Consider two well-diversified portfolios, A and C, rf = 4%, E(rA) = 10%, E(rC) = 6%,...

Consider two well-diversified portfolios, A and C,

rf = 4%, E(rA) = 10%, E(rC) = 6%, bA = 1, bC = ½

If the maximum amount you can borrow is $1,000,000, what is your arbitrage strategy and profit?

A. Long 1 A , short 0.5 C , short 0.5 rf, profit=$5,000

B. Long 1C , short 0.5 A, short 0.5 rf, profit=$5,000

C. Long 0.5 C, Long 0.5 rf, short 1 A, profit=$10,000

D. Long 0.5 A, Long 0.5 rf, short 1 C, profit=$10,000

Expert Solution

We will short Portfolio C and receive +$ 1,000,000.

For every 1 unit of Portfolio C we will BUY only 0.5 units of portfolio A.
As we have to match the Beta of the two portfolios ( the beta of A is 1 and beta of C is 0.5 therefore to replicate the beta of short C i.e. -0.5Beta we’ll only BUY 0.5 units of A that will be 0.5UnitsA*1BetaA = +0.5Beta).

Though we’ll Long A, invest $1,000,000*0.5 = ($500,000) and now will invest remaining ($500,000) at 4% in rf asset which has Beta=0.

jeff jeffy answered 1 year ago

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