You own a portfolio that has a total value of $145,000 and a beta of 1.31. You have another $58,000 to invest and you would like the beta of your portfolio to decrease to 1.19. What does the beta of the new investment have to be in order to accomplish this

0.89

Explanation:

The total portfolio beta is a weighted average of the constituent security betas.

145,000 + 58,000 = $203,000

The total portfolio beta of 203,000 should have a beta of 1.19.

Proportion of New investment = 58,000/203,000

= 28.57%

Proportion of old portfolio = 145,000/203,000

= 71.43%

(0.7143 * 1.31) + (0.2857 * x) = 1.19

0.9357 + 0.2857x = 1.19

0.2857x = ‭0.2543‬

x= 0.89

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