# Beta Coefficient

Beta coefficient is a measure of sensitivity of a company's stock price to movement in the broad market index. It is an indicator of a stock's systematic risk which is the undiversifiable risk inherent in the whole financial system.

Beta coefficient is an important input in the capital asset pricing model (CAPM). CAPM estimates a stock's required rate of return (cost of equity) as the sum of the risk free interest rate and the stock's equity risk premium. A stock's equity risk premium is the product of the stock's beta coefficient and the market risk premium, the difference between equity market return and the risk free interest rate.

Cost of Equity (CAPM)
= Risk Free Rate + Equity Risk Premium
= Risk Free rate + Beta × Market Risk Premium
= Risk Free Rate + Beta &times: (Market Return - Risk Free Rate)

Beta coefficient is the slope of the security market line. It also features in the Treynor Ratio where it is used to work out a stock's excess return per unit of systematic risk.

## Formula

Beta coefficient is calculated by dividing the covariance of a stock's return with market returns by variance of market return.

 β = Covariance of Market Return with Stock Return Variance of Market Return

Covariance equals the product of standard deviation of the stock return, standard deviation of the market return and correlation coefficient. Using this relationship, we arrive at another formula for beta coefficient which shows that the beta coefficient equals correlation coefficient multiplied by standard deviation of stock returns divided by standard deviation of market returns.

 β = Correlation Coefficient × Standard Deviation of Stock Returns Between Market and Stock Standard Deviation of Market Returns

Portfolio beta can be estimated as the weighted-average of beta coefficients of individual stocks.

## Analysis

The broad equity market has a beta coefficient of 1 and beta coefficients of different stocks are measured with reference to the market beta. A beta coefficient below 1 means that the stock has a systematic risk lower than the market and a beta coefficient greater than 1 shows that the stock has an above-average risk and return.

Information about a company's beta can be obtained from popular financial information websites such as Yahoo Finance.

Currently (April 2019), ExxonMobil (NYSE: XOM) has a beta of 1.07 which shows that it has average systematic risk. The Boeing Company (NYSE: BA), on the other hand, has a beta of 1.43 which shows that its stock is relatively more risky than the broad market.

## Estimating Beta Coefficient

If the correlation coefficient between market and share price of Company P is 0.85; standard deviation of market is 10% and that of share price is 8%, beta coefficient works out to 0.68 (=0.85 × 8%/10%) which shows a below-market risk and return.

If we do not have these variables estimating beta from raw data is not very difficult. Just follow these simple steps to estimate beta:

1. Obtain historical share price data for the company's share price.
2. Obtain historical values of an appropriate capital market index (say S&P 500).
3. Convert the share price values into daily return values by using the following formula: return = (closing share price − opening share price)/opening share price.
4. Convert historical stock market index values in similar way.
5. Align the share return data with index return such that there is 1-on-1 correspondence between them. For share price return, there should be a corresponding index return.
6. Using SLOPE function to find the slope between the both arrays of data and resultant figure is beta.