Beta
A measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is used in the capital asset pricing model (CAPM), a model that calculates the expected return of an asset based on its beta and expected market returns..
Also known as "beta coefficient".
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Beta is calculated using regression analysis, and you can think of beta as the tendency of a security's returns to respond to swings in the market. A beta of 1 indicates that the security's price will move with the market. A beta of less than 1 means that the security will be less volatile than the market. A beta of greater than 1 indicates that the security's price will be more volatile than the market. For example, if a stock's beta is 1.2, it's theoretically 20% more volatile than the market.
Many utilities stocks have a beta of less than 1. Conversely, most high-tech Nasdaq-based stocks have a beta of greater than 1, offering the possibility of a higher rate of return, but also posing more risk.
Beta (finance)
In finance, the Beta (β) of a stock or portfolio is a number describing the relation of its returns with that of the financial market as a whole.[1]
An asset with a beta of 0 means that its returns change independently of changes in the market's returns. A positive beta means that the asset's returns generally follow the market's returns, in the sense that they both tend to be above their respective averages together, or both tend to be below their respective averages together. A negative beta means that the asset's returns generally move opposite the market's returns: one will tend to be above its average when the other is below its average.[2]
The beta coefficient is a key parameter in the capital asset pricing model (CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because of the correlation of its returns with the returns of the other assets that are in the portfolio. Beta can be estimated for individual companies using regression analysis against a stock market index.
Beta, volatility and correlation
A misconception about beta is that it measures the volatility of a security relative to the volatility of the market. If this were true, then a security with a beta of 1 would have the same volatility of returns as the volatility of market returns. In fact, this is not the case, because beta also incorporates the correlation of returns between the security and the market. The formula relating beta, relative volatility (sigma) and correlation of returns is:
For example, if one stock has low volatility and high correlation, and the other stock has low correlation and high volatility, beta cannot decide which is more "risky".
This also leads to an inequality (because |r| is not greater than one):
In other words, beta sets a floor on volatility. For example, if market volatility is 10%, any stock (or fund) with a beta of 1 must have volatility of at least 10%.
Another way of distinguishing between beta and correlation is to think about direction and magnitude. If the market is always up 10% and a stock is always up 20%, the correlation is one (correlation measures direction, not magnitude). However, beta takes into account both direction and magnitude, so in the same example the beta would be 2 (the stock is up twice as much as the market).
[edit]Choice of benchmark
Published betas typically use a stock market index such as S&P 500 as a benchmark. The benchmark should be chosen to be similar to the other assets chosen by the investor. Other choices may be an international index such as the MSCI EAFE. The choice of the index need not reflect the portfolio under question; e.g., beta for gold bars compared to the S&P 500 may be low or negative carrying the information that gold does not track stocks and may provide a mechanism for reducing risk. The restriction to stocks as a benchmark is somewhat arbitrary. Sometimes the market is defined as "all investable assets" (see Roll's critique); unfortunately, this includes lots of things for which returns may be hard to measure.
[edit]Investing
By definition, the market itself has a beta of 1.0, and individual stocks are ranked according to how much they deviate from the macro market (for simplicity purposes, the S&P 500 is usually used as a proxy for the market as a whole). A stock whose returns vary more than the market's returns over time can have a beta whose absolute value is greater than 1.0 (whether it is, in fact, greater than 1.0 will depend on the correlation of the stock's returns and the market's returns). A stock whose returns vary less than the market's returns has a beta with an absolute value less than 1.0.
A stock with a beta of 2 has returns that change, on average, by twice the magnitude of the overall market's returns; when the market's return falls or rises by 3%, the stock's return will fall or rise (respectively) by 6% on average. (However, because beta also depends on the correlation of returns, there can be considerable variance about that average; the higher the correlation, the less variance; the lower the correlation, the higher the variance.) Beta can also be negative, meaning the stock's returns tend to move in the opposite direction of the market's returns. A stock with a beta of -3 would see its return decline 9% (on average) when the market's return goes up 3%, and would see its return climb 9% (on average) if the market's return falls by 3%.
Higher-beta stocks tend to be more volatile and therefore riskier, but provide the potential for higher returns. Lower-beta stocks pose less risk but generally offer lower returns. Some have challenged this idea, claiming that the data show little relation between beta and potential reward, or even that lower-beta stocks are both less risky and more profitable (contradicting CAPM). In the same way a stock's beta shows its relation to market shifts, it is also an indicator for required returns on investment (ROI). Given a risk-free rate of 2%, for example, if the market (with a beta of 1) has an expected return of 8%, a stock with a beta of 1.5 should return 11% (= 2% + 1.5(8% - 2%)).
Coefficient bêta
Le coefficient bêta est le coefficient clé du MEDAF.
C'est un rapport historique de la volatilité du prix d'un actif (par exemple le cours de bourse d'une action) sur celle des prix du marché en général (par exemple un indice boursier significatif).
C'est un indicateur utile pour mettre en place une stratégie de diversification des risques.
Sommaire[masquer] |
Calcul du bêta [modifier]
Le bêta d'un fonds se définit mathématiquement comme le rapport de la covariance de la rentabilité implicite du portefeuille avec celle du marché et de la variance de la rentabilité implicite du marché, soit : 
Rôle du bêta par rapport à la rentabilité [modifier]
Le bêta est aussi le rapport entre la rentabilité de cet actif et celui du marché puisque la volatilité concerne les variations de cours qui sont un élément essentiel de rentabilité.
Par exemple, si le bêta d'une action est de 0.8, son cours a varié en moyenne dans la periode précédente de 0,8 % quand le marché variait de 1 %. Autrement dit c'est la sensibilité ouélasticité du cours du titre par rapport à l'indice boursier représentant le marché.
Rôle du bêta par rapport au risque [modifier]
C'est aussi un indicateur de risque : si l'évolution du marché est à la baisse, l'action sera susceptible de baisser moins que le marché s'il est inférieur à 1 et plus que le marché s'il est supérieur à 1.
Il y a donc un lien entre la rentabilité et le risque : plus le cours est censé pouvoir progresser fortement quand le marché est haussier, plus il a de risque de baisser fortement quand il est baissier.
On peut aussi démontrer que plus le risque est élevé, plus le cours tend à être bas (phénomène de prime de risque), mais cela indépendamment du bêta puisque la prime de risque s'applique à l'ensemble du marché (risque systématique).
Les limites de cet indicateur [modifier]
Il y a lieu toutefois de se méfier quelque peu de ces diverses relations arithmétiques. Elles supposent notamment d'admettre l'hypothèse que les marchés financiers sont parfaits ( ce qui implique aucun coût de transaction (or en pratique frais de courtage), aucun différentiel de taxes (législations fiscales différentes d'une place à une autre), un même niveau de taux de prêt et d'emprunt pour tous les investisseurs (or ces taux varient dans le temps, dans l'espace, en fonction de chaque investisseur et ne sont pas identiques l'un l'autre) mais aussi que l'écart type du rendement est une mesure du risque.
Modèle Multi-bêta [modifier]
Le modèle APT (Arbitrage pricing theory) de Ross est une généralisation du Modèle d'évaluation des actifs financiers qui utilise, non pas un seul bêta, mais une série de plusieurs coefficients bêta dont chacun correspond à un facteur particulier de variation du cours et du rendement.
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