Event Drive Hedge Funds Ezra Zask October 24, 2005 Event Driven Strategies • Bankruptcy (in and out of…) – High Yield/Distressed – Credit Swaps • Corporate reorganization; restructuring • Fundamental change in business environment; competition • Lawsuits; legislation • M&A • Structured Bonds (Mortgage Backed Securities) High Yield/Distressed Debt Investing Fixed Income Markets and Funds Fixed Income Strategies • Relative Value – • Capital Structure Arbitrage – – – – • Long debt of one company and short debt of another in same industry; US and International Long municipal debt, short corporate debt Long senior debt, short subordinated Long high yield, short equity Long 1 year short 10 year of same company Event Driven – Relies on catalyst to release value • • • • • Credit/Distressed – Relies on mispricing of security risk • • • • M&A arbitrage Bankruptcy or exit from bankruptcy Corporate restructuring, exchange offers, recapitalization, asset sales, debt buyback Ratings trigger downgrading from investment to high yield High yield Corporate credit arbitrage Distressed securities (debt and equity) Directional Long/Short – Long • • • – Safer end of distressed (between high yield and distressed) Secured Financing Loan syndicated debt Short negative credit view of industry of issuer Spectrum of Fixed Income Investing Asset Backed Securities Equipment Commercial Future Flow Consumer Special Situations Direct Portfolio Lending Mezzanine Lending Distressed Derivatives CDO’s Middle Market Loans High Yield Bonds Real Estate ABS CDO High Grade Commercial Real Estate Large Loans Subordinated Classes Direct Lending Special Situations Mezzanine Lending Credit Derivatives Correlation Trading Credit Default Swaps Baskets Indices Leveraged Credit Leveraged Loans Distressed Mezzanine Debt Special Situations Direct Placement High Yield Bonds Convertibles PIPES ETC’s Derivatives Residential Mortgages Home Equity Alt-A Prime Whole Loans CMO’s Mezzanine Lending Derivatives High Grade Credit Agencies US Treasuries Non-Dollar Treasuries Repo Futures Interest Rate Derivatives Governments Agencies US Treasuries Non-Dollar Treasuries Repo Futures Interest Rate Derivatives Emerging Markets Sovereigns Corporate Asset-Backed Securities Direct Lending Derivatives Project Finance Structured Finance Commercial Real Estate Municipals General Obligations Letters of Credit Healthcare Moral Obligations Project Finance Revenue Bonds Distressed Derivatives Trade Strategies and Risk Trade Strategies Return Sources Risk Characteristics Typical Risk Allocation HY Commercial Paper Carry Low 10-30% Default Arbitrage Carry and Price Action Low 10-20 Short HY Basket, Long HY Market Basket Carry and Price Action Low 20-30 Index Carry Trading Carry Low 10 Long HY Loan Market, Short HY Loan Basket Price Action and Carry Low 20 HY Arbitrage Price Action and Carry Medium 0-30 Intracapital Price Action and Carry Medium 10-20 Long/Short Market Subsectors Price Action Medium 10 New Issues Price Action Medium 5 L/S Specific Names Price Action High 30 Long Specific names Price Action, Carry High 10 Short Specific Names Price Action and Carry High 10 HY Municipals Price Action and Carry High 5 Cash/Derivatives Basis Trading Price Action and Carry High 5 Single Name Volatility Price Action High 5 Global Fixed Income Market Risk Sector Issues Duration Credit Treasuries; Global AAAs High Yield, Distressed, Emerging Market Volatility Mortgages Currency Non-dollar sovereigns; AAAs Credit/Distressed/High Yield Sector Opportunities • Stable credit markets and economic growth • Lack of integration across credit spectrum (inflection points) – Investment to high yield – High yield to distressed – Across capital structure – Across term structure of debt in a company Correlation of Monthly Returns 1991-2004 High Yield 10 Year Treasuries High Yield (1) 10 year Treasuries (2) MBS (3) ThreeMonth Treasuries (4) High Grade Corporates (5) Stocks (6) 1.00 0.06 0.295 0.0348 0.3123 0.5120 1.00 0.83 0.72 0.93 (0.04) 1.00 0.29 0.09 0.23 1.00 0.18 0.09 1.00 0.12 MBS 3-mos Treasuries High Grade Corporates Stocks Notes: (1) ML High Yield Master Index (2) ML 10 Year Treasury Index (3) ML Mortgage-Backed Index (4) ML three-month Treasury Index (5) ML High Grade Index (6) Wiltshire 5000 Stock Index 1.00 Benefits of High Yield and Distressed Investing • Capital appreciation and high current income • Diversified returns from various asset classes • Market liquidity • Lower volatility than equities, other Correlation to Treasuries and Corporate Securities 1992-2004 US IT Govt US LT Govt LB Aggregate Bond CSFB High Yield Index 0.00 0.11 0.19 CSFB Lev Loan Distressed Index -0.05 0.00 -0.01 High Yield Investment Thesis • Record new capital inflows, migration from other asset classes • Interest rates near four decade lows – Search for yield, income – Rising rates hurt Treasury/Corporate debt • Default rate in decline after 2002 peak • New issue market biased to stronger credits • Improving corporate balance sheets, corporate governance, disclosure • Increase presence of commercial banks in underwriting and trading High Yield Investment Thesis (Continued) • HY market remains inefficient – Long only charter of majority of investor base – Limited price transparency – Price sensitivity to funds flows – Dealer dominated market; liquidity “gaps” – Market not integrated to other parts of the capital structure State of High Yield Distressed Markets • Historically low spreads • Near record level of issuance • Default rate in 2004 fell from 3.2% to 1.2% – Long term average of 4.4% – 1994-1998 average of 2.1% • Credit quality of new issues deteriorated by ratings, leverage and coverage ratio – Maintain discipline in high lead; leads to opportunities in distressed Definition of Distressed Investing • Undervalued, under followed, out of favor of oversold securities • Small to middle market companies • “Distressed” segment – Companies in or near reorganization and/or default – Undervalued securities trading at deeply discounted prices resulting from severe financial, operational or economic problems • “Stressed” segment – Under followed or out of favor securities trading at discounted prices resulting from cyclical or sector downturns, financial stress and uncertainties Distressed Debt Opportunities • • Low interest rates, thirst for yield and improving economy led to record issuance of junk bond and leveraged loans in 2003-5 Combined with mortality rates will yield high supply of distressed Year Bonds Bor Lower Leveraged Loans B+ or Lower 2002 3.4% 7.5% 2003 10.1% 20.8% 2004 20.6% (record) 34.5% (record) Years After Issuance Until Default Rating B CCC Marginal Default Rate 2.9% 6.9% 7.4% Cumulative Default Rate 2.9% 9.5% 16.2% Marginal DR 8.0% 15.6% 19.6% Cumulative DR 8.0% 22.3% 37.5% Credit Markets and Credit Derivatives Market Forces Change the Rules of Credit Investing • Equity declines drove re-allocations to fixed income – Simultaneously government yields decreased to all time lows – Credit default rates neared all time highs – Pension fund shortfalls (Focus on ALM) • Credit markets are increasingly Currently Very Few Easy Opportunities • End of the bear credit market in 2003 • Spreads have tightened to extreme levels – Lowest since 1998 • Demand still high Source: S&P Outperformance Is More Demanding Than Ever • Are we being correctly compensated? – Risk premium close to zero • How does a long-only investor win/outperform? – Spreads have nowhere to go • Move to – Lower-quality / higher-yielding – Find names with value still Discussion Outline • Recent market environment • New market-implied techniques to manage credit risk • Introduction to the BDP (Barra Default Probability) • Practical Examples • Questions and answers Market-Implied Measures Provide Additional Insight Market-implied measures from the: Equity Market – Barra Default Probabilities (BDP) Bond Market – Barra Implied Ratings (BIR) Derivatives Market – Credit Default Swaps (CDS) Coming soon… Crossover – (ECR) Empirical Credit Risk Merton’s Structural Model of Default • Default occurs at debt maturity if the firm value is below the liabilities value • We thus need – A model of firm value process – Estimate of default point • Merton identified equity as being long a call option on the firm value • Merton identified a bond as being short a put option on the firm value Merton’s Structural Model of Default No Default V0 D Default 0 T Probability of Default Agenda • The Credit Market • Single name credit • Correlation products • Latest Innovation • Risk Vision Agenda • The Credit Market • Single name credit • Correlation products • Latest Innovation • Risk Vision The Market of Credit • Size and sophistication of market has grown enormously - Notional exceed $2 trillion - Single name (CDS, CLN) to full blown portfolio based instruments (FtD, Synthetic loss tranches, CDO squared) • Initially used by bank loan managers to hedge • Now: insurance companies, hedge funds, asset managers, etc Credit Derivatives • Instruments whose payoff is a function of a reference assets credit characteristics • Transfer the ownership of credit risk between buyers (of protection) and sellers (of protection) • Diversification, yield enhancement • Credit risk is traded independently of the instruments that generate the risk Agenda • The Credit Market • Single name credit • Correlation products • Latest Innovation • Risk Vision Single Name Credit Modelling • Structural approach: default when the company asset value is less than its liabilities • Spread relies on the internal structure of the company • Can’t exactly fit a spread curve and can’t be used to price complex credit derivatives • Reduced-form approach: the credit process is directly modelled via its probability of occurence Credit Default Swaps • Most common credit derivative (over 50% of the market) • Provides protection against default of a reference entity (isolates credit risk component) - Protection buyer retains market exposure of reference entity - Protection seller gets leveraged exposure to reference entity Agenda • The Credit Market • Single name credit • Correlation products • Latest Innovation • Risk Vision Correlation Products Modelling • Contracts that reference the default of more than one obligor • One of the fastest growing areas of credit derivatives – nth-to-Default Baskets – CDO’s (static, managed, synthetic etc) • Methodologies used to price these instruments – Default-time simulation (Normal, t, Archimedean copulas) – Semi-analytical approach Collateralised Debt Obligations • Application of securitisation technology – Synthetically transferring assets off balance sheet via credit derivatives • Asset pool is divided into tranches – Tranches have different risk/return characteristics – Payment to tranches is subordinated • Risk on a CDO arises from the loss distribution of the underlying asset pool – Characteristics of individual underlying’s – Joint correlated behaviour of underlying’s Agenda • The Credit Market • Single name credit • Correlation products • Latest Innovation • Risk Vision Latest Innovation • CDS options • Default Swaptions • Credit Default Swap Index (Trac-x, iBoxx) • CDO squared • Option on CDO tranches • Constant Maturity Default Swap (CMDS) Growth of Credit Default Swaps 2000 2001 2002 2003 2004 Global CDS 893 1,189 2,306 3,500 4,920 US Corporate (IG + HY) 3,359 3,835 4,094 4,462 4,636 Special Situations/Events • Identify Drivers/Destroyers of Value – – – – – – • Overcapacity Cyclical downturns Rising raw material costs Outsourcing manufacturing and service Elimination of trade/tariff barriers Aging populations in developed nations Extraordinary events – – – – – – – – – Re-capitalization Restructurings Liquidations Spin-offs Management Changes Contests for Control; Proxy Contests Stock Repurchase; Special Dividend Business Repositioning Regulatory review/investigation Credit Analysis • Net income is not cash – EBITDA • • • • – – – – – • EBITDA/Interest Expense Long Term Debt/EBITDA (EBITDA-Capital Expenditures)/Interest EBITDA/Revenues Interest Expense Capital Expenditures Free Cash Flow Long Term Debt Debt Repayment Requirements Qualitative Analysis – – – – – – Quality of management Equity sponsors Event Risk (Consolidation; IPO; Technology or Regulation issues; Refinancing Cyclical vs. Defensive industry Ranking and Capital Structure Bond Covenants Examples of MultiStrategy/Event Funds Examples of Multi-Strategy Funds • Concordia – 25% to distressed, 12% to credit relative value and 11% to volatility arbitrage. • Wexford – 35% net long high yield against which they are carrying a 15% duration weighted short in treasuries and a 25% long position in the distressed book; 25% net long special situation equities. • Deephaven – 30% in relative value equity, 25% in convertible arbitrage, 20% in event driven, 10% in distressed/ capital structure arbitrage, 5% in global macro and 5% in credit opportunities. Etolian Capital Credit Arbitrage Kellner DiLeo Cohen & Co • Investment Strategies (market neutral) – – – – – Merger Arbitrage Fund Convertible Arbitrage Fund Distressed and High Yield Securities Fund Special Situations Fund Multi-Strategy Fund • • • • 40% Distressed/high yield 23% Convertible Arbitrage 27% Merger Arbitrage 10% Special Situations • Investment Professionals – CIO – Three Portfolio Managers – Four analysts Distressed Analyst • $600 mm under management Pinewood Capital Partners • Long, short and long/short positions in high yield & investment grade debt, commercial and industrial loans, municipal bonds and exchange traded and OTC derivatives • Staffing – – – – CIO Director of Reseach + 3 analysts Head Trader Risk Manager Dickstein Partners • Event Driven Situations – Merger Arbitrage – Distressed/High Yield Securities – Event Driven Strategies • $450 Capital • Six Investment Professionals Dickstein Partners Canyon Capital Canyon Organization Canyon Credit Culture Canyon Capital Canyon Capital Direct Debt Investments Canyon Capital Angelo Gordon Alpha Credit Fund • $8.5 billion in assets – 116 staff • 56 investment professionals • 22 accounting/operations • 6 client service professional • Percent of assets by strategy – – – – – – – Distressed securities – 30% Leveraged loans (CLO) – 18% Real estate – 18% Convertible arbitrage – 12% Merger Arbitrage – 4% Cash – 10% Other (Credit arbitrage, private equity, etc) – 18% Angelo Gordon Alpha Credit Fund • Intra-Company Credit Arbitrage – – – – – Senior vs. Subordinated Parent vs. subsidiary Short vs. long maturities Bond vs. credit default swap Bond vs. equity • Inter-Company Arbitrage – Relative value within industry of credit rating – Individual credits vs. credit indices • Outright Longs/Shorts – Longs/Shorts based on fundamental research • Structured Transactions – Long/Short CDO hedging – Exploiting differences in instrument characteristics – Options on default swaps Taconic Event Investing • Portfolio Composition – Merger Arbitrage – 23% – Distressed/Stressed – 49% – Capital Structure Arbitrage – 32% • Distressed/Stressed – Invest at the senior level (secured or senior); turns into cash and/or credit worthy senior debt • Capital Structure Arbitrage – Mispricing of different levels of stressed company’s capital structure • Bonds underpriced because of bondholder fear and equity overpriced because of equity investors greed – Long senior bond and short junior bond or equity Sagamore Hill Multi-Strategy Market Neutral Investment Fund • Net Return Target = Risk Free + 5-8% • Areas of Focus – Event Driven • Distressed, Special Situations, Merger Arb. – Relative Value • Capital Structure, Equity Neutral, Long/Short Credit – Volatility Capture • Convertibles, Volatility Trading Strategy Current Allocation Event 16% Distressed 16% Merger Arbitrage 15% Capital Structure 14% Long-Short Credit 7% Equity Market Neutral 7% Convertible Arbitrage 16% Volatility Arbitrage 9% Sagamore Hill Strategies: Event Driven • Distressed – Fundamental-driven research of securities in, near or recently emerged from bankruptcy – Domestic and European allocation – Deal sourcing; on the run; private opportunities • Event Driven – Special Situations – Mispriced securities with clear valuation catalysts including litigation, regulatory actions, spin-offs, refinancing – Excess returns from superior due diligence to capture excess risk premiums created by risk averse investors • Merger Arbitrage – Quantitative, fundamental and regulatory concerns – Use of options to mitigate risk and add value – Domestic and European focus Sagamore Hill Strategies: Relative Value • Capital Structure Arbitrage – Intra-company relative value among securities and derivatives within a capital structure • Debt-equity, debt-option, senior-subordinated, structural arbitrage and pari-passu • Balanced portfolio has minimal risk exposures • Long-Short Credit – Fundamental credit research • Asset values, business fundamentals, legal considerations and capital structure – Domestic and European allocation – Isolate mispriced credit risk • Equity Market Neutral – Equity Long/Short – Statistical quantitative equity portfolio construction Sagamore Hill Strategy: Volatility Capture • Convertible Arbitrage – – – – Global portfolio Mispriced volatility, credit risk, event risk Quantitative and fundamental valuation techniques Integration of convertible with other strategies within the firm • Volatility Arbitrage – Relative value trading (time spreads, skew and dispersion trades) – Relative value between derivatives of related securities – Focus on equity and foreign exchange markets Structured Credit Programs Mortgage Backed Securities • Value Proposition – Mortgage market is large, liquid but not entirely efficient – Preferred Habitat by major players indifferent to relative value • Banks buy to yield; shorter-duration mortgages • Homeowners borrow to buy/refinance; must pay current coupon • Mortgage servicers driven by hedging needs • Mortgage Backed Securities and Related Instruments – Mortgage pools; adjustable rate loans; interest only loans; balloon payment loans; non-performing loans; Commercial MBS; Private Label Mortgage Securities; CMOs, Mortgage derivatives, etc. • Position Analysis – Risk/cheapness; Carry; Duration; Convexity – Identify shifts in investor preferences JP Morgan Asset Management • Program Details – Leverage of 10-15 times net assets – Return objective 8-12% over full market cycle (3-5 years) – $30 bln in long and long/short • Organization – Three senior mortgage portfolio managers – Three quantitative research and risk management analysts – Support from head of fixed income Mortgage Backed Securities Common Types of Trades • Coupon Swap: Long one coupon vs. duration-neutral short position in another coupon – Buy FNMA 6%, Sell FNMA 5.5% • Trading Rolls: Long coupon in one settlement month vs. short same coupon in different month – Buy Sep GNMA 6%; Sell Oct GNMA 6% • Butterfly: Long “center” short “wings” – Buy FNMA 6%, Sell FNMA 5.5% and 6.6% • Agency-to-Agency: Long/short agencies in same coupon – Buy FNMA 5.5%, sell GNMA 5.5% • 30-year vs. 15-year: Buy FNMA 20 year 5%, Sell FNMA 15 year 4.5% • Mortgage vs. Treasuries or Swaps: Long (or Short) mortgage basis with expectation of spread compression (or widening) vs. Treasuries or swaps Basis Yield Alpha Fund • Diversified Global Structured Credit Securities and Derivatives – – – – Asset Backed Securities (ABS) Mortgage Backed Securities (MBS) Collateralized Debt Obligations (CDO) Collateralized Loan Obligations (CLO) • Market Opportunities – – – – Diversification benefits of pool of assets and high recovery rates Lower default risk and credit migration Uncorrelated to other asset classes Premium from Illiquidity and complexity and because traditional fund manager investment mandates stop at investment grade – Issuance in 2004 of $160 billion • Personnel – Three portfolio managers – Four analysts Concordia Advisors • Concordia Advisors hired Christopher Dillon and James Wise, former co-heads of JPMorgan’s tax-exempt structured product group to manage a new fund, The Concordia Municipal Opportunities Fund, which will launch Oct. 1. • Fixed income, interest rate neutral relative value fund will invest exclusively in the U.S. municipal bond market. • Concordia has $1.2 billion in assets under management in eight other hedge funds. Introduction to Asset Securitization • “What is a Mortgage” • Mortgages as a Fixed Income investment • What else can you securitize? Tradable Fixed Income Supply U.S. Dollar Denominated Debt Market US Treasuries 25% Mortgages 43% US Agency 15% ABS 2% Sov/Supers 2% Corporates 13% (2002 Information) What are Mortgage Backed “Pass-Through” Securities? + + = Securitized Mortgage Pool or Pass-throughs • A number of similar mortgages (underlying collateral, design, rates and maturities) are combined into a single group • Mortgage documents associated with this group are delivered to a custodian and are assigned an identification (pool) number • A Mortgage Backed Security (MBS) is issued with a face amount equal to the cumulative outstanding principal balance of the mortgages (original balance) • The mortgages that have been pooled together serve as the collateral for the security • Most MBS are guaranteed and/or issued by a U.S. Government Agency (FNMA, Freddie Mac or GNMA) Agency Conforming MBS Origination Process Individual Mortgages Residential loans originated within the conforming Agency guidelines are guaranteed by an Agency, sold to the Street then either traded in passthrough form or used to structure a CMO… Average Balance $125,000 Gross WAC: 8.50% Pooled by Mortgage Banks Conforming gg GNMA BOUGHT BY AGENCIES FHA/VA 8.50% -.44 % -.06 % (servicing fee) (guarantee fee) 8.00% Judged for Sale by Balance (2000 cap of $275,000), Documentation and Pay Histories 8.50% -.25 % -.25 % FNMA/FHLMC 8.00% FNMA or FHLMC 30 Yr. Mortgage Banking (Sells - Buys) TRADING Trading Desk CMO Desk PO 6.5 yr STRUCTURING CMOs REMICs E.G.: $500 FNMA issue END PURCHASERS PA $250mm 5 yr Agencies ~ 20% PB $50mm 10 yr Banks & Mortgage Servicers ~ 40-50% P2 $100mm 4 yr F Floater $40mm 6.5 yr Z $50mm 20 yr S Inverse Floater $10mm 6.5 yr Insurance Companies & Regional Desks ~ 20% Non-Conforming (next page) Non-Conforming MBS Origination Process Individual Mortgages Loans that do not conform to Agency standards are sold in “whole loan” form or structured into a senior/subordinate private label CMO… Average Balance $125,000 Gross WAC: 8.50% Pooled by Mortgage Banks Conforming (previous page) Judged for Sale by Balance (2000 cap of $275,000), Documentation and Pay Histories Non-Conforming Whole Loans Either Loan Characteristics Reviewed: Geographical locations, zip code, property type, pay history, original and current LTV, occupancy, purpose, insurance Willingness to Pay Ability to Pay Value of Asset D e t e r m i n e d B y: Credit Underwriters GSMC - Income verification - Asset verification - Financial ratios (FICOs) - Tape data - Current 12 month pay history - 30,60,90, 120+ day delinquencies - Age Or Custodian - BPO - Appraisal - Geography - Zip Code Senior/Subordinate 96% 4% Tranche by Credit Tranche by Time Aaa $50 mm 6 yr $30 mm 12 yr Subordinated Tranche AA A BBB BB B UR 15% 15% 12% 19% 12% 27% 13.1 yr 13.5 yr 13.8 yr 14.2 yr 15 yr 16 yr Who Buys Mortgages? Banks and Agencies drive investment flows in the mortgage market, holding nearly 60% of all MBS Mortgage Security Holdings by Investor Type in 2002… Amounts in $US billions Agencies 32% Pension Funds 9% Life Insurance Co's 11% Foreign Investors 15% Banks 24% Other 8% Overview of the U.S. Mortgage Securities Market • Largest Sector of the U.S. Debt Market: – – • MBS can enhance portfolio performance significantly – – • Aggregate current principal amount outstanding mortgage loans is over $4.9 trillion as compared to about $3.3 trillion of government securities and $4.4 trillion of Corporate bonds. Mortgage backed securities (MBS) are an integral part of any broad portfolio exposure to the U.S. Government securities. The U.S. investment grade corporate debt market is less than 1.5 trillion in size. Major mortgages indices have outperformed comparable duration U.S. Treasuries by an average of more than 140 bp over the past 10 years. The U.S. mortgage market consists of a wide array of securities to suit most investor needs. A full range of credit qualities, durations, risk profiles and yields exist in this market. High Credit Quality – – Most of the MBS market is issued by U.S. Government agencies which have an implied AAA rating: GNMA issues carry full faith and credit of the U.S. Government, Fannie Mae and Freddie Mac have the implicit backing of the U.S. Government. Non-agency mortgage securities mostly consist of AA or better rated bonds. Lower rated securities (down to single-B) are also available. 72 What’s the catch? • You are purchasing a product with an imbedded call option – Duration is very hard to determine. – Variability in Average Life can be substantial • You are purchasing an amortizing product – Reinvestment of Principal monthly can reduce yield. "Duration" Deserves Special Focus in Mortgages... • Modified duration, Macaulay duration, cashflow duration: all measure a mortgage's price sensitivity to rate movements, assuming the cashflows are held constant. – Usually not a good assumption in mortgage product owing to prepayments – Durations often quoted as a percentage of modified duration • Option-adjusted duration (OAD), model duration: measure price sensitivity for small rate movements, assuming constant OAS – Doesn't account for how securities actually trade – Reliant on prepayment model • Empirical duration, EOAD: regression of performance vs rates – can be price or OAS vs rates – adjusted for volatility, slope of the curve Prepayment Risk • Prepayment Option – Any payments by borrower made in excess of scheduled principal payments are called prepayments – The option is defined by the borrower's right to prepay all or part of the mortgage at any given time – The uncertainty for the mortgage holder which results is termed prepayment risk • Prepayment Motivation – Prepayment may occur for one of several reasons • sale of property • default • refinancing – Motivations beyond rational economic considerations play an important roll in assessing prepayment risk • Risk for Mortgage Holder – Interest rate risk (re-investment risk): Should mortgage be fixed-rate, market risk arises as a result of prepayment if rates fall and coupons are above market 75 Duration and Convexity price • Duration (simply): • Convexity is the change in Duration as yields change yield Positive Convexity Negative Convexity Price Price 45 40 40 35 35 30 30 25 gain from convexity 25 20 15 15 10 10 5 5 2 3 gain from convexity (negative) 20 4 5 Yield (%) 6 7 8 0 2 3 4 5 Yield (%) 6 7 8 Options and Convexity • If you are long a call option – are you long gamma or short gamma? • Why is being long an MBS similar to being short a call option? Who are you short this option to? • Can you hedge this with options?