Introduction to Equity Derivatives
Course Agenda Part 1: Introduction to Equities The Basics Types of Stock Dividends Corporate Actions Underlyings Market Institutions Part 2: Introduction to Derivatives Definition Origins Asset Classes, Types & Products Trading Methods Settlement Methods Part 3: Forwards & Futures Contract Features Valuation Spot vs. Forward The Distribution Graph
Course Agenda Part 4: Options Options vs. Forwards Contract Features Basic Option Valuation The Greeks Option Strategies Part 5: Equity Swaps & Dividend Swaps The Basics Price Return vs Total Return Bullet Swaps vs Resets Trading Strategies Dividend Swaps Part 6: Variance, Exotics & Correlation Variance Definition Variance Derivative Products Exotic Terms & Features Correlation Definition Correlation Derivative Products
Introduction to Equity Derivatives Part 1: Introduction to Equities 4
Stocks and shares: The basics Why do shares get issued? How are share prices determined? What drives share prices up and down? Why do people invest in shares? 5
Stocks and shares: Shareholder rights Part ownership Voting rights: A vs B shares Concept of limited liability Dividends Common Stock vs Preferred Stock 6
Company Payment Obligations Company Employees Premises Taxes & Svcs Loans Bonds Dividends on Preferred Shares Dividends on Ordinary Shares 7
Dividends: the basics Why are they issued? How are they determined? Company obligations re dividends Dividend dates: declaration, ex-dividend, record & payment Cash vs Stock dividendsid d Regular vs Extraordinary dividends 8
Corporate actions Stock Splits & Consolidations Mergers & Acquisitions Rights Issues Bonus Issues (aka Scrip or Capitalisation Issues) Spin-offs Nationalisation Delistings 9
Mergers & Acquisitions: Pros & Cons Pros - Increase in sales/revenues ie Procter & Gamble takeover of Gillette - Venture into new businesses and markets - Profitability of target company - Increase market share - Decrease competition (from the perspective of the acquiring company) - Reduction of overcapacity in the industry - Synergy of resources - Enlarge brand portfolio ie L'Oréal's takeover of Bodyshop Cons - Reduced competition and choice for consumers in oligopoly markets - Likelihood of price increases and job cuts - Cultural integration/conflict with new management - Hidden liabilities of target entity 10
Mergers & Acquisitions: Top 5 in 2000s Rank Year Company A Company B Value (USD) 1 2000 AOL Time Warner 164,747,000,000 2 2007 RBS, Fortis, Santander ABN AMRO 95,500,000,000 3 2000 Glaxo Wellcome SmithKline Beecham 75,961,000,000 4 2004 Royal Dutch Shell 74,559,000,000 5 2006 AT&T Inc BellSouth Corp 72,671,000,000 11
Equity Underlyings Shares Indices Baskets ADRs 12
Underlyings: Basket Example Share Share Price Shares of each Share start value A 10 2.5 25 B 20 1.25 25 C 30 0.8333 25 D 40 0.625 25 Total: 100 100 13
Stock Exchanges Tokyo Stock Exchange London Stock Exchange New York Stock Exchange 14
Stock Exchanges: the basics Products Listings Primary Market vs Secondary Market Open Outcry vs Electronic Clearance Systems 15
Stock Exchanges: its roles The main roles of stock exchanges are: - Raising capital for businesses - Mobilizing savings for investment - Facilitating company growth - Redistribution of wealth - Corporate governance - Creating investment opportunities for small investors - Government capital-raising for development projects - Barometer of the economy 16
Stock Exchanges: Black Monday DJIA Drops 22.6% (508 points) 604.33 million shares traded (a new record) Previous record set on the previous Friday (338 million shares) Only half a day of trading on Black Monday overtook this number Ticker board was so heavily inundated it ran 2 hours behind the market 17
Stock Exchanges: Black Monday (cont d) Possible Factors - Share Overvaluation? - Programme Trading? - Trade & Budget Deficits? Resulting Changes - Restriction of Programme Trading - Introduction of circuit breakers ie the SEC now requires that all exchanges cease trading in the event that one of these circuit breakers is triggered 18
Introduction to Equity Derivatives Part 2: Introduction to Derivatives 19
What is a Derivative? Definition History Asset Classes Leverage Future Settlement 20
Creation of a Derivative CHOICE ASSET CLASSES INTEREST RATES EQUITIES F/X DERIVATIVE TYPE CREDIT COMMODITIES OTHER SINGLE NAME DERIVATIVE PRODUCTS BASKET INDEX FORWARD SWAP OPTION EXOTIC OPTION CORRELATION 21
Derivatives Overview Long vs Short OTC vs ETD Cash vs Physical 22
ETD vs OTC Overview Contract Specifications Contract Payments Contract Flexibility ETD Standardised by derivatives exchange Margin paid into exchange clearing house account Freely tradable on exchange OTC Determined on trade-bytrade basis between parties Paid directly between parties Unbreakable unless agreed otherwise by parties Contract Agreement of trade verified Legal confirmation signed Obligation by exchange between parties 23
Introduction to Equity Derivatives Part 3: Forwards & Futures 24 24
Forwards: Contract Specifications Number of Forwards Forward Price Valuation/Settlement Date Settlement Terms 25
Forwards vs Futures Overview Futures Forwards Contract Standardised by derivatives Determined on trade-by- Specifications exchange trade basis between parties Contract Payments Contract Flexibility Margin paid throughout life of trade into exchange clearing house account Freely tradable on exchange Paid directly between parties at maturity Unbreakable unless agreed otherwise by parties Contract Buyer pays seller current Buyer pays seller agreed Obligation market price forward price Contract Agreement Agreement of trade verified by exchange Legal confirmation signed between parties 26
Forwards vs Futures: An example Today Share price of XYZ Ltd = $100 per share Both Bank A and Bank B believe the price will increase over the next year Bank A elects to buy a 1 year forward contract from another bank Bank B elects to buy a 1 year futures contract on the derivatives exchange 27
Forwards vs Futures: An example (cont d) In one year s time Share price of XYZ Ltd = $200 per share Bank A obliged to buy shares @ $100 = Bank A net + $100 Bank B obliged to buy shares @ $200 & receives $100 from margin account Bank B net + $100 Both banks net the same amount although the cash flows are slightly different 28
Forward Valuation Forward Price = Spot Price + (Carry Cost Benefit) Basis Spot vs Forward Arbitrage 29
Spot vs Forward 30
Forward Trading Example 1 Forward Price = $105 (ie too high) Today Borrow $100 from bank & buy shares now Sell forward @ $105 In one year s time Deliver shares & receive $105 Receive $2 dividends (total receivables $107) Repay the bank your original $100 plus rate @ 5% = $105 Therefore total = + $107 - $105 = + $2 31
Forward Trading Example 2 Forward Price = $101 (ie too low) Today Borrow the shares from the stock-borrow market & sell them for $100 Invest $100 in bank Buy forward @ $101 In one year s time Receive shares & pay $101 Give back these shares to lender & pay $2 dividends (total payments $103) Withdraw your original $100 from bank plus interest @ 5% = $105 Therefore total = - $103 + $105 = + $2 32
Forward Price Distribution Graph Forward Price distribution chart assumes that the forward price will not move outside the 200-400 400 range Forward Price Distribution is centred around its mean 33
Forward Price Distribution Graph (cont d) Forward Trading Example Shape of Normal Distribution Normal Distribution is Bell shaped 34
Introduction to Equity Derivatives Part 4: Options 35 35
Options vs. Forwards Forward Price Forward Buyer obligated to buy at Forward Price Call Option Buyer has the right to buy at Strike Price 36
Options: Contract Specifications Option Style Option Type Number of Options Strike Price Expiration Date Settlement Terms 37
Options: Standard Option Formulae Call: N x Max (S K, 0) Put: N x Max (K S, 0) Where: N = Number of Options K = Strike Price of the Underlying S = Price of the Underlying when exercised 38
Options: Long Call P&L Graph 39
Options: Long Put P&L Graph 40
Options: Short Call P&L Graph 41
Options: Short Put P&L Graph 42
Option Valuation: the basics Option Value = Intrinsic Value + Time Value Intrinsic Value Time Value Volatility Length of Time to Expiry Other Factors 43
Option Valuation: The Greeks Delta Gamma Vega Theta Rho 44
Option Strategies: The Basics Synthetic Forwards Spreads Straddles Strangles Collars Butterfly 45
Option Strategies: Synthetic Forwards Number Of Option Trades = 2 Different Components: Seller Buyer Option Type Usually Net Premium = 0 46
Option Strategies: Synthetic Forwards 47
Option Strategies: Synthetic Forwards 48
Option Strategies: Spreads Vertical Spreads Horizontal Spreads Diagonal Spreads Ratio Spreads 49
Spreads: Vertical Spreads Number Of Option Trades = 2 Different Components: Seller Buyer Strike Price Premium (usually) 50
Spreads: Bull Call Spread Example: Buy 330 Strike Call Sell 350 Strike Call 51
Spreads: Bear Call Spread Example: Sell 310 Strike Call Buy 330 Strike Call 52
Spreads: Put Spreads Bear Put Spread Buy 330 Strike Put Sell 310 Strike Put Bull Put Spread Sell 350 Strike Put Buy 330 Strike Put 53
Spreads: Horizontal Spreads Number Of Option Trades = 2 Different Components: Seller Buyer Expiration Date Premium (usually) 54
Spreads: Diagonal Spreads Number Of Option Trades = 2 Different Components: Seller Buyer Strike Price Expiration Date Premium (usually) 55
Spreads: Ratio Spreads Vertical or Horizontal Spreads Other Different Components (ie Number of Options) 56
Option Strategies: Straddles Number Of Option Trades = 2 Different Components: Option Type Premium (usually) 57
Option Strategies: Straddles 58
Option Strategies: Straddles 59
Option Strategies: Strangles Number Of Option Trades = 2 Different Components: Option Type Strike Price Premium (usually) 60
Option Strategies: Strangles 61
Option Strategies: Strangles 62
Option Strategies: Collars Number Of Option Trades = 2 Different Components: Seller Buyer Option Type Strike Price Premium (usually) 63
Option Strategies: Collars 64
Option Strategies: Collars 65
Option Strategies: Butterfly Number Of Option Trades = 2 Different Components: Buy 1 call at (X a) strike with expiration date Z Sell 2 calls at X strike with expiration date Z Buy 1 call at (X + a) strike with expiration date Z 66
x-a x x+a 67
Introduction to Equity Derivatives Part 5: Equity Swaps & Dividend Swaps 68 68
Equity Swaps: the basics Swaps Equity Leg vs Interest Leg 69
Equity Swaps: Equity Return Notional x (Final Initial / Initial) Where: Notional = Agreed size of trade Final = Price of the underlying on valuation date Initial = Price of the underlying on start date Share Swap =Noof Shares x (Final Initial) Equity Leg vs Forward 70
Equity Swaps: Interest Return Notional x Interest Rate x Day Count Fraction Where: Notional = Agreed size of trade Interest Rate = Floating Rate or Fixed Rate Floating Rate = Rate for period +/- spread Fixed Rate = A predetermined rate for all periods Day Count Fraction = Fraction used for rate (ie Act / 360) 71
Equity Swaps: Price Return vs Total Return What is Price Return? What is Total Return? Standard Defaults: Index & Share Swaps 72
Equity Swaps: Price Return Swap Cashflows 73
Equity Swaps: Total Return Swap Cashflows 74
Equity Swap Periods: Bullet Swap 75
Equity Swap Periods: Resetting Swap 76
Equity Swaps: Applications Avoid transaction costs (including tax) Avoid locally based dividend taxes Avoid limitations on leverage To get around rules governing the particular type of investment that an institution can hold Banks make money on commissions, interest rate spreads & dividend spreads (risk-neutral position) 77
Equity Swap: A Real Life Example Client Situation An Italian corporate wants to buy a 500,000 shares of ENI Spa BUT they don t have enough cash Bank A Solution Client can gain exposure via a swap with nominal of 500,000 Italian Corporate Pays/receives ENI Spa performance + pays dividends Bank A Equity Swap Buyer Pays Libor + 50bp Equity Swap Seller Client doesn't put up capital and pays financing at Libor + 50bp Bank A makes 50bp spread 78
Example of a Yield Enhancement Trade Client Situation - Client has cash to invest - Dividend income it generates is tax exempt Bank A Solution - Bank A sells shares to Spanish bank - Spanish bank writes Bank A an equity swap on the shares - Bank A covers short by borrowing from the street at 92% Bank A sells shares Spanish bank Pays/receives performance + 100% of dividends Receives Funding Bank A Client pays cash MOD 92% Borrows shares Lender Client receives Funding Bank A Receives 100% of the dividend but only pays out 92% of manufactured dividend 79
Long Total Return Swap with Hedges 80
Short Total Return Swap with Hedges 81
Dividend Swap Cashflows 82
Introduction to Equity Derivatives Variance, Exotics & Correlation 83 83
Variance: the basics Variance = Volatility 2 (σ 2 ) Derivatives annualise (x 252 days) the average daily percentage gain/loss in an underlying's price Variance Swaps Variance Options Conditional Variance Swaps 84
Variance: Variance Swaps Swap or Forward? Payout = Variance Amount x (FRV 2 - Variance Strike Price) FRV = 100 x N 252 t = 1 N LN P t P t 1 2 Index vs Share Variance Swaps Advantages 85
Variance: Variance Swaps Example Example: Spot Vol = 18% Vega = 10,000 Variance Amount = Vega/(100x2xSpot Vol) = 277.7 18% FRV = 22% Payout = 277.7 x (22 2 18 2 ) = 44,432 FRV = 16% Payout = 277.7 7 x (22 2 16 2 )= - 63,316 316 Final Realised Volatility 86
Variance: Variance Options Option vs Forward Payout = MAX[0; Variance Amount x (FRV 2 - Variance Strike Price)] 87
Variance: Variance Options Example Example: Desired Strike = 20% (OTM) Spot Vol = 18% Vega = 10,000 Variance Amount = Vega/(100x2xSpot Vol) = 277.7 Premium = 2000 Final Realised Volatility Strike Price (20%) FRV = 22% Payout = 277.7 x (22 2 20 2 ) = 23,326 Profit = 21,236 FRV = 16% Payout = Zero Profit = - 2000 88
Variance: Conditional Variance Swaps Up-Variance Down-Variance Corridor Variance Swaps 89
Exotics: Option Payout Formulae Call: Notional x Max [(S K) / R, 0] Put: Notional x Max [(S K) / R, 0] Where: K = Strike Price of the underlying S = Price of the underlying when exercised R = Spot price of the underlying at the time of trade 90
Exotics: Funded Options What are Funded Options? Options or Swaps? 91
Exotics: Forward Starts & Lookbacks Call Payout: Max(S-K,0) Standard: K = Actual level (ie 5000 or EUR 50) Forward Start: K = Trade Date + 3 months Lookback: K = Min(P1, P2, P3) where P1 = Price of underlying on Date 1 P2 = Price of underlying on Date 2 P3 = Price of underlying on Date 3 92
Exotics: Asians Call Payout: Max(S-K,0) Standard: K = Actual level (ie 5000 or EUR 50) S = Price of underlying on Expiration Date Asian In: Asian Out: K = (P / N) OR S = (P / N) where P = Price of underlying on the Asian dates N = Number of Asian valuation days 93
Exotics: Composite Composite = Cross Option + FX Fluctuation Risk Example Call on IBM standard payout: $ = No of Options x Max(S-K,0) Call on IBM composite payout: = No of Options x Max(S/Q 1 -K/Q 2,0) where S = $ Settlement Price K = $ Strike Price Q 1 = Prevailing $/ FX rate at time Strike Price taken Q 2 = Prevailing $/ FX rate at time Settlement Price taken 94
Exotics: Quanto Quanto = Cross Option - FX Fluctuation Risk Example Call on IBM standard payout: $ = No of Options x Max(S-K,0) Call on IBM quanto payout: = No of Options x Max(S/Q 1 -K/Q 1,0) where S = $ Settlement Price K = $ Strike Price Q 1 = Prevailing $/ FX rate at time Strike Price taken 95
Exotics: Out Of Currency Out of Currency = Standard Option + Payout FX Conversion Example Call on IBM standard payout: $ = No of Options x Max(S-K,0) Call on IBM OOC payout: = [No of Options xmax(s-k,0)]/q 2 where S = $ Settlement Price K = $ Strike Price Q 2 = Prevailing $/ FX rate at time Settlement Price taken 96
Exotics: Barriers Up-and-out Down-and-out Up-and-in Down-and-in Rebates 97
Exotics: Bermudan & Binary Bermudan vs American & European Binary vs Standard Payout 98
Exotics: Rainbow Options Worst of/best Of: Min(Perf1;Perf2)/Max(Perf1;Perf2) Call on Best Of: Max (0; Max(Perf1; Perf2)) Put on Worst Of: Max(0; Min(Perf1; Perf2)) Outperformance: Max(0; Perf1 - Perf2) 99
Exotics: Correlation Correlation: The Basics Positive Correlation Negative Correlation Dispersions & Correlation Swaps 100