Question

Please help. Need step by step instructions.

Given: The excess returns of two stocks X and Y and a market portfolio M in the table below over the past 5 years:

Year	Stock X-Rf	Stock Y-Rf	Market M-Rf
2010	14.00%	13.00%	12.00%
2011	19.00%	7.00%	10.00%
2012	-16.00%	-5.00%	-12.00%
2013	3.00%	1.00%	1.00%
2014	20.00%	11.00%	15.00%

What is the beta for Stock X and Stock Y?

Answer 1

Average Return of Market=(12%+10%-12%+1%+15%)/5 =5.20%
Variance of Market =((12%-5.20%)^2+(10%-5.2%)^2+(-12%-5.20%)^2+(1%-5.20%)^2+(15%-5.20%)^2)/(5-1))=0.01197

Average Return of X =(14%+19%-16%+3%+20%)/5 =8%
Covariance of X and Market =((14%-8%)*(12%-5.20%)+(10%-5.20%)*(19%-8%)+(-12%-5.20%)*(-16%-8%)+(1%-5.20%)*(3%-8%)+(15%-5.20%)*(20%-8%))/(5-1))=0.016125
Beta =Covariance of X and Market/Standard Deviation of Market =0.016125/0.01197 =1.35

Average Return of Y =(13%+7%-5%+1%+11%)/5 =5.40%
Covariance of Y and Market =((13%-5.40%)*(12%-5.20%)+(7%-5.40%)*(10%-5.20%)+(-5%-5.40%)*(-12%-5.20%)+(1%-5.20%)*(1%-5.40%)+(15%-5.20%)*(11%-5.40%))/(5-1))=0.00779
Beta =Covariance of X and Market/Standard Deviation of Market =0.00779/0.01197 =0.65