion are the following. Is there a linear link between the asset value of an investor’s portfolio and the investor satisfaction? And what is the expected probability distribution of an instrument value at a given point in the future knowing its current value? For the first question, the answer reaches philosophical and psychological issues, but the efficient frontier theory assumes a non-linear link (with a negative second order derivative). For the second question, the best answer – even if not perfect – is a lognormal distribution, instead of a normal distribution, and this generates mathematical corrections in the optimizable risk/return ratio formula. For those reasons, it is better to consider the risk attitude as an individual property, rather than considering it as a always-to-be-minimized parameter. So an extended theory should allow specifying various risk targets for different investor profiles, and the always-to-be-minimized situation is only one of the possible situations.

Regarding these 2 questions, and on various other points the new ODIAM model may be considered as a wide extension of the efficient frontier model.

In the ODIAM model, the expected return is replaced by a set of opinion-related concepts. These concepts include:

- the opinion : a subjective forecast on a financial instruments, expressed thru quantitative data on a conventional scale
- the opinion source : an analyst, a group of analysts, or any individual issuing such opinions, and updating them in the course of time
- the explicit versus implicit opinions : a way to generate opinions on instruments both directly (explicit opinions) or indirectly (implicit opinions) through group opinions, and preferably taking advantage of fuzzy classification.

In the ODIAM model, the more generic key concepts are

- A suggestion generator, who is able to create an optimal allocation (similar to an efficient frontier allocation), but also to increment the quality of an existing portfolio through several optimal sets of atomic operations (one or many buys, combined with one or many sales).
- Portfolio profiles, including several driving forces. The driving forces are weighted, and include among other the Markowitz equivalent: the opinion-based forces and the risk related force. But they also include several other profile-specific forces, like allocation target fitting.
- The opinion-based forces linked to a portfolio profile allow driving a portfolio using various simultaneous opinion sources, possibly giving them different relative weights.

Given the previous remarks, and without going into details, we claim that the ODIAM model includes a wide generalization of the efficient frontier model, allowing reaching the same goals when profiles are limited to basic parameters, but also allowing to take in account more profile factors, and to search optimal changes besides optimal allocations.

Philippe Gonze