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                                  Weight in          Weight in           Weight in       Weight in                                      stock G             stock H             stock I            stock J Portfolio 1                      25%                  25%                 25%               25% Portfolio 2                       30%                 40%                  20%              10% Portfolio 3                       10%                 20%                  40%               30% The beta of four stocks - G, H, I and J - are 0

Finance Mar 27, 2021

                                  Weight in          Weight in           Weight in       Weight in 

                                    stock G             stock H             stock I            stock J

Portfolio 1                      25%                  25%                 25%               25%

Portfolio 2                       30%                 40%                  20%              10%

Portfolio 3                       10%                 20%                  40%               30%

The beta of four stocks - G, H, I and J - are 0.48, 0.86, 1.05 and 1.58 respectively.

What is the beta of a portfolio with the following weights in each asset?

Expert Solution

Computation of the beta of portfolio 1:-

Beta of portfolio 1 = (Weight in stock G*Beta of stock G)+(Weight in stock H*Beta of stock H)+(Weight in stock I*Beta of stock I)+(Weight in stock J*Beta of stock J)

= (25%*0.48)+(25%*0.86)+(25%*1.05)+(25%*1.58)

= 0.12+0.21+0.26+0.40

= 0.99

 

Computation of the beta of portfolio 2:-

Beta of portfolio 2 = (Weight in stock G*Beta of stock G)+(Weight in stock H*Beta of stock H)+(Weight in stock I*Beta of stock I)+(Weight in stock J*Beta of stock J)

= (30%*0.48)+(40%*0.86)+(20%*1.05)+(10%*1.58)

= 0.14+0.34+0.21+0.16

= 0.86

 

Computation of the beta of portfolio 3:-

Beta of portfolio 3 = (Weight in stock G*Beta of stock G)+(Weight in stock H*Beta of stock H)+(Weight in stock I*Beta of stock I)+(Weight in stock J*Beta of stock J)

= (10%*0.48)+(20%*0.86)+(40%*1.05)+(30%*1.58)

= 0.05+0.17+0.42+0.47

= 1.11

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