Question

The standard deviation of a stock's annual returns is 51.1%. The standard deviation of market returns is 20.9%. If the correlation between the returns of the stock and the market is 0.5, what is this stock's beta? Round to two decimal places

Answer 1

The formula for calculating beta can be given as

$\beta = Correlation between Asset and Market * \frac{Standard Deviation of Asset}{Standard Deviation of Market}$

$\beta = \rho * \frac{\sigma(Asset Returns)}{\sigma (Market Market Returns)}$

As per the given values

standard deviation of stock = 0.511

standard deviation of market = 0.209

correlation between the returns of the stock and the market = 0.5

Entering values in formula

$\beta = \0.5* \frac{0.511}{0.209}$

$\beta = 1.2224$

Hence Stock's Beta is 1.2224