MATH 534 Midterm: MATH 537 UMass Amherst midtermS05
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Instructions: show all your work for full credit, and box your answers when appropriate. At bank uconn, a loan (or deposit) accrues an interest rate of 4% per annum with continuous compounding. Carefully describe an arbitrage opportunity that will you earn you a risk-free pro t of in two years. Solution: for each you borrow from umass and invest with uconn, when you close your position in 2 years your net risk-free pro t is 1e0. 04 2 1. 08 = 0. 003287. So borrow today 1000/0. 003287 = 304222. 52 dollars from umass and deposit it all with uconn: the spot price of facebook (fb) stock is . Justify your answer. (b) you borrow money to buy ten fb shares today. In 3 months you close out your position. Give answer in terms of (t = 3/12)-dollars. Solution: (a) we have erw [s3/12] = 0. 6 165 + 0. 4 135 = 153. 151. 89 = 150e0. 05 3/12 = s0ert the real world is risk-averse.
