Derivative Securities Homework 1 1. When Referring to the Term Structure

Derivative Securities Homework 1 1. When referring to the term structure of futures contracts, the term contango refers to an upward sloping curve and the term backwardation refers to a downward sloping curve. Oil futures are typically in backwardation. Give an example in real life of a contango situation. (a) Explain why oil (e.g. NYMEX CL contracts) should be in backwardation. Go to the NYMEX website and check that this is the case. Define convenience yield in this case. (b) Going to the EIA website, look at the historical series for the first four contracts in Light Sweet Crude from January 1985 to the present date. By looking at the difference in prices between the first and fourth contracts, and assuming futures=forwards, compute the implied convenience yield for each day. You will also need a daily time series of 3 month rates, which you can download from the Federal Reserve H15 website. (c) Are daily changes in interest rates and oil futures prices correlated? What about monthly? Quarterly? 2. A trucking company projects that it will buy at the pump (spot price) 1,000,000 gallons of regular gasoline per month over the next four months. It wishes to hedge its exposure by selling NYMEX gasoline futures. Construct a quantitative hedging policy using the RBOB Regular Gasoline futures. [You can get the weekly retail (spot) gasoline historicals from EIA, as well as the RBOB Gasoline futures.] Find out the number of contracts that you will use. Which contract month gives a better hedge in terms of variance? 3. The two month interest rate in Switzerland and the U.S. with continuous compounding are 3% and 8% respectively. Swiss spot is 0.65 USD, the futures price for a contract deliverable in 2 months is 0.66 USD. What arbitrage opportunities does this create? 4. Consider the Dow Jones Industrial Index and the corresponding ETF (Diamonds Trust (DIA) ). The DJ index is the sum of an equal number of shares of each of the component stocks. Compute the actual amount of shares for each company represented in the DIA. Using www.finance.yahoo estimate the equivalent continuous dividend yield for each component stock, corresponding to the next 6 months. Estimate the associated dividend yield for DIA using the ``center of mass’’ formula and the estimated single-name dividends, Compare this answer with the continuous dividend yield that you obtain using the actual dividend payments of DIA (again from yahoo) over the next 6 months. .

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