1. November 30, 2010MATH 2510: Fin. Math. 2 1 Hand-out/in Graded Course Works #3 These slides Repeat appearences Hull’s Chapter 7 on swaps Mock Exam #1

2. November 30, 2010MATH 2510: Fin. Math. 2 2 Today’s Topics: A Mixed Bag Hull Section 3.3-4: Hedging w/ futures especially w/ less-than-perfect correlation (“cross hedging”.) Comments to Course Work 3 Student surveys Hull Chapter 7 on swaps.

3. November 30, 2010MATH 2510: Fin. Math. 2 3 Futures and forward contracts Very briefly: A bet that the underlying goes up (long) or down (short). To hedge: To bet against your own assets. Win some, lose some. In the same way, fire insurance is a bet that your house burns down.

4. November 30, 2010MATH 2510: Fin. Math. 2 4 Futures Hedges Futures contracts are suitable for hedging i.e. for “covering you your bets”. When/what you lose one thing, you gain on another. A long (short) futures hedge is appropriate when you know you will purchase (sell) an asset in the future and want to lock in the price.

5. November 30, 2010MATH 2510: Fin. Math. 2 5 Basis Risk Basis is the difference between spot and futures prices. Basis risk arises because of the uncertainty about the basis when the hedge is closed out. (Say you can’t match w/ exact delivery date and/or underlying asset for futures.)

6. November 30, 2010MATH 2510: Fin. Math. 2 6 Long Hedge Suppose that F(1): Initial Futures Price F(2): Final Futures Price S(2) : Final Asset Price You hedge the future purchase of an asset by entering into a long futures contract Cost of Asset= S(2) – (F(2)– F(1)) = F(1) + Basis

7. November 30, 2010MATH 2510: Fin. Math. 2 7 Hull’s Example 3.2 A company knows it needs to buy 20,000 barrels of crude oil. Doesn’t know exactly when. Now is June 8. Futures contracts are for 1,000 barrels. December-futures price is $18 (per barrel). Company goes long 20 Dec.-futures.

8. November 30, 2010MATH 2510: Fin. Math. 2 8 On Now. 10, the company buys the oil. Spot price is, say, $20 and Dec.-futures price is $19.10. It closes the futures contract. Gain on futures (ignoring time value of money) is $1.10, and the effective price paid for oil is $20-1.1 = $18.90 (per barrel; 20,000*$18.90= $378,000 is paid in total).

9. November 30, 2010MATH 2510: Fin. Math. 2 9 Optimal Hedge Ratio Proportion of the exposure that should optimally be hedged is where  S is the standard deviation of  S, the change in the spot price during the hedging period,  F is the standard deviation of  F, the change in the futures price during the hedging period and  is the coefficient of correlation between  S and  F.

10. November 30, 2010MATH 2510: Fin. Math. 2 10 Less-than-perfectly futures-spot correlation? If the futures contact is on a (slightly) different underlying than your asset: Jet fuel vs. crude oil Profit of a tire manufactures vs. oil prices The price of your house vs. an index …

11. November 30, 2010MATH 2510: Fin. Math. 2 11 If the ”buy the underlying for borrowed money and hold on to it”-argument does not work Storage not possible (electricity) or costly No spot market; the underlying good does not exist (corn not harvested yet) Convinience yield (more or less tangible) from holding the underlying

12. November 30, 2010MATH 2510: Fin. Math. 2 12 Course Work #3; Stochastic Rates of Return Q1+3: Standard CT1, Unit 14, Table 1.3.1. This will be on the exam. For the annuity case, you will only be required to use recursive formulas. Careful w/ expectations and non- linear functions. Q2: Pascal’s triangle. Q4: Non-identical distributions can be handled too. Could come at the exam.

13. November 30, 2010MATH 2510: Fin. Math. 2 13 Q5: Promises may sound alike but be very different. Based on a true story. If you think this was difficult to understand, imagine having it written by lawers. Things don’t always go as easlily as in CT1, Unit 14. Simulation is then a powerful tool.

14. November 30, 2010MATH 2510: Fin. Math. 2 14 Student Surveys I’n not angry, I’m disappointed. And so are you. (Or some combination.) The first time the course in given. (So the lack of exam papers will solve itself over time.) Mix of slides and whiteboard: Completely intentional, but culture chock. Hard-to-read handwriting: Not so much.

15. November 30, 2010MATH 2510: Fin. Math. 2 15 CT1 Exam exemption imposes contraints. Course Works Yes, they are demanding. (I.e. not the easiest way to get 5%.) No, they are not unrelated to lectures, workshops, text-books - or even Math 1510. And you’re doing fine.