# Beta Coefficient

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

Beta coefficient is an important input in the capital asset pricing model (CAPM). CAPM estimates a stock's required rate of return i.e. (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 the broad 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 ×: (Market Return - Risk Free Rate)

Beta coefficient is the slope of the security market line.

## Formula

Beta coefficient is calculated by dividing the covariance of a stock's return with market returns by the 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 returns, standard deviation of the market returns and their correlation coefficient. Using this relationship, we arrive at another formula for beta coefficient which shows that the beta coefficient equals the correlation coefficient multiplied by the standard deviation of stock returns divided by the standard deviation of market returns.

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

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

## Analysis

The market has a beta coefficient of 1 and beta coefficients of different stocks are measured with reference to the market. A beta coefficient below 1 means that the stock has a systematic risk lower than the market, and hence would offer below-market return; and a beta coefficient greater than 1 shows that the stock has an above-average risk and hence, must provide above-average return.

Different financial information websites, such as Yahoo Finance, provide beta coefficient for most listed companies.

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 returns and returns on the stock of Company P is 0.85; the standard deviation of market is 10% and that of stock 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 data for the company’s stock price. 2. Obtain historical values of an appropriate market index (say S&P 500). 3. Convert the stock price values to daily return values by using the following formula: Return = (Closing Price − Opening Price)/Opening Price. 4. Convert historical stock market index values to return values. 5. Align the share return data with index return such that there is 1-on-1 correspondence between them. For each stock return, there should be a corresponding index return. 6. Use Excel SLOPE function to find the slope between both arrays of data and resultant figure is beta.