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Q#4 Assume that the following two-index model describes returns: Assume that the following three portfolios are observed. PortfolioExpected Returnbilbi2 12.0 13.4 12.0 1 0.5 3 0.2 3 -0.5 a. Find the equation that must describeeuibrium returns. b.Illustrate the arbitrage opportunities that would exist if a portfolio called D with the following properties were observed: bpz-2
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Answer #1

R(A) = ai + 1 x I1 + 0.5 x I2 = 12.0%... 1)

R(B) = ai + 3 x I1 + 0.2 x I2 = 13.4%....2)

R(C) = ai + 3 x I1 - 0.5 x I2 = 12.0%....3)

Subtracting 2 and 3,

=> 13.4% - 12.0% = 0.7 x I2

=> I2 = 2%

Substituting I2 in 1 and 3,

R(A) = 12% = ai + 1 x I1 + 0.5 x 2%

=> 11% = ai + I1

R(C) = 12% = ai + 3 x I1 - 0.5 x 2%

=> 13% = ai + 3I1

Subtracting one from another, we get

=> I1 = 1% and ai = 10%

Two-index model equation

Ri = 10% + bi1 x 1% + bi2 x 2% + ei

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