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Question: Miracle Hedge Fund (MHF) buys 50 shares of Phantastic Corp. at $10 each. Its brokerage rm SuperBroke Brothers Inc. (SBB) sets a margin requirement of 20% and charges an interest rate of r = 6% on the loan for purchasing the shares.
(a) How much cash does MHF need to invest?
(b) Calculate the margin call of SBB if the price falls to $8.
(c) What is the return for MHF on the transaction after the price decline?
(d) How is the return on cash inuenced by a change in the interest rate r? Does your answer depend on the size of the margin requirement? [Hint: For this sensitivity analysis use a derivative with respect to r and, then, m.]
Suppose that instead MHF short sells 20 shares of Awful Inc. at $20 each. Again, SBB now sets a margin requirement of 30%.
(e) How much cash does MHF need to invest?
(f) Calculate the margin call of SBB if the price increases to $25.
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