[Derivatives Consulting Group] Introduction to Equity Derivatives

Introduction to Equity Derivatives

© February 2008 - The Derivatives Consulting Group Ltdwww.dcgconsultants.com

C A dCourse Agenda

Part 1: Introduction to Equities

• The Basics• The Basics• Types of Stock• Dividends• Corporate Actions• Underlyings• Market InstitutionsMarket 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 AgendaCourse Agenda

Part 4: Options

• Options vs. Forwardsp• 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



Part 1: Introduction to EquitiesPart 1: Introduction to Equities

© February 2008 - The Derivatives Consulting Group Ltdwww.dcgconsultants.com 4

Stocks and shares: The basics

• Why do shares get issued?

• How are share prices determined?• How are share prices determined?

• What drives share prices up and down?

• Why do people invest in shares?


55

Stocks and shares: Shareholder rights

• Part ownership

• Voting rights: A vs B shares• Voting rights: A vs B shares

• Concept of limited liability

• Dividends

• Common Stock vs Preferred Stock


66

Company Payment Obligations

Company

Employees Premises Taxes & Svcs

Loans Bonds

Dividends on Preferred SharesDividends on Preferred Shares

Dividends on Ordinary Shares


7

Dividends: the basics

• Why are they issued?

• How are they determined?How are they determined?

• Company obligations re dividends

• Dividend dates: declaration, ex-dividend, record & payment

C h St k di id d• Cash vs Stock dividends

• Regular vs Extraordinary dividends


88

Corporate actions

S k S l & C l d• Stock Splits & Consolidations

• Mergers & Acquisitions

• Rights Issues

• Bonus Issues (aka Scrip or Capitalisation Issues)• Bonus Issues (aka Scrip or Capitalisation Issues)

• Spin-offs

• Nationalisation

• Delistings


g

99

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- Reduction of overcapacity in the industry- Synergy of resources - Enlarge brand portfolio ie L'Oréal's takeover of BodyshopCons- 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

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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 Gl W ll S ithKli B h 75 961 000 0003 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 72,671,000,0005 2006 AT&T Inc BellSouth Corp 72,671,000,000


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Equity Underlyings

• Shares

• Indices• Indices

• Baskets

• ADRs


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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 Tokyo Stock ExchangeExchange

London Stock London Stock ExchangeExchange New York Stock New York Stock

ExchangeExchange


14

ExchangeExchange

Stock Exchanges: the basics

• Products

• Listings• Listings

• Primary Market vs Secondary Market

• Open Outcry vs Electronic

• Clearance Systems


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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- Corporate governance- Creating investment opportunities for small investors- Government capital-raising for development projects- Barometer of the economyy


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Stock Exchanges: Black Monday

• DJIA Drops 22.6% (508 points)

• 604.33 million shares traded ( d)(a new record)

• Previous record set on the previous Friday (338 million shares)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? 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


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Part 2: Introduction to Derivatives


What is a Derivative?

• Definition

• History• History

• Asset Classes

• Leverage

• Future Settlement


2020

Creation of a Derivative

CHOICEASSET

CLASSESCLASSES

DERIVATIVE

F/XEQUITIES OTHERCREDIT COMMODITIESINTERESTRATES

DERIVATIVE TYPE

SINGLE NAME

INDEXBASKET

DERIVATIVE PRODUCTS

NAME


21

FORWARD SWAP OPTION EXOTIC OPTION CORRELATION

Derivatives Overview

• Long vs Short

• OTC vs ETD• OTC vs ETD

• Cash vs Physical


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ETD vs OTC Overview

ETD OTC

ContractSpecifications

Standardised by derivatives exchange

Determined on trade-by-trade basis between parties

Contract Payments

Margin paid into exchange clearing house account

Paid directly between partiesPayments clearing house account

Contract Flexibility

Freely tradable on exchange Unbreakable unless agreed otherwise by parties

Contract Agreement of trade verified Legal confirmation signed ContractObligation

Agreement of trade verified by exchange

Legal confirmation signed between parties


23


Part 3: Forwards & Futures


Forwards: Contract Specifications

• Number of Forwards

• Forward Price• Forward Price

• Valuation/Settlement Date

• Settlement Terms


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Forwards vs Futures Overview

Futures Forwards

ContractS ifi ti

Standardised by derivatives h

Determined on trade-by-t d b i b t tiSpecifications exchange trade basis between parties

Contract Payments

Margin paid throughout life of trade into exchange clearing house account

Paid directly between parties at maturity

g

Contract Flexibility

Freely tradable on exchange Unbreakable unless agreed otherwise by parties

Contract Buyer pays seller current Buyer pays seller agreed Obligation market price forward price

ContractAgreement

Agreement of trade verified by exchange

Legal confirmation signed between parties


2626

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 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


2727

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 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


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Forward Valuation

Forward Price = Spot Price + (Carry Cost – Benefit)

• Basis• Basis

• Spot vs Forward Arbitrage


2929

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


• 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


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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• Buy forward @ $101


• 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

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Forward Price Distribution Graph

• Forward Price distributionchart assumes that the forwardprice will not move outside the£200-£400 range£200 £400 range

• Forward Price Distribution iscentred around its mean


33

Forward Price Distribution Graph (cont’d)

• Shape of “Normal” Distribution

• Normal Distribution is “Bell”shaped

Forward Trading Example


34


Part 4: Options


Options vs. Forwards

Forward Price

Forward – Buyer obligated to buy at Forward Price

Call Option – Buyer has the rightto buy at Strike Price


36

Options: Contract Specifications

• Option Style

• Option Type• Option Type

• Number of Options

• Strike Price

• Expiration Date




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Options: Standard Option Formulae

Call: N x Max (S – K, 0)

Put: N x Max (K – S 0)Put: N x Max (K – S, 0)

Where:

N = Number of OptionsK = Strike Price of the Underlyingy gS = 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• Intrinsic Value

• Time Value

• Volatility

• Length of Time to Expiry

• Other Factors


43

• Other Factors

43

Option Valuation: The Greeks

• Delta

• Gamma

• Vega

• Theta

• Rho• Rho


4444

Option Strategies: The Basics

• Synthetic Forwards

• Spreads• Spreads

• Straddles

• Strangles

• Collars

• Butterfly


• Butterfly

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Option Strategies: Synthetic Forwards

• Number Of Option Trades = 2

• Different Components:• Different Components:

SellerBuyerOption Type

• Usually Net Premium = 0


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47



48

Option Strategies: Spreads

• Vertical Spreads

• Horizontal Spreads• Horizontal Spreads

• Diagonal Spreads

• Ratio Spreads


49

Spreads: Vertical Spreads



SellerBuyerStrike PricePremium (usually)( y)


5050

Spreads: Bull Call Spread

Example:B 330 St ik C ll• Buy 330 Strike Call

• Sell 350 Strike Call


51

Spreads: Bear Call Spread

Example:S ll 310 St ik C ll• Sell 310 Strike Call

• Buy 330 Strike Call


52

Spreads: Put Spreads

Bull Put SpreadBear Put Spread• Sell 350 Strike Put• Buy 330 Strike Put

• Buy 330 Strike Put• Sell 310 Strike Put


53

Spreads: Horizontal Spreads



SellerBuyerExpiration DatePremium (usually)( y)


5454

Spreads: Diagonal Spreads



SellerBuyerStrike PriceExpiration DatepPremium (usually)


5555

Spreads: Ratio Spreads

• Vertical or Horizontal Spreads

• Other Different Components (ie Number of Options)• Other Different Components (ie Number of Options)


5656

Option Strategies: Straddles



Option TypePremium (usually)


5757



58



59

Option Strategies: Strangles



Option TypeStrike PricePremium (usually)


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61



62

Option Strategies: Collars



SellerBuyerOption TypeStrike PricePremium (usually)


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64



65

Option Strategies: Butterfly


• Different Components:Different Components:

Buy 1 call at (X − a) strike with expiration date ZSell 2 calls at X strike with expiration date ZSell 2 calls at X strike with expiration date ZBuy 1 call at (X + a) strike with expiration date Z


6666

x x+ax-a


67


Part 5: Equity Swaps & Dividend Swaps


Equity Swaps: the basics

• Swaps

• Equity Leg vs Interest Leg


6969

Equity Swaps: Equity Return

Notional x (Final – Initial / Initial)

Where:Where:Notional = Agreed size of tradeFinal = Price of the underlying on valuation dateInitial = Price of the underlying on start date

• Share Swap = No of Shares x (Final – Initial)p ( )

• Equity Leg vs Forward


70

Equity Swaps: Interest Return

Notional x Interest Rate x Day Count Fraction

Where:Where:Notional = Agreed size of tradeInterest Rate = Floating Rate or Fixed RateFloating Rate Rate for period +/ spreadFloating Rate = Rate for period +/- spreadFixed Rate = A predetermined rate for all periodsDay 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?• What is Total Return?

• Standard Defaults: Index & Share Swaps


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Equity Swaps: Price Return Swap Cashflows


7373

Equity Swaps: Total Return Swap Cashflows


7474

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 aninstitution can hold

• Banks make money on commissions interest rate spreads & dividend• Banks make money on commissions, interest rate spreads & dividendspreads (risk-neutral position)


7777

Equity Swap: A Real Life Example

An Italian corporate wants to buy a 500,000 shares of ENI Spa Client can gain exposure via a swap

Client SituationClient Situation Bank A SolutionBank A Solution

BUT they don’t have enough cashwith nominal of 500,000

Italian CorporateBank A

Pays/receives ENI Spaperformance + pays dividends

Client doesn't put up capital and pays financing at Libor + 50bpB k A k 50b d

Pays Libor + 50bpEquity Swap Buyer Equity Swap Seller


Bank A makes 50bp spread

78

Example of a Yield Enhancement Trade

Client SituationClient Situation Bank A SolutionBank A Solution

- Client has cash to invest- Dividend income it generates is tax exempt

- 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

Bank A sells shares

Pays/receives performance + 100% of dividends

Bank ASpanish bank

Receives Funding

Client pays cashBorrows shares

MOD92%Client pays cash

Client receives Funding

Lender

shares92%


Client receives FundingBank 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


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Variance, Exotics & Correlation


Variance: the basics

• Variance = Volatility2 (σ2)

• Derivatives annualise (x 252 days) the average daily Derivatives annualise (x 252 days) the average daily percentage gain/loss in an underlying's price

• Variance Swaps• Variance Swaps

• Variance Options

• Conditional Variance Swaps


8484

Variance: Variance Swaps

• Swap or Forward?

• Payout = Variance Amount x (FRV2 - Variance Strike Price) Payout Variance Amount x (FRV Variance Strike Price)

N2

tPLN252 ∑× ⎟

⎟⎞

⎜⎜⎛

N1t 1tP

LN252

x 100FRV

∑= −

×

=⎟⎟⎠

⎜⎜⎝

• Index vs Share Variance Swaps

• Advantages


85

Advantages

85

Variance: Variance Swaps Example

Example:

S V l 18%• Spot Vol = 18%• Vega = £10,000• Variance Amount = Vega/(100x2xSpot

Vol) = 277.7

• FRV = 22%• Payout = 277.7 x (222 – 182) = £44,432

• FRV = 16%Payout = 277 7 x (222 162) = £63 316

18%

• Payout = 277.7 x (222 – 162) = -£63,316

Final Realised Volatility


8686

Variance: Variance Options

• Option vs Forward

• Payout = MAX[0; Variance Amount x (FRV2 - Variance Strike Price)]y [ ; ( )]


8787

Variance: Variance Options Example

Example:

• Desired Strike = 20% (OTM)S V l 18%• Spot Vol = 18%

• Vega = £10,000• Variance Amount = Vega/(100x2xSpot

Vol) = 277.7• Premium = £2000e u £ 000

• FRV = 22%• Payout = 277.7 x (222 – 202) = £23,326• Profit = £21,236Strike Price (20%)

• FRV = 16%• Payout = Zero• Profit = -£2000Final Realised Volatility


8888

Variance: Conditional Variance Swaps

• Up-Variance

• Down-Variance• Down-Variance

• Corridor Variance Swaps


8989

Exotics: Option Payout Formulae

Call: Notional x Max [(S – K) / R, 0]

Put: Notional x Max [(S – K) / R 0]Put: Notional x Max [(S – K) / R, 0]

Where:K = Strike Price of the underlyingS = Price of the underlying when exercisedR = Spot price of the underlying at the time of tradep p y g


90

Exotics: Funded Options

• What are Funded Options?

• Options or Swaps?• Options or Swaps?


91

Exotics: Forward Starts & Lookbacks

Call Payout: Max(S-K,0)

Standard: K = Actual level (ie 5000 or EUR 50)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 1y gP2 = Price of underlying on Date 2P3 = Price of underlying on Date 3


9292

Exotics: Asians

Call Payout: Max(S-K,0)

Standard: K = Actual level (ie 5000 or EUR 50)Standard: K = Actual level (ie 5000 or EUR 50)S = Price of underlying on Expiration Date

Asian In: K = ∑(P / N) ORAsian Out: S = ∑(P / N) where

P = Price of underlying on the Asian datesy gN = Number of Asian valuation days


9393

Exotics: Composite

• Composite = Cross Option + FX Fluctuation Risk

ExampleExample

Call on IBM standard payout: $ = No of Options x Max(S-K,0)Call on IBM composite payout: £ = No of Options x Max(S/Q1-K/Q2,0) whereS = $ Settlement Price$K = $ Strike PriceQ1 = Prevailing $/£ FX rate at time Strike Price takenQ2 = Prevailing $/£ FX rate at time Settlement Price taken


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Exotics: Quanto

• Quanto = Cross Option - FX Fluctuation Risk

ExampleExample

Call on IBM standard payout: $ = No of Options x Max(S-K,0)Call on IBM quanto payout: £ = No of Options x Max(S/Q1-K/Q1,0) whereS = $ Settlement Price$K = $ Strike PriceQ1 = Prevailing $/£ FX rate at time Strike Price taken


9595

Exotics: Out Of Currency

• Out of Currency = Standard Option + Payout FX Conversion

ExampleExample

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)]/Q2 whereS = $ Settlement Price$K = $ Strike PriceQ2 = Prevailing $/£ FX rate at time Settlement Price taken


9696

Exotics: Barriers

• Up-and-out

• Down-and-out• Down-and-out

• Up-and-in

• Down-and-in

• Rebates


9797

Exotics: Bermudan & Binary

• Bermudan vs American & European

• Binary vs Standard Payout• Binary vs Standard Payout


9898

Exotics: Rainbow Options

Worst of/Best Of: Min(Perf1;Perf2)/Max(Perf1;Perf2)

Call on Best Of: Max (0; 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)


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Exotics: Correlation

• Correlation: The Basics

• Positive CorrelationPositive Correlation

• Negative Correlation

• Dispersions & Correlation Swaps


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[Derivatives Consulting Group] Introduction to Equity Derivatives