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# Investment Management

Assume that the following portfolios A and B are well diversiﬁed, with E[ra] = 9% and E[rb] = 11%.

In a one factor economy with βa = 0.8 and βb = 1.2 and a risk-free rate of 8%:

(a) establish an arbitrage. Especially, derive the exact holdings in A, B, and the risk free rate of a

new portfolio (called X) so that X is an arbitrage opportunity.

(b) Explain why X (from part i) of this question) is an arbitrage opportunity.

(c) Now assume that B is the market portfolio and A is a single stock (IBM). Draw the SML. Argue

why (or why not) you can still construct an arbitrage opportunity using A, B, and the risk-free

rate. Can you think of a diﬀerent theory that might provide investment advice in this situation?

52. Suppose that the borrowing rate that your client faces is 2%. A