Question

How to calculate B when there is many risk free?

• Use the following information to answer the question below. Year 2008 2009 2010 2011 Risk-free Return 1.75% 1.25% 1.25% 1.50% Market Return 7.50% -30.00% 9.50% 11.50% PE-Waters Return 4.50% -31.50% 6.00% 5.50% Using the historical average excess retums and historical volatilities of both PE- Waters and Market portfolio that you can calculate from the information above, your estimate of PE-Waters' Beta is closest to: A) 2.065 0.384 0.927 1.122 D)

Answer 1

The Capital Asset Pricing Model (or CAPM) describes individual stock returns as a function of the overall market’s returns.

Re = B x [Rm – Re] + Re or Re- Rp = B x [Rm- Re] Re = Stock Return B = Beta Coefficient Rm = Market Return Rp = Risk-Free Rate

To calculate the Beta of a stock or portfolio, divide the covariance of the excess asset returns and excess market returns by the variance of the excess market returns over the risk-free rate of return:

B = - 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 the 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.

B = Correlation coefficient Between Market and Stock X Standard Deviation of Stock Returns Standard Deviation of Market Returns

The approximate value from calculations is Beta = 1.25702.

Thus, the closest value of beta as mentioned in the options is: (d) 1.122