# Beta Coefficient

Beta coefficient is a measure of sensitivity of a share price to movement in the market price. It measures systematic risk which is the risk inherent in the whole financial system. Beta coefficient is an important input in capital asset pricing model to calculate required rate of return on a stock. It is the slope of the security market line.

## Formula

Beta coefficient is calculated as covariance of a stock's return with market returns divided by variance of market return. A slight modification helps in building another key relationship which tells that beta coefficient equals correlation coefficient multiplied by standard deviation of stock returns divided by standard deviation of market returns. Beta coefficient is given by the following formulas:

β = | Covariance of Market Return with Stock Return |

Variance of Market Return |

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

Between Market and Stock | Standard Deviation of Market Returns |

## Analysis

A beta coefficient of 1 suggests that the stock carries the same risk as the overall market and will earn market return only. A coefficient below 1 suggests a below average risk and return (where the average means the overall market) while on the other hand a coefficient higher than 1 suggests an above average risk and return.

At the time of writing (Dec 2012), ExxonMobil (NYSE: XOM) has a beta of 0.63 which suggests that less risky than average market. JPMorgan Chase (NYSE: JPM) on the other hand has a beta of 1.58 and we can conclude it is more risky than the market in general.

## Estimating Beta Coefficient

Suppose correlation coefficient between market and share price of Company P is 0.75; standard deviation of market is 15% and that of share price is 8%, beta can equals 0.40 (=0.75 × 8%/15%).

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

- Obtain historical share price data for the company's share price.
- Obtain historical values of an appropriate capital market index (say S&P500).
- Convert the share price values into daily return values by using the following formula: return = (closing share price − opening share price)/opening share price.
- Convert historical stock market index values in similar way.
- Align the share return data with index return such that there is 1-on-1 correspondence between them. For share price return on 11 December 2011 there should be a corresponding index return.
- Using SLOPE function to find the slope between the both arrays of data and resultant figure is beta.

Written by Obaidullah Jan, ACA, CFA