To this end, it is generally assumed that the different risk profiles of investors involve different combinations of portfolios, more or less aggressive or risky. A conservative investor, ie more risk-averse, will be proposed a portfolio whose the proportion of bonds in relation to shares would be relatively higher. The more the investors would be willing to take risks, the more the part of shares in his portfolio is likely to be high. The selection of the investor risk profile on the other hand is not easy. In general, professionals in charge of clients, try to identify it from questionnaires and interviews. Grids of more or less risky portfolios, ie shares to bonds ratios higher or lower, are then offered to clients.

Note however that this approach is not entirely consistent with the teaching of the theoretical literature. Indeed, the fund separation theorem explains that investors should build portfolios by combining the risk free interest rate with the so-called market portfolio. Indeed, the theory assumes that investors arbitrate between the portfolio expected return and its variability, as measured by the standard deviation or variance, a measure of the average deviation of returns relative to the average profitability. It is also assumed that all assets are freely traded without debt limits. Finally, if investors have more or less the same information (assuming market efficiency), investment opportunities are the same. We can then show that there is a market portfolio that everyone should own. Actually, the risk profile should only and exclusively determine the part invested in the risk free rate.

The first economists to show the inconsistency between theoretical and practical recommendations were canner and al. (1997) [1]. In fact, the authors showed that the recommendations of the major fund managers at the time (Fidelity, Merrill Lynch, Bryant Quinn) differed greatly from an allocation between non-risky asset and a portfolio consisting of a constant ratio between shares and bonds. This discrepancy between theoretical and practical recommendation results in a conundrum, known as "The asset allocation enigma" (Asset Allocation Puzzle). A number of factors were cited, however, according to the authors mentioned, none is likely to provide a satisfactory explanation for this puzzle. Recent developments in behavioral economics, however, have opened a promising avenue. Thus, Shefrin and Statman (2000) [2] developed the Behavioral Portfolio Theory.

The purpose of these authors was to create a portfolio theory that is more realistic in terms of assumptions about investors behavior vis a vis of risk. Indeed, the standard literature in finance assumes that investors are more concerned about the variance of returns. However this variance is a measure of how far the returns are spread around the expected average return. What is embarrassing here is that the deviations around the mean have the same impact have the same impact on this measure either positive or negative. This variance is called volatility by finance practitioners. Where the rub is that people are generally more sensitive to the achievements of returns below the average as those above. it is the loss aversion debate. However this loss aversion notion must be understood with critical sense and it needs to dwell a little on the modeling of behavior in uncertainty.

The body of theory referred to by Shefrin and Statman is the SP/A choice model in uncertain. The capital letters refer to Security, and Potential Aspiration. The concept of security means that the investor wishes to insure loss up to his portfolio. Aspiration is about the return of reference from the investor, ie that to which he expects regarding the risks. Potential is about his willingness for huge gains. This component can be illustrated by the behavior of individuals confronted with lotteries. even though most people are reluctant to risk - the purchase of insurance is an evidence - many of them still buy lottery tickets. The explanation for such behavior, which is difficult to explain in the standard theoretical framework, can easily be explained with the SP/A model . In fact, the individual buys insurance for security reasons and he bought the lottery ticket for potential reasons. This behavior would come from two contradictory forces: fear and hope..

How are these components modeled compactly? First, the security component results in a limit on the probability of the portfolio value to fall below a certain value. however, fear often results in an excessive weighting of probabilities (observed) of loss in the portfolio. Note that this measure of risk of loss on the portfolio is calculated by financial institutions. This is the famous Value-at-Risk, which indicates the maximum loss for a threshold probability value and time interval given. Investors are expected to select portfolios based on a Value-at-Risk and expected probabilities adjusted to their risk profile.

This result is in contrast to the framework in which investors choose in relation with the expected return and the variance, both derived from objective data, ie there is no adjustment to consider the subjective profile of risk. The approach proposed by Shefrin and Slatman does not imply that investors invest in the same benchmark. On the contrary, according to his risk profile, investors are expected to include various investment categories (styles) in the portfolio. For example, to insure against a decline in the portfolio value, he would include bonds relatively less risky, but to have a low chance to have high earnings, he would also include a proportion of assets with low return that may result in huge gains as lottery tickets.

Behavioral Portfolio Theory seems to be of paramount importance, and this both in terms of explaining the observed behavior in the markets and decision-making tools for the "Asset Managers" and private bankers. Most importantly, this approach gives a satisfactory explanation of the financial products tradable, ie a different partitioning of funds based on investors profiles, proposed by these institutions. In this regard, recent research on risk measurement and the categorization of typical profiles of investors will certainly be of great assistance to these institutions.