Class 3 Derivatives 1 Why should we

Class 3. Derivatives 1

Why should we study derivatives? q Second level securities – Payoff depends on the value of other (underlying) securities / variables – Possibility for an arbitrage in case of price disparity between derivative and underlying q Huge volume of financial derivatives – Notional over $700 trln q Many instruments are like derivatives – Bonuses are tied to performance – Prices of stocks and bonds depend on the company’s value – Value of the investment project depends on future cash flows FMI 3 -2

How it started q Antiquity: first contracts (written on clay tablets) appeared in Mesopotamia around 2000 BC as contracts for future delivery of goods – E. g. merchant receives 6 shekels of silver and, in exchange, will repay it in 6 months with sesame, at the going rate – Played an important role in financing long-distance trade q Middle ages: most contracts were private, between parties – Byzantine Roman emperors Theodosian and Justinian (~400 AD) developed laws which allowed contracts to be traded q Renaissance: shares and bills of exchange were first issued by Italian city-states and then by other European cities – Amsterdam: emergence of cash-settled contracts (like CFD, contracts for difference), options on shares, and short-selling – 1637: crash of tulip market (largely consisting of CFD and options, OTC) FMI 3 -3

How it continued q Great Britain: – South Sea Company was created in 1711, its stocks and options were actively traded, the bubble collapsed in 1720 – 1734: CFDs and options on stocks became unenforceable in courts and continued trading only OTC – Commodity-based contracts continued trading at the Royal Exchange q France: – John Law founded Compagnie des Indes whose shares rose 20 -fold and then collapsed in 1720 – Contracts for future delivery and short-sale were banned, done OTC – 1853: first book on options & forwards, Manuel du Speculateur by Proudhon FMI 3 -4

How it evolved q 1848: creation of the Chicago Board of Trade, with `To-Arrive’ contract for grains q 1925: first futures clearinghouse q 1970 s: currency and interest rate futures, equity options q 1980 s: interest rate swaps traded OTC q 1983: Freddie Mac issues first Collateralized Mortgage Obligation q 1990 s: credit derivatives (CDS, CDO = Collateralized Debt Obligations) q 2008: subprime global financial crisis

Example: How to sell oil? q An oil company needs to sell 1 mln. barrels in 1 year – The current oil price is $108 q Strategy 1: sell at the market price – What if the market price falls to $90? – Strategy 1 does not protect from the oil price risk q Strategy 2: sell now at one-year forward price $100 – What if the market price rises to $120? – Strategy 2 does protect from the downside risk, but also eliminates an upside potential FMI 3 -6

What is the forward’s payoff? q Obligation to buy / sell the underlying asset at T at the settlement price K – Long / short position – May be offset by the counter deal q There is no exchange of payments when the contract is signed – The settlement price is chosen to make the contract worth exactly zero q Payoff at T: ST-F – Symmetric for the buyer and seller 3 -7 FMI Payoff at maturity

How can one apply forward (futures)? q Hedging: reducing undesirable risks arising from the underlying business activity – E. g. , the farmer grows grain to sell in September – By selling September forward on grain in spring, he can eliminate the price risk (though not the risk of a poor crop) q Speculating: taking risky position in hope for profit – If you expect bullish market, buy futures on the stock market index – Derivatives give leverage and increase both expected return and risk q Arbitrage: finding a riskless profit opportunity – Buy an undervalued asset and sell an overvalued asset with the same risk characteristics: e. g. , buy oil and sell oil futures – However, pure arbitrage is very rare: there always some risks FMI 3 -8

How to make forward an exchange-traded contract? Forward q Specific terms Futures q Standardized exchange-traded contract – Very flexible for the initiating side q Low liquidity – Amount, quality, delivery date, place, and conditions of the settlement q High liquidity → popular among speculators – Spot settlement – Hard to find the counterparty q Credit risk – Usually, cash settlement – Can be offset by taking an opposite position – Most contracts are eliminated before the delivery q Credit risk taken by the exchange – The possibility of the counterparty’s default – The exchange clearing-house is a counterparty – Collateral: the initial / maintenance margin • The margin account guarantees the settlement for the exchange – Marking to market daily • E. g. , long position: receive A*(Ft-Ft-1) into account • A is the position size, Ft is the settlement price at t 3 -9 FMI

Example: Futures on Gold (two contracts, each for 100 ounces) FMI 3 -10 Source: Hull

Discussion topic Are futures markets driven by speculators driving prices away from the fundamentals?

What are swaps? q Exchange of cash flows (‘legs’) linked to the underlying – Like a portfolio of forwards (same settlement price, different dates) q Currency swap – Periodic exchange of principal and/or interest payments denominated in different currencies at a fixed exchange rate q Interest rate swap – Periodic exchange of fixed-rate and floating-rate interest payments for a fixed notional value • E. g. , fixed 4% for floating LIBOR What are swaps usually used for? 3 -12 FMI

Example cont. : How to sell oil? q Can we protect from downside losses while keeping upside profits? q Strategy 3: – Buy the right to sell oil at a fixed price $90 –. . at a cost of $5 q This is a put option – $90 is strike price – $5 is option’s premium 3 -13 FMI

Options terminology q European call (put): – Right to buy (sell) the underlying asset at the expiration/maturity date T at strike/exercise price K q American call (put): – Can be exercised at any time before T – Always more expensive than European one q Option is a right for the buyer, only exercised if profitable – An obligation for the option writer to fulfil his promise, if necessary – The payoff function is asymmetric! q The option is worth at least zero – You can’t lose by holding an option – In some scenarios you win 3 -14 FMI

What is the main factor driving the option’s premium? q The option’s premium is higher than intrinsic value (profit from the option if exercised now) q Time value (option’s premium - intrinsic value) is positive, since the stock price can change before maturity – If the stock price goes up, the call option will give a higher profit – If the stock price falls, the call option’s losses are limited to 0 q The higher the stock’s volatility, the better! 3 -15 FMI

How to price options? q No-arbitrage approach – If two portfolios yield the same payoff in the future, they must have the same price now q Example: synthetic forward = long call + short put q European call-put parity: – Call with cash = covered put c 0 + Ke-r. T = p 0 + S 0 q Black-Scholes model (1973) – Represent European options as dynamic portfolio of stocks and bonds FMI 3 -16

Are options used for hedging oil? q Mexico hedged its oil exports for year 2014 – Options locked in a price of just over $90 per barrel – “Despite the shale oil boom, the reality is that today we are in a high cost environment, and that will find its ways into long-term price arrangements” q Most producers tend to sell oil at market prices. Mexico uses options to ensure a minimum price for its exports. q The country’s oil hedging programme is the largest of its kind in commodity markets, creating significant downward pressure on futures prices. q This year’s trades took place over the past four weeks as oil prices climbed to more than $115 per barrel. – “The price was high and volatility was low by historical standards so the moment was right” q The fees paid for the investment banks ranged from $750 m to $1. 2 bn in recent years.

Where else are options used? q Convertible bonds: embedded call option on a stock q Equity as a call option – Shareholders ‘buy’ their company when they pay off fixed amount of debt – They can’t incur losses due to limited liability – Bondholders may receive a share in the company’s profits q Redeemable bonds: embedded short call option on the bond – The company can buy out the bond for the face value if the interest rates fall q Real options – E. g. , the oil company may invest into extra transportation capacity – Then it will be able to sell more oil in case of high oil price q Executive stock options – Call on the company’s stock given to the managers for proper incentives 3 -18 FMI

Financial engineering: Exotic options q Bermudan option – Can be exercised at several exercise dates q Exchange option: max(SA-SB, 0) – Gives right to exchange one asset for another q Binary option: I{ST-X>0} – Fixed payoff q Asian option: max(Savg-X, 0) – Payoff depends on average rather than final price FMI 3 -19

Derivatives statistics q How can we measure derivatives’ volume? – Notional / market value / turnover q Where are the largest volumes of derivatives (by notional)? – At the exchanges or OTC? q Where are the largest trading volumes of derivatives? – At the exchanges or OTC? q What is the most popular underlying? – Equities / currencies / interest rates / commodities q Which type of derivatives is most popular? – Forward / futures / swap / option FMI 3 -20

OTC derivatives statistics ($bln) FMI 3 -21

Derivatives traded on the organized exchanges: Futures ($bln) FMI 3 -22

Derivatives traded on the organized exchanges: Options ($bln) FMI 3 -23

Discussion topic What are main benefits and main costs of derivatives?

Mini-case: Warren Buffet’s view on derivatives in 2002 q We view [derivatives] as time bombs, both for the parties that deal in them and the economic system. q Derivatives business [is] like hell …easy to enter and almost impossible to exit. Once you write a contract - which may require a large payment decades later - you are usually stuck with it. q. . . the macro picture is dangerous. Large amounts of risk …concentrated in the hands of relatively few derivatives dealers. q had [the Fed] not intervened, …the LTCM could well have posed a serious threat to the stability of American markets. q The derivatives genie is now well out of the bottle. …derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal. FMI 3 -25

Many cases of big losses Year Company Instruments Losses 1994 Orange County interest rate derivatives $1. 7 bln 1995 Barings stock index futures $1. 4 bln 1996 Sumitomo copper options $2. 6 bln 2006 Amaranth energy futures/options $6. 2 bln 2008 Societe Generale stock index futures € 4. 8 bln 2008 - Bear Sterns, Lehman subprime mortgages, Brothers, Citi, MBS, CDO, CDS UBS, … FMI >$1 trln 3 -26

Derivatives: Pros and cons Efficient risk management at q Derivatives allow companies low cost increase leverage q Hedging risks – This may lead to excessive risks and ultimately to the bankruptcy – Make risk-offsetting bets q Speculating – Take a view on the future direction of the market q Derivatives are hard for accounting – Esp. illiquid (traded OTC) – May be used for manipulations q Doing arbitrage – Long-short (self-financed) portfolio q Changing the nature of liability/investment q Derivatives increase systemic risks – Four megabanks – JPM, Bo. A, Citi, Goldman – control a large share of the derivatives market – Without a need to remove it FMI 2 -27