Introduction to Derivatives Advanced Investments 1 Introduction to Derivatives What Is a Derivative? Uses and Misuses Forwards Futures Options

What Is a Derivative? Definition Types Uses Advanced Investments 1 What Is a Derivative? Definition An agreement between two parties which has a value determined by the price of something else Types Options, futures and swaps Uses Risk management (hedging risks) Speculation Reduce transaction costs Regulatory arbitrage Investments 21

Increased Volatility… Advanced Investments 1 Increased Volatility… Oil prices: DM/$ rate: Investments 21

…Led to New and Big Markets Advanced Investments 1 …Led to New and Big Markets Exchange-traded derivatives Over-the-counter traded derivatives: even more! Investments 21

It’s Not What It Is, It’s How You Use It… Risk management or speculation? How big a bet can you make with derivatives? Q: How can one trader bring down the oldest British bank? A: Futures and Options! (see Nick Leeson) What about closer to home? Orange County, CA went bankrupt in 1994 When Genius Failed - LTCM debacle in 1998 Avoiding regulations, taxes, and transaction costs – is it always worth it? Investments 21

Financial Engineering Advanced Investments 1 Financial Engineering The construction of a financial product from other products New securities can be designed by using existing securities Financial engineering principles Facilitate hedging of existing positions Enable understanding of complex positions Allow for creation of customized products Render regulation less effective Investments 21

Forward Contracts Advanced Investments 4 Definition: a binding agreement (obligation) to buy/sell an underlying asset in the future, at a price set today Hedges risk by locking in future price A forward contract specifies The features and quantity of the asset to be delivered The delivery logistics, such as time, date, and place The price the buyer will pay at the time of delivery Pros: Flexible Cons: Lack of liquidity: hard to find counterparty Subject to default risk: requires information to screen good from bad risk Today Expiration date Investments 21

Payoff on a Forward Contract Advanced Investments 4 Payoff on a Forward Contract Long position = agree to buy securities (commodities) at future date Short position = agree to sell securities (commodities) at future date Payoff for a contract is its value at expiration: Long forward = Spot price at expiration – Forward price Short forward = Forward price – Spot price at expiration Example 2.1: S&R (special and rich) index: Today: Spot price = $1,000, 6-month forward price = $1,020 In six months at contract expiration: Spot price = $1,050 Long position payoff = $1,050 – $1,020 = $30 Short position payoff = $1,020 – $1,050 = ($30) Investments 21

Payoff Diagram for Forwards Advanced Investments 4 Payoff Diagram for Forwards Long and short forward positions on the S&R 500 index Investments 21

Futures Markets Financial Futures Contract Advanced Investments 4 Financial Futures Contract Futures are just standardized forward contracts that are traded on exchanges At expiration date, price of contract = price of the underlying asset delivered Prior to the expiration date, it is easily prices using the “cash and carry” approach Exchanges: CBOE, CME, etc. Regulated by CFTC (Commodity Futures Trading Comission) Success of Futures Over Forwards Futures more liquid: standardized, can be traded again, delivery of range of securities Mark to market and margin requirements: avoids default risk Anybody can write (issue) futures and options Flexible types of settlement Cash settlement by netting: less costly and more practical Physical delivery: often avoided due to significant costs Investments 21

Options - Introduction BUSI 186: Investments 19 Options - Introduction Definition Option is a right to buy or sell an underlying asset at a specified price on or before a specified date Key Elements Specified Price: Exercise or Strike Price Specified date: Expiration date Exercise only on expiration date: European Option Exercise on or before expiration: American Option Option Premium or Price: the price of the option Call: Right to buy Put: Right to sell Investments 21

Options - Introduction BUSI 186: Investments 19 Options - Introduction Example: on 11/29/2005, MSFT Jan 27 Call trades at $1.20; MSFT stock price is $27.68 What does it tell us? Style: American Call Underlying Security: MSFT Stock Strike Price: $27 Expiration Month: Jan, 2006 Expiration Date: The 3rd Friday Current asset price: $27.68 Call price (premium): $1.20 Investments 21

Option Values Option Creation and Exercise: 11/29/2005: 1 contract of MSFT Jan 27 call created 1/20/2006 or before: buyer exercises call When to exercise? Decision: exercise if St > $27 Payoff per share: St - $27 Pay Option Premium = $1.20 x 100 Option Buyer (Long position) Option Seller (Short position) MSFT Jan 27 Call Pay $27 x 100 Option Buyer (Long position) Option Seller (Short position) 100 shares of MSFT stock Investments 21

Option Values Moneyness In-the-money (ITM): positive payoff for immediate exercise For call: St – X > 0 For put: St – X < 0 At-the-money (ATM): zero payoff for immediate exercise For both call and put: St – X = 0 Out-of-the-money (OTM): negative payoff for immediate exercise For call: St – X < 0 For put: St – X > 0 Investments 21

Option Values Example: If current MSFT stock price $27 Option 1: Jan 25 MSFT call in-the-money call Option 2: Jan 27 MSFT call at-the-money call Option 3: Jan 30 MSFT call out-of-the-money call Option 4: Jan 30 MSFT put in-the-money put Investments 21

Option Values Payoff versus P/L (Profit/Loss) Notation Security Price: St Strike (Exercise) Price: X Payoff per share at expiration for a call Payoff = max(ST – X, 0) Payoff = ST –X if ST > X or the option is in-the-money Payoff = 0 if ST < X or the option is out-of-the-money Profit or loss P/L = Payoff – Option Premium Investments 21

Option Values MSFT Jan 27 call trading at $1.20 Decision Time: 1/20/2006 Possible Price of ST - X Exercise Option Option MSFT on 1/20/06 (X = $27) Decision Payoff P/L $25 $25-$27 < 0 No Exercise 0 -1.20 $26 $26-$27 < 0 No Exercise 0 -1.20 $27 $27-$27 = 0 No Exercise 0 -1.20 $28 $28-$27 > 0 Exercise $1 -0.20 $29 $29-$27 > 0 Exercise $2 0.80 Investments 21

Option Values Payoff Diagram of MSFT Jan 27 Call X = $27 Payoff of A Call Option Value P/L ITM Region OTM Region X = $27 ST MSFT price at T -$1.20 (Premium) Investments 21

Options magnify both gains and losses Option Value Leverage Effect of a Call MSFT price $20; MSFT Jan 20 ATM call price $4 Start with $1,000 in the account Strategy 1 (all equity): buy 50 shares of MSFT Strategy 2 (all option): buy 2.5 contract* call Strategy 1 Strategy 2 ST Gain at T Return Gain at T Return $30 50*10 50% 2.5*100*6 150% $10 50*(-10) -50% 2.5*100*(-4) -100% Options magnify both gains and losses * for 100 shares each Investments 21

Option Value Payoff Diagram for MSFT Jan 27 Put Value Payoff of Puts at T: = X - ST if ST < X = 0 if ST > X $27 Payoff P/L X = $27 ST MSFT Price at T ITM Region OTM Region -$0.30 Investments 21

Option Strategy Building Blocks: Call and long stock Payoff at T long call call - premium ST Payoff at T long stock at $27 X=27 -$1.20 stock - $27 Payoff at T ST X=27 $1.20 -$27 ST X short a call + premium short call Investments 21

Option Strategy Building Blocks: put and short stock long a put short a stock at 27 ST X ST X short a put ST X Investments 21

Option Strategy Protective Put Long stock + Long put Pay put premium for downside protection Long a stock ST X Protective put X ST X X Long a put ST X Investments 21

Option Strategy Covered Call Long stock + short call Sacrifice upside potential for call premium Payoff at T Write a call X ST Keep the Stock X Sell the stock for X Payoff at T Long a stock at X ST X ST X Investments 21

Example – BXM Index Covered Index Strategy BXM – CBOE Buy-Write Monthly Index Introduced in 2002 Long S&P 500 Index Exposure Short at-the-money 1-month call option on the S&P 500 Rebalance monthly on expiration Friday Idea: ATM S&P 500 call options are relatively overpriced Investments 21

BXM Index Performance In 1990 – 2004: Recent developments: PBP ETF HVPW ETF   Annual Return (%) Annual Risk (%) S&P 500 10.94 14.65 BXM 11.34 9.92 Investments 21

Option Strategy Vertical Spread Long call with strike X1 and short a call with X2 Limited up- and down-side P/L Payoff at T Long Jan 27 call Bullish Spread X2 > X1 X2 - X1 ST ST X1=27 X2=30 X1 X2 X2 X1 ST Short Jan 30 call Bearish Spread X2 < X1 ST X2 - X1 X1 X2 Investments 21

Option Strategy Straddle Long a call and a put with the same strike price Benefit from big jumps in stock prices Payoff at T Long Jan 30 call ST X=30 Straddle X X ST X Long Jan 30 Put ST X Investments 21

Variations Index Options Futures Options Foreign Currency Options Options on index level: e.g. call on S&P 500, NASDAQ100, etc. Futures Options Options on futures: e.g. put on gold futures Foreign Currency Options Options on foreign currency: e.g. call on Euro Interest Rate Options Options on interest rate: e.g. Interest rate caps as call option on LIBOR rate Investments 21

Other Options Warrants Bermudan Options Asian Options Essentially call options issued by a firm Bermudan Options Discrete time multiple exercises Asian Options Payoff based on average price Investments 21

Option Pricing and Volatility Options price uncertainty (or volatility)! Example: Call Option Prices Option price prior to expiration Option price at expiration Investments 21

Implied vs. Realized Volatility Which one is more useful? Investments 21

Wrap-up Futures markets – hedging or speculation? What is an option? Why do we need options? What are the common investment strategies involving options? What is in the price of an option, and what it tells us about the underlying security? How big a bet can you make with derivatives? Can one trader bring down a bank? Investments 21