Justin invests in Stock X that has a beta of 0

Finance Aug 05, 2020

Justin invests in Stock X that has a beta of 0.7 and an Index Fund Y. Index Fund Y replicates the market portfolio. Justin’s portfolio that consists of Stock X and Index Fund Y has a beta of 0.9. His total portfolio investment is $42000. What is the dollar amount of Index Fund Y in Justin’s portfolio?

Expert Solution

Stock X Beta = 0.70

Stock Y Beta = 1 [ Market has beta of 1]

So, Portfolio Beta = 0.90

So, Weightage of X and Y = ( Stock Y Beta - Portolfio Beta) / ( Portfolio Beta- Stock X Beta)

= ( 1 - 0.90) / ( 0.90 - 0.70)

Weight of X and Y = 0.10 / 0.20

So, Total Weight = 0.10 + 0.20

= 0.30

Weight of X = 0.10 / 0.30

= 0.33

Weight of Y = 0.20 / 0.30

= 0.66

So, Amount invested in Y = Total amount * Weightage of Y

= 42000* 0.66

Amount Invested in Y = $28000

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