Midterm Review Fall 2014

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<ul><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 1/12</p><p>15.437 Midterm Review</p><p>Michael Abrahams</p><p>MIT Sloan School of Management</p><p>miabraha@mit.edu</p><p>Fall 2014</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 2/12</p><p>Agenda</p><p>1) Some Tips for the Midterm</p><p>2) Bonds</p><p>3) Swaps</p><p>4) Forwards</p><p>5) Options</p><p>Key Concepts + Exercises</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 3/12</p><p>Some Tips for the Midterm</p><p> Read each question very carefully!</p><p> Since this is an open book exam, dont expect simple</p><p>plug and chug type problems</p><p>Attempt to understand the intuition before focusing onthe equations</p><p> Expect to draw information from the whole course</p><p> It is important to explain your answers and show</p><p>intermediate steps for full (or partial) credit</p><p> Remember your calculator - laptops are not allowed</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 4/12</p><p>Bonds Key Concepts</p><p> Replication can allow you to price, hedge, or</p><p>build an arbitrage portfolio if it is mispriced </p><p>know how to do all of these!</p><p> Know the standard terminology and how the</p><p>different terms relate to each other:a.Coupon bond</p><p>b.Zero coupon bond and zero coupon yield curve</p><p>c.Par bond and par bond yield curve</p><p>d.Forward rates</p><p>e.Floating-rate bond</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 5/12</p><p> Know how to: replicate and price both sides of a swap</p><p> find the fair value swap rate</p><p> value a swap with changing notional value an existing swap position</p><p> Key result: value of individual floating</p><p>payment at time t is (Zt-1 Zt) per unit of</p><p>notional amount</p><p>Swaps Key Concepts</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 6/12</p><p>Exercise (Swap)</p><p>Consider a newly-issued 2-year swap with the following characteristics:</p><p> Notional values: $1M at period 1, $1.5M at 2, $2.0M at 3, and $2.5M at 4.</p><p> The fixed side pays every six months (i.e., at the end of 1,2,3, and 4).</p><p> The floating side makes a single payment at the end of period 4 (based on</p><p>the given notional).</p><p>What is the swap rate in this contract?</p><p>Exercise 4.1</p><p>t (6-mth) 1 2 3 4</p><p>Zt 0.970 0.941 0.912 0.883</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 7/12</p><p>Forwards Key Concepts</p><p> Know how to: find the forward price</p><p> replicate a forward contract</p><p> exploit arbitrage opportunities value an existing forward position</p><p> Key result:F = FVT[spot price] FVT [forgone cash flows]</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 8/12</p><p>Options Key Concepts</p><p> Learn the standard terminology (puts, calls, option</p><p>premium, strike price, American vs. European, etc.)</p><p> Put-Call Parity for European options: S = C P + PV(K) if no intermediate cash flows on S</p><p> S = C P + PV(K) + PV(D) if there are dividends or other</p><p>intermediate cash flows</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 9/12</p><p>Options Key Concepts</p><p> Know how options relate to forward contractsa. A call and put with strike equal to the forward price must</p><p>have the same premium</p><p>b. Rewrite put-call parity as S PV(D) = C P + PV(K). What</p><p>does S PV(D) look like? The present value of the forward</p><p>price (spot minus PV of forgone cash flows)! Thus, we also</p><p>have PV(F) = C P + PV(K), for any K.</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 10/12</p><p>Exercise 4.2</p><p>Exercise (Previous Exam Question)A year ago your firm took a long position in a three-year forward contract on</p><p>100,000 pounds of copper. The forward price when the contract was initiated</p><p>was $3.20 per pound. The forward price for that delivery date has since risen to</p><p>$4.00 per pound.</p><p>Two-year European options, each covering 100 pounds of copper, are availableon the following terms:</p><p>Striking Price Call Put</p><p>350 80 35</p><p>400 52 52</p><p>450 30 75The current price of a zero coupon bond maturing in two years is $.90. Your</p><p>counterparty on the forward contract has just offered your firm $70,000</p><p>to cancel the contract. Should your firm take this offer?</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 11/12</p><p>Exercise (Previous Exam Question)</p><p>A firm has created a ten-year trust that holds one thousand shares of ABC stock.</p><p>This stock serves as collateral for three securities that the firm has issued. These</p><p>securities represent different claims on the stock.</p><p>The first security receives all of the dividends paid by the stock during the ten-</p><p>year period. The residual value of the trust on the termination date is then</p><p>divided between the remaining securities. The second security receives anycapital appreciation the stock has experienced over the ten-year period. If the</p><p>stock has declined in value, the second security receives nothing. The third</p><p>security receives the full value left in the trust after the second security has been</p><p>paid.</p><p>The price of the stock when the trust was created was $100 per share. Show how</p><p>you could express the current value of each of the three securities in terms of the</p><p>current value of ABC stock, the current value of a zero coupon bond maturing</p><p>on the termination date of the trust, and the current value of European options</p><p>on ABC stock that expire on the termination date.</p><p>Exercise 4.3</p></li><li><p>8/21/2019 Midterm Review Fall 2014</p><p> 12/12</p><p>Exercise (Forward on a Swap)</p><p>Consider a forward on a swap (distinct from a forward swap), that is, a</p><p>forward contract that requires you to buy an existing swap contract at a given</p><p>price in the future.</p><p>Specifically, determine the appropriate forward price on a 1-year forward ona newly-issued, 2-year plain vanilla floating-for-fixed swap with notional of</p><p>$100. The forward matures just after the 1-year swap payment date. The</p><p>prices of 0.5, 1.0, 1.5, and 2.0 year zeros are 0.95, 0.90, 0.85, and 0.80</p><p>respectively. Assume that you will receive floating payments.</p><p>Exercise 4.4</p></li></ul>