November 25, 2010MATH 2510: Fin. Math. 2 1 Hand-out/in A template exam-paper (pink.) Hull’s Chapter 7 on swaps (or next week.) Course plan (blue) and these slides. And can I have your Course Works #3, please?

November 25, 2010MATH 2510: Fin. Math. 2 2 The Template Exam-Paper 17 numbered questions each worth 5%. (Answers: Next week.) The exam-paper in January will be quite similar in content and organization. There will be one more template in the last week. Do you want it “simulation style” w/ mock grading”?

November 25, 2010MATH 2510: Fin. Math. 2 3 General – But Useful – Exam Advice Short answers. Be quick. Questions are quite independent, so if you get stuck, go on. Partial credit is given (a lot.) Give it the old college try. And, oh: Solving two linear equations w/ two unknowns will come up --- without warning.

November 25, 2010MATH 2510: Fin. Math. 2 4 The Cash-Flows of a Futures Contract Entering into a futures contract costs nothing (when you do it.) When you enter a long position in a futures contract at time t-dt (think dt~1 day), you recieve Fut(t) – Fut(t-dt) at time t, where Fut(t) is the co-called futures price. At the delivery date T: Fut(T) = S(T)

November 25, 2010MATH 2510: Fin. Math. 2 5 When interest rates are constant, futures and foward prices are equal – or else arbitrage. (And we/Hull then just write F). That’s a theorem. (Hull Ch. 5; proof in Appendix.) Futures and fowards do not have the same cash-flows or values (Business Snapshot 5.2) – but we can transform on into the other (proof of theorem.)

November 25, 2010MATH 2510: Fin. Math. 2 6 We can think of a futures contract as a forward contract where gain/loss are settled each day. (This happens via a margin account, where collateral is posted --- lower credit risk.) Or in a tight spot: ”futures is forward”.

November 25, 2010MATH 2510: Fin. Math. 2 7 Remember our theoretical expression for arbitrage-free forward prices where ”to correct” means to: Subtract in case of cash dividends. Multiply by in case of a dividend yield (or a foreign interest rate.)

November 25, 2010MATH 2510: Fin. Math. 2 8 Futures Hedges Futures contracts are suitable for hedging.e. for “covering you your bets”. When/what you loose 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.

November 25, 2010MATH 2510: Fin. Math. 2 9 Arguments in Favor of Hedging Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables.

November 25, 2010MATH 2510: Fin. Math Arguments Against Hedging Shareholders are usually well diversified and can make their own hedging decisions It may increase risk to hedge when competitors do not Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult

November 25, 2010MATH 2510: Fin. Math 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.)

November 25, 2010MATH 2510: Fin. Math 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

November 25, 2010MATH 2510: Fin. Math 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.

November 25, 2010MATH 2510: Fin. Math On Hull’s Futures Chapters This week we’ve covered more pages than in all of CT1. We skip and jump in Hull. Same level of detailed knowledge as for CT1 is not required on the exam. Skip pages on ”changing beta”. (It’s not deep, but one needs to know what the ”Capital Asset Pricing Model” is for it to make sense.)