# Beta coefficient

The Beta Index, or Beta Coefficient, is a measure used in finance that relates the sensitivity of an asset within an investment portfolio.

This theoretical index is used to highlight the behavior of the asset in the financial market, during a certain period of time, through its level of risk.

In addition to correlating the investment within a portfolio, the beta version also allows you to identify the direction in which the return of the asset varies, in the face of changes in a market index, such as the Bovespa Index for example.

## How the beta index is calculated

The coefficient calculated by the beta is made through a relationship between the change in the profitability of an asset or security to be analyzed, with the change in the profitability of the entire market.

In a simplified way, the formula considers the division of the two variations:

ΔRa – change in the value of the asset or security;
ΔRm: variation of the market index, such as Ibovespa.

In a more structured way, the Beta is calculated by the covariance between the return of the portfolio and the asset, divided by the variance of the return of the portfolio or the market:

The beta of a complete portfolio, on the other hand, can be represented by the weighted average of all the assets that comprise it.

## What Beta Values ​​Mean

β greater than 1

It means that the asset is high risk, since its profitability varies more than that proportional to the market. This indicates that, in positive variations, the investment performs more than the market index, but otherwise, the negative variation may also be greater.

For example: increase in “Ra” by 5% and “Rm” by 3%, or decrease in “Ra” by -5% and “Rm” by -3%, resulting in an equal beta to 1.66.

β less than 1

It means that the asset is low risk, since its profitability varies less than that proportional to the market.

For example: increase in “Ra” by 2% and “Rm” by 6%, or decrease in “Ra” by -2% and “Rm” by -6%, resulting in an equal beta to 0.33.

β is equal to zero

It can indicate that the asset is indifferent to market variations, or little associated, and it can happen in the event of positive or negative variations in the market index, keeping the asset’s profitability constant.

negative β

A negative beta indicates an asset that performs in the opposite direction to the market, as in the case of precious metals that are valued in times of financial crisis.

For example: positive variation of the asset by 5% and negative of the market index by -3%, resulting in a beta equal to -1.66.

## Beta used in CAPM

The  Capital Asset Pricing Model  (CAPM) is a model that calculates the return to be expected from an asset, based on the financial characteristics of this investment, beta being one of them.

The CAPM considers, in addition to the beta, the rate of return of a risk-free asset, which defines the minimum to expect the return of the invested asset and the market rate of return “Rm”.

### Example

Considering a risk-free security with a return of 5% and a beta of 1.2 with a return to the market (Rm) of 8%, the expected return should be:

E (Ra) = 5% + 1.2 x (8% – 5%)
E (Ra) = 9.8%

In other words, the expected return for assets invested with a beta of 1.2 is 9.8%.

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