williams                NYSE

-0.05                   -0.12
 0.05                    0.01
 0.08                    0.06
 0.15                    0.10
 0.10                    0.05

a. What are the average returns on williams stock and on the market?
b. Compute the beta of Williams stock.

Hi!!

a. Calculate the average return for Williams stock and the market. 

This is the easy part:
AvRW = (-0.05 + 0.05 + 0.08 + 0.15 + 0.10) / 5 =
     = 0.066

AvRM = (-0.12 + 0.01 + 0.06 + 0.10 + 0.05) / 5
     = 0.02

The average return on Douglas stock is 6.6% and average return on market is 2%.



b. Compute the beta of Williams stock.

The beta is the covariance between the stock's return and the market's
return divided by the variance of the market return:

Beta = Cov(AvRW,AvRM)/Var(AvRM)

Cov(AvRW,AvRM) = Sum[(RD-AvRD)*(RM-AvRM)] =
               = [-0.116*(-0.14)+(-0.016)*(-0.01)+0.014*0.04+
                  +0.084*0.08+0.034*0.03] =
               = 0.0247

Var(RM) = Sum[(RM-AvRM)^2] =
        = [0.0196+0.0196+0.0016+0.0064+0.0009] =
        = 0.0286

Beta = 0.0247 / 0.0286 = 0.86364

The beta of Williams stock is 0.86364 .


For references see:
"Beta coefficient - Wikipedia, the free encyclopedia":
http://en.wikipedia.org/wiki/Beta_coefficient


Search strategy:
beta covariance


I hope this helps you. Feel free to request for a clarification if you need it.


Best regards,
livioflores-ga

pls. explain further each data ( where they came from ) of solution b.
Beta = Cov(AvRW,AvRM)/Var(AvRM)

Cov(AvRW,AvRM) = Sum[(RD-AvRD)*(RM-AvRM)] =
               = [-0.116*(-0.14)+(-0.016)*(-0.01)+0.014*0.04+
                  +0.084*0.08+0.034*0.03] =
               = 0.0247

Var(RM) = Sum[(RM-AvRM)^2] =
        = [0.0196+0.0196+0.0016+0.0064+0.0009] =
        = 0.0286