Question

The possible outcomes for the returns on Stock X and the returns on the market portfolio have been estimated as follows:                                                              
                                    Scenario          Stock X Market portfolio                                 
                        1          9%                   9%                               
                        2          21%                 13%                             
                        3          13%                 11%                             
Each scenario is considered to be equally likely to occur. Calculate the market beta for Stock X. Round your answer to the nearest tenth.    

A. None of them

B. 3.0

C. 1.0

D. 0.3

Answer 1

Expected Return of Stock X = (9%+21%+13%)/3 = 43%/3
Expected Return of Market Portfolio = (9%+13%+11%)/3 = 33%/3

Covariance = (1/3) *(9%-43%/3)*(9%-33%/3) +(1/3)*(21%-43%/3)*(13%-33%/3)+ (1/3)*(13%-43%/3)*(11%-33%/3) =0.0008

Variance of Market Portfolio = (1/3)*(9%-33%/3)²+(1/3)*(13%-33%/3)²+(1/3)*(11%-33%/3)²​​​​​​​= 0.000267

Beta = Covariance/Standard Deviation of Market = 0.0008/0.000267 = 3

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