Coefficient beta

The coefficient beta is the key coefficient of MEDAF.

It is a historical relationship between

the Volatilité of the price of a credit (for example the stock exchange courts of a Action)
and that of the market prices in general (for example a significant Market index).

Calculation of beta

Beta of funds is defined mathematically as the report/ratio of the covariance of the implicit profitability of the wallet with that of the market and of the variance of the implicit profitability of the market, that is to say: $\ beta \ = \ frac {Cov (r_p, r_m)}{VAr (r_m)}$

Role of beta compared to profitability

Beta is also the relationship between the Rentabilité of this credit and that of the market since volatility relates to the variations of courses which are an essential component of profitability.

For example, if beta of an action is of 0.8, its course varied on average during the previous time of 0,8% when the market varied from 1%. If it is of 1.5, it varied from 1.5%. In other words it is the Sensibilité or elasticity of the course of the title compared to the market index representing the market.

Role of beta compared to the risk

It is also an indicator of risk: if the market evolution is with the fall, the action will be likely to drop less than the market if it is lower than 1 and more than the market if it is higher than 1.

There is thus a bond between profitability and the risk: the more the course is supposed capacity to strongly progress when the market is bull, the more it has of risk to strongly drop when he is bear.

One can as show as the more the risk is raised, the more the course tends to being low (phenomenon of Allowance for risk), but that independently of beta since the allowance for risk applies to the whole of the market (systematic Risque).

Limits of this indicator

It is necessary however to be wary somewhat of these various arithmetic relations. They suppose to admit the assumption of Efficience of the market. Nevertheless they are indicators for a strategy of Diversification of the risk S.

Model Multi-beta

Model APT (Arbitration pricing theory) of Ross is a generalization of the Modèle of financial valuation of assets which uses, not only one beta, but a series of several coefficients beta of which each one corresponds to a particular factor of variation of the course and output.

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