Equity Swaps

8/7/2019 Equity Swaps

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Equity Swaps

Copyright 1998-2006Investment Analytics

1


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Agenda

Equity Swaps

ApplicationsValuation

Slide: 2Copyright 1998-2006 Investment Analytics Equity Swaps


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Roadmap: Equity Swaps

Debt Stock Short PutBuy-write PERCSPut Warrants SHIELDSPRIMES ELKS

OTMCallEquity SwapCall

DECSFloor PRIDESWarrantsSCORES

Call SpreadPENS Convertibles Collar SUPERSGROIS



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Swaps

What are Equity Swaps

How they are TradedSwaps MarketsApplications of Equity Swaps

Swap Pricing



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Swaps

Arrangements between counter-parties to exchange

Swap TransactionPrincipal:

Notional (not actually exchanged) - Interest rate, Equity swaps

Actual (principal actually exchanged) - Forex swaps

Service Payments:Made at designated periods over life of swap (the tenor)

One party pays fixed price (rate) - swap coupon

Other party pays floating price - pegged to some floating index



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Swap Dealer

Matches counter-parties

Prices swapsMakes marketActs as counter-party

Warehouses swapsTrades own book Takes bid-offer spread



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A Generic Swap Structure

Fixed Price Fixed Price

SwapA BDealer Floating Price Floating Price

Fixed Price Floating Price

Counterparty A converts from fixed to floatingCounterparty B converts from floating to fixed



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Equity for Fixed Swap

Fixed rate %

SwapStock ADealer Portfolio

stock return Index return

Swaps stock portfolio return for fixed incomeHedges a stock portfolio for the tenor of the swapAlternative to selling index futures or shorting stock

Index returnS&P500, Nikkei 225, DAX, CAC-40, FT-SE 100



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Equity for Fixed Swap

PrincipalNotional Principal typically $50mm - $100mm

nonamortizing swap

Fixed over tenor of swap -

Tenors 1 - 3 year typical

Service PaymentsService payments quarterly

Equity return can fluctuate

Cash flows on equity leg can be +ve or -ve

If -ve, dealer pays this as well as swap coupon



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Payment Calculations

Concurrent (typical):Equity leg pays total return on index over current qtr

In Arrears:Uses return over previous qtr to calculate paymentsFirst payment occurs 3 months after swap inception

First payment known at inception

Equity payer pays:NP x (R - I) / 4

NP = Notional principal

R = annualized equity returnI = Fixed interest rate per annum



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Equity for Fixed Swap Payoff

Equity Payer:

Short index futuresLong a coupon bondEquity Markets

Rise Fall

-- -+

+ - ++



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Equity for Floating Swap

Floating rate %

SwapStock ADealer Portfolio

stock return Index return

Swaps stock portfolio return for floating rateFloating rate typically LIBOR based

Index returnS&P500, Nikkei 225, DAX, CAC-40, FT-SE 100



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Equity for Floating Swap

Equity Payer:Short index futuresShort a zero coupon bond

Equity MarketsRise Fall

+ - ++

-- -+



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Equity Swap Payer

Typical User: Stock Portfolio Manager Application: HedgingAdvantages

Avoids restrictions of shorting stocksLower cost than cash transactions (borrowing stock to short)Avoids cost of rolling futures

Outlook: Bearish stock market, interest rates falling:

Strategy: Equity for fixedOutlook: Bearish stock market, interest rates rising:

Strategy: Equity for floating



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Equity Receiver

Interest incomeInterest rate %

FixedSwap B IncomeDealer PortfolioIndex return

Converts fixed income to equity returnGain equity exposure at lower cost than cash transactionsGuarantees index outperformance if FI income exceeds swapcoupon



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Applications (Receiver)

Asset Allocation

Change equity exposure & fixed income durationAvoids need for cash transactions

Alternative is to use futures

Passive Fund - Index Tracking / Out-performanceAlternative to constructing replicating portfolio

Use cash & equity swap to guarantee index return (or better)



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Equity Swap Receivers

More natural equity receivers than

payers:Passive index fundsHedge FundsPension FundsInsurance companies

Mutual funds



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Rationale for Equity Swaps

Cost Advantages

Tax AdvantagesLeverageRestrictions on Investment


C h i S ( )


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Cash vs Equity Swap (UK)

CASH Equity Swap

No stamp duty50 bp stamp dutyWithholding tax on dividends No withholding tax(15% )

No custody feesCustody feesNo restriction on effectivelyRestriction on shorting stock shorting stock US Regulation T: leverage of

2:1 max. Leverage of up to 20:1


T & R l F


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Tax & Regulatory Factors

Insurance CompaniesPension Funds

Tax-exempt status NAIC reserve Requirements:IRS UBIT letter on swaps 30% for stocks

Problem of Foreign Tax 0.3% for fixed incomeCredit usageERISA regulations Mutual Funds

Pass-through tax status

Foreign tax creditsrequire over 50% foreignsource income


Th Withh ldi T T


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The Withholding Tax Trap

XForeign Tax 5% reclaim underCredit 15%

US/UK Tax TreatyUS PensionFund

UK Inland80% of RevenueDividends

20% ACTCant use: UK Investmentsno taxable

income


How Equity Swaps Help


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How Equity Swaps Help

Pension FundsMinimizes withholding tax on dividends

Swap income not subject to UBIT (unrelated business income tax)

Does not endanger tax-exempt status

Mutual FundsCreates foreign income to allow use of foreign tax credits

Insurance CompaniesAllows minimum NAIC reserve requirements to be appliedIncreases max. leverage from 0.3% to 30% (x 100)

Improves return on assets


Swap Pricing


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Swap Pricing

Find fixed rate I, such that PV of fixedpayments = PV of equity leg cash flows

Fixed Leg

I

Ei

Equity Leg


Swap Pricing Formula


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Swap Pricing Formula

Fixed Rate Payments:

Equal payments, I = NP x c / Nswap couponc is the %Equity Leg Payments:

Variable payments E = NP x ei i

forward rate of equity indexreturns

e is the for i

period i

Determine Swap Coupon, c, by:()N

= -NPV EI

i

+ =()1 0 r 1 i


F P i i Th


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Futures Pricing Theory

Futures Price at Time t:

f = S (1 + E[r ] - d . t)t 0 tS is the index spot price0

d is the dividend yield

Proof from Expectations Theory:E[r ] = E[S ] - S + d . t

t t 0S

0

f = E[S ]t t

So E[r ] = f -S + d . tt t 0S0


Equity Term Structure


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Equity Term Structure

Now obtain unbiased estimate of r :t

E[r ] = f /S + (d x t) - 1t t 0Spot Rate of Equity Index Returnsr is the at time t

t

TermStructure

The of Equity Index Returns:. . . .,

The series [r ,r , r ] is called the termt1 t2 tn

structure

Like the term structure of interest rates


Term Structure & Cash Flows


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Term Structure & Cash Flows

Total Return R = NP x r R i ti

3E = R = NP x r 1 1 t1

EE = R -R = NP (r -r ) R 32 2 1 t2 t1 2

E ER 2 21

E EE 1 11

t1 t2 t3t = 0


Determining the Swap Coupon


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Determining the Swap Coupon

NPV of Swap:

E - I + E - I + . . . + E -I = 01 2 tN(1 + r ) (1 + r )(1 + r )t1 t2 tN

r and E are knownti i

Swap Coupon:I = NP x c /N

Find c so that NPV is zero


Example: Equity Swap


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p q y p

Swap Details:

Notional Principal = $100MMEquity Index: S&P500Tenor: 1 year Resets: quarterlyDividend Yield: 2.3% per annum


Setting up the Problem


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g p

Date 14/6/96 22/6/86 20/9/96 20/12/96 21/3/97 20/6/97

S&P500 667.92 668.75 674.65 680.85 687.95 694.65

Coupon Dates 14/6/9 14/9/86 14/12/96 14/3/97 14/6/97Interpolated Prices 667.78 674.26 680.44 687.40 694.21F/S 1.009 1.019 1.029 1.039Spot Rates r 1.528% 3.028% 4.637% 6.236%

iR = NP x Spot Rate

i

Vary coupon rate c, usingE = R -R i i i-1Coupon Interest =NP x c / 4

Goal Seek to set NPV to zeroNet Period Return = E -IiDiscount Factor (1/(1+ r )

i

NPV $0 (29,456) (57,250) 48,941 37,766


Lab: Pricing a Vanilla Swap


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g p

Worksheet- Equity Swap

Compute spot rates, etc.Use Goal Seek to set the coupon rate


Solution: Pricing a Vanilla Swap


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Date 14/6/96 22/6/86 20/9/96 20/12/96 21/3/97 20/6/97

S&P500 667.92 668.75 674.65 680.85 687.95 694.65

Coupon Dates 14/6/9 14/9/86 14/12/96 14/3/97 14/6/97Interpolated Prices 667.78 674.26 680.44 687.40 694.21F/S 1.009 1.019 1.029 1.039Spot Rates r 1.528% 3.028% 4.637% 6.236%

iR = NP x Spot Rate (000s) 1,528.4 3,027.8 4,637.4 6,235.8

iE = R -R (000s) 1,528.4 1,499.4 1,609.6 1,598.5

i i i-1Coupon Interest =NP x c / 4 (000s) 1,558.3 1,558.3 1,558.3 1,558.3Net Period Return = E - I (29,907) (58,984) 51,210 40,121

iDiscount Factor (1/(1+ r ) 0.9849 0.9706 0.9557 0.9413

i

Coupon = 6.2334%NPV $0 (29,456) (57,250) 48,941 37,766


Lab: Off-Market Swaps


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At Market SwapNPV = 0, Coupon = 6.2334%

Buy Down, Coupon = 6%What would the equity receiver pay up front?

Equivalently: How much less than the S&P return wouldthe equity receiver get?

Buy Up, Coupon = 7%How much would the equity receiver get up front?

Equivalently: How much more than the S&P return would

the equity receiver get?


Solution: Off-Market Swaps


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Buy Down, Coupon = 6%

Fixed payer (equity receiver) would pay$224,792 up frontOr receive S&P - 0.2334%

Buy Up, Coupon = 7%Fixed payer (equity receiver) would get$738,343 up frontOr receive S&P + 0.7666%


Floating Rate Equity Swaps


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Valuation procedure:Equity Leg: as beforeInterest Rate Leg: similar procedure

Use LIBOR rates to back out:Spot rates

Forward rates

Calculate expected interest costUse forward rates

Discount cash flows using spot rates


Portfolio Hedging with Swaps


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Hedging a PortfolioManager has portfolio size $P, beta bEquity swap (pays S&P500, receives fixed)Equity swap hedge: NP = P x b

Example: P = $24MM, beta = 1.2Equity Swap NP = $24MM x 1.2 = $28.8MMSuppose S&P500 declines 5%

Loss on portfolio = 5% x $24MM x 1.2 = $1.44MM

Gain on swap = $28.8 x 5% = $1.44MM


Market Timing with Swaps


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Market Timing with Swaps

Portfolio Manager anticipates bullishconditions over next year:

Wants to increase portfolio beta from b to b*

Enters Equity Swap:Pays fixed, receives S&P500NP = (b* - b) x Portfolio Value

Note: hedging is a special case with * = 0


Benefits of Swap Hedging


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p g g

Swap vs. Cash

Faster (single transaction)Less costly than multiple cash transactionsNo problems effectively shorting stock

Swap vs. FuturesAvoids having to roll over on expiryLess costly than transacting multiple futures

contracts


Extensions of Equity Swaps


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Power Swaps

Inverse Equity FloatersFixed/Inverse Equity FloatersChooser Swaps

Relative Performance SwapsRainbow Swaps


Power Swaps


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To increase market exposureStrongly bullish view on market direction

S&P x NFixed SwapC AIncome Dealer

Coupon x NPortfolio

Choose NP = N x Portfolio SizeNet return = (N x S&P) - (N-1) x C

Assuming FI portfolio matches coupon


Inverse Equity Floaters


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Strongly bearish view on market direction

S&P x NStock SwapS&P A

Portfolio Dealer Coupon x N

Choose NP = N x Portfolio SizeNet return = (N x C) - (N-1) x S&P

Assuming stock portfolio matches S&P


Fixed/Inverse Equity Floaters


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Scenario:Expect S&P returns remain stable for next year, then fall

S&P x 22-year S&P x 3 1-year ASwap Swap

(3 x NP) Coupon x 2Coupon x 3 S&P (2 x NP)Stock

Portfolio

Year 1: (3C - 3xS&P) + (-2C + 2xS&P) + S&P = CYear 2: 3C - 2xS&P


Chooser Swaps


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Equity return pegged to greater of two

indicesHigher swap coupon

Max[S&P, Nikkei]SwapADealer

Coupon


Outperformance Swaps


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Two Equity Legs:

Applications:Take view on relative performance of equity marketsTransport alphas from one equity market to another

S&PSwapA

Dealer Nikkei

US Stock Portfolio


Rainbow Swaps


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Equity leg combines returns from several indices

Used for hedging aggregate equity portfolios0.5S&P + 0.5 Nikkei

SwapADealer

Coupon

JapanUSPortfolioPortfolio


Summary Equity Swaps


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Important component of many structured

productsModifies exposure amongst different asset classesSignificant tax/regulatory & cost benefitsWide range of applications


Equity Swaps

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