1. 1.1 Asset Management and Derivatives Lecture 1

2. 1.2 Course objectives Why an asset management course on derivatives? A derivative is an instrument whose value depends on the values of other more basic underlying variables. Examples: swaps, futures, options,... 1. They can increase the efficiency of the investment process 2. Their non-linear payoff can be attractive for improving the risk-return profile of the managed portfolio 3. We can borrow from their hedging/pricing techniques new ways of managing portfolios 4. They can enlarge the asset classes on which we can invest

3. 1.3 Improve the efficiency a quicker way for tactical market timing. Imagine that you are the manager of an equity fund and you want to take a positive bet on the entire stock market (+1% on the benchmark). Since you are actually neutral and you want to go long, you can borrow money and buy all the stocks that are in your portfolio in the existing proportions. This is a complex operation. The typical shortcut is through a futures contract. if you want to replicate an index where a single stock weights more than the max allowed by regulators, you have to resort to derivates to reach synthetically the desired exposure. another example of use of derivatives is when you want to hedge your fund from currency fluctuations.

4. 1.4 Modify risk-return mapping traditional long-only asset management has a linear pay-off one can use derivative both for going short and for introducing some non- linearity in a fund which remains in any case essentially long-only Apart from the “simple” buying or selling of options either because of particular views that we have on stock/market or because of arbitrage opportunities between the cash and the derivatives market, we can use derivatives to tilt the management result on a given time horizon. This can be useful if you want a floor on your profits (think about the possibility of locking- in the profits through a put option)... or if you want a cap (think about the possibility of improving your return by selling an out-of-the money call option on a stock held in your portfolio. In any case, you may end up buying options also if are not perfectly aware of it (see convertible bonds). So beware

5. 1.5 new ways of managing money Derivatives can be useful to learn new ways of managing money and then structuring products helpful for more sophisticated clients’ needs. The pricing of a derivatives is based on the concept that if market is efficient there should be no arbitrage opportunities between the cash market and the derivatives. The pricing is then strictly linked to replicating the pay-off of the derivatives via a portfolio of basic financial instrument. The portfolio has to be managed dynamically. So it is possible to manage a fund in a way that it replicates the pay-off of an option. This principle is behind portfolio insurance and other dynamic techniques that are currently used in the asset management industry.

6. 1.6 enlarging the universe Many asset classes cannot be invested in, by regulatory reasons and by objective difficulties inherent to the markets nature. Those asset classes might be very useful in diversifiyng the portfolio. For example, it can be very difficult to access certain emerging markets, either because they are protected by cumbersome administrative rules or simply because foreign investors are not allowed to hold them. Another example is instead the one of an asset class that cannot be accessed by an asset manager because of the market’s nature. Think about mortgages or loans. This is a market that can be accessed only by banks. Credit derivatives are a new class of financial instruments that allow an asset manager to access them. Think about re-insurance risks (weather or earthquake risks). ART instruments can help asset managers to access them

7. 1.7 The Playground

8. 1.8 Derivatives Markets Exchange Traded –standard products –trading floor or computer trading –virtually no credit risk Over-the-Counter –non-standard products –telephone market –some credit risk

9. 1.9 Types of Traders Hedgers Speculators Arbitrageurs Some of the large trading losses in derivatives occurred because individuals who had a mandate to hedge risks switched to being speculators

10. 1.10 Hedging Examples A US company will pay £1 million for imports from Britain in 6 months and decides to hedge using a long position in a forward contract An investor owns 500 IBM shares currently worth $102 per share. A two- month put with a strike price of $100 costs $4. The investor decides to hedge by buying 5 contracts

11. 1.11 Speculation Example An investor with $7,800 to invest feels that Exxon’s stock price will increase over the next 3 months. The current stock price is $78 and the price of a 3- month call option with a strike of 80 is $3 What are the alternative strategies?

12. 1.12 Arbitrage Example A stock price is quoted as £100 in London and $172 in New York The current exchange rate is 1.7500 What is the arbitrage opportunity?

13. 1.13 Forward Contracts A forward contract is an agreement to buy or sell an asset at a certain time in the future for a certain price (the delivery price) It can be contrasted with a spot contract which is an agreement to buy or sell immediately

14. 1.14 How a Forward Contract Works The contract is an over-the-counter (OTC) agreement between 2 companies The delivery price is usually chosen so that the initial value of the contract is zero No money changes hands when contract is first negotiated and it is settled at maturity

15. 1.15 The Forward Price The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) The forward price may be different for contracts of different maturities

16. 1.16 Terminology The party that has agreed to buy has what is termed a long position The party that has agreed to sell has what is termed a short position

17. 1.17 Example On January 20, 1998 a trader enters into an agreement to buy £1 million in three months at an exchange rate of 1.6196 This obligates the trader to pay $1,619,600 for £1 million on April 20, 1998 What are the possible outcomes?

18. 1.18 Profit from a Long Forward Position Profit Price of Underlying at Maturity, S T K

19. 1.19 Profit from a Short Forward Position Profit Price of Underlying at Maturity, S T K

20. 1.20 Futures Contracts Agreement to buy or sell an asset for a certain price at a certain time Similar to forward contract Whereas a forward contract is traded OTC a futures contract is traded on an exchange

21. 1.21 Exchanges Trading Futures Chicago Board of Trade Chicago Mercantile Exchange BM&F (Sao Paulo, Brazil) LIFFE (London) TIFFE (Tokyo) and many more (see list at end of book)

22. 1.22 1. Gold: An Arbitrage Opportunity? Suppose that: -The spot price of gold is US$300 -The 1-year forward price of gold is US$340 -The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?

23. 1.23 2. Gold: Another Arbitrage Opportunity? Suppose that: -The spot price of gold is US$300 -The 1-year forward price of gold is US$300 -The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?

24. 1.24 The Forward Price of Gold If the spot price of gold is S & the forward price for a contract deliverable in T years is F, then F = S (1+r ) T where r is the 1-year (domestic currency) risk- free rate of interest. In our examples, S=300, T=1, and r=0.05 so that F = 300(1+0.05) = 315

25. 1.25 Gold Example For the gold example, F 0 = S 0 (1 + r ) T (assuming no storage costs) If r is compounded continuously instead of annually F 0 = S 0 e rT

26. 1.26 When an Investment Asset Provides a Known Dollar Income (page 58) F 0 = (S 0 – I )e rT where I is the present value of the income

27. 1.27 When an Investment Asset Provides a Known Dividend Yield F 0 = S 0 e (r–q )T where q is the average dividend yield during the life of the contract

28. 1.28 Valuing a Forward Contract Page 59 Suppose that K is delivery price in a forward contract & F 0 is forward price that would apply to the contract today The value of a long forward contract, ƒ, is ƒ = (F 0 – K )e –rT Similarly, the value of a short forward contract is (K – F 0 )e –rT

29. 1.29 Stock Index Can be viewed as an investment asset paying a continuous dividend yield The futures price & spot price relationship is therefore F 0 = S 0 e (r–q )T where q is the dividend yield on the portfolio represented by the index

30. 1.30 Stock Index (continued) For the formula to be true it is important that the index represent an investment asset In other words, changes in the index must correspond to changes in the value of a tradable portfolio The Nikkei index viewed as a dollar number does not represent an investment asset

31. 1.31 Index Arbitrage When F 0 >S 0 e (r-q)T an arbitrageur buys the stocks underlying the index and sells futures When F 0 <S 0 e (r-q)T an arbitrageur buys futures and shorts or sells the stocks underlying the index

32. 1.32 Index Arbitrage (continued) Index arbitrage involves simultaneous trades in futures & many different stocks Very often a computer is used to generate the trades Occasionally (e.g., on Black Monday) simultaneous trades are not possible and the theoretical no-arbitrage relationship between F 0 and S 0 may not hold

33. 1.33 Hedging Using Index Futures To hedge the risk in a portfolio the number of contracts that should be shorted is where P is the value of the portfolio,  is its beta, and A is the value of the assets underlying one futures contract

34. 1.34 Changing Beta What position in index futures is appropriate to change the beta of a portfolio from  to  *

35. 1.35 A foreign currency is analogous to a security providing a continuous dividend yield The continuous dividend yield is the foreign risk-free interest rate It follows that if r f is the foreign risk-free interest rate Futures and Forwards on Currencies

36. 1.36 Futures on Consumption Assets F 0  S 0 e (r+u )T where u is the storage cost per unit time as a percent of the asset value. Alternatively, F 0  (S 0 +U )e rT where U is the present value of the storage costs.

37. 1.37 The Cost of Carry The cost of carry, c, is the storage cost plus the interest costs less the income earned For an investment asset F 0 = S 0 e cT For a consumption asset F 0  S 0 e cT The convenience yield on the consumption asset, y, is defined so that F 0 = S 0 e (c–y )T

38. 1.38 Futures Prices & Expected Future Spot Prices Suppose k is the expected return required by investors on an asset We can invest F 0 e –r T now to get S T back at maturity of the futures contract This shows that F 0 = E (S T )e (r–k )T

39. 1.39 Futures Prices & Future Spot Prices If the asset has –no systematic risk, then k = r and F 0 is an unbiased estimate of S T –positive systematic risk, then k > r and F 0 < E (S T ) –negative systematic risk, then k E (S T )

40. 1.40 1. Oil: An Arbitrage Opportunity? Suppose that: -The spot price of oil is US$19 -The quoted 1-year futures price of oil is US$25 -The 1-year US$ interest rate is 5% per annum -The storage costs of oil are 2% per annum Is there an arbitrage opportunity ?

41. 1.41 2. Oil: Another Arbitrage Opportunity? Suppose that: -The spot price of oil is US$19 -The quoted 1-year futures price of oil is US$16 -The 1-year US$ interest rate is 5% per annum -The storage costs of oil are 2% per annum Is there an arbitrage opportunity ?