Question

Stock Investment Beta A $2,000,000 2.00 B 3,000,000 0.80 C 3,000,000 1.10 D 1,000,000 .60 a....

Stock Investment Beta

A $2,000,000 2.00

B 3,000,000 0.80

C 3,000,000 1.10

D 1,000,000 .60

a. Use stock A and B above to design a $10 million portfolio with a beta of 1.60.

b. Do the same as in ‘a’ with stock B and D (no short restrictions).

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Homework Answers

Answer #1

Portfolio Beta is equal to weighted average beta

a. Let the investment in Stock A be x, Investment in Stock B = 10,000,000 - x

1.60 = 2*x/10,000,000 + 0.80*(10,000,000-x)/10,000,000

16,000,000 = 2x + 8,000,000 - 0.8x

x = $6,666,667

Hence, investment in Stock A = $6,666,667

Stock B = $3,333,333

b.Let the investment in Stock B be x

Investment in Stock D = 10,000,000 - x

1.60 = 0.80*x/10,000,000 + 0.60*(10,000,000-x)/10,000,000

16,000,000 = 0.80x + 6,000,000 - 0.6x

x = $50,000,000

Hence, investment in Stock B = $50,000,000

In Stock D = -$40,000,000

i.e. Sell Stock D worth $40,000,000 and buy B $50,000,000

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