Fixed Income The Financial Institute of Israel Zvi Wiener Fixed Income

Zvi WienerFI - 1 slide 2 Plan Pricing of Bonds Measuring yield Bond Price Volatility Factors Affecting Yields and the Term Structure of IR Treasury and Agency Securities Markets Corporate Debt Instruments Municipals

Zvi WienerFI - 1 slide 3 Plan Non-US Bonds Mortgage Loans Mortgage Pass-Through Securities CMO and Stripped MBS ABS Bonds with Embedded Options Analysis of MBS Analysis of Convertible Bonds

Zvi WienerFI - 1 slide 4 Plan Active Bond Portfolio Management Indexing Liability Funding Strategies Bond Performance Measurement Interest Rate Futures Interest Rate Options Interest Rate Swaps, Caps, Floors

Zvi WienerFI - 1 slide 5 Characteristics of a Bond Issuer Time to maturity Coupon rate, type and frequency Linkage Embedded options Indentures Guarantees or collateral

Zvi WienerFI - 1 slide 6 Sources Fabozzi, “Bond Markets, Analysis and Strategies”, Prentice Hall. P. Wilmott, Derivatives, Wiley. Hull, White, Manuscript.

Zvi WienerFI - 1 slide 7 Sectors Treasury sector: bills, notes, bonds Agency sector: debentures (no collateral) Municipal sector: tax exempt Corporate sector: US and Yankee issues – bonds, notes, structured notes, CP – investment grade and noninvestment grade Asset-backed securities sector MBS sector

Zvi WienerFI - 1 slide 8 Basic terms Principal Coupon, discount and premium bonds Zero coupon bonds Floating rate bonds Inverse floaters Deferred coupon bonds Amortization schedule Convertible bonds

Zvi WienerFI - 1 slide 9 Basic Terms The Money Market Account LIBOR = London Interbank Offer Rate, see BBA Internet site FRA = Forward Rate Agreement Repos, reverse repos Strips = Separate Trading of Registeres Interest and Principal of Securities

Zvi WienerFI - 1 slide 10 Basic Terms gilts (bonds issued by the UK government) JGB = Japanese Government Bonds Yen denominated issued by non-Japanese institutions are called Samurai bonds

Zvi WienerFI - 1 slide 11 Major risks Interest rate risk Default risk Reinvestment risk Currency risk Liquidity risk

Zvi WienerFI - 1 slide 12 Time Value of Money present value PV = CF t /(1+r) t Future value FV = CF t (1+r) t Net present value NPV = sum of all PV -PV

Zvi WienerFI - 1 slide 13 Term structure of interest rates Yield = IRR How do we know that there is a solution?

Zvi WienerFI - 1 slide 14 Price-Yield Relationship Price and yield (of a straight bond) move in opposite directions. yield price

Zvi WienerFI - 1 slide 15 General pricing formula

Zvi WienerFI - 1 slide 16 Accrued Interest Accrued interest = interest due in full period* (number of days since last coupon)/ (number of days in period between coupon payments)

Zvi WienerFI - 1 slide 17 Day Count Convention Actual/Actual - true number of days 30/360 - assume that there are 30 days in each month and 360 days in a year. Actual/360

Zvi WienerFI - 1 slide 18 Floater The coupon rate of a floater is equal to a reference rate plus a spread. For example LIBOR + 50 bp. Sometimes it has a cap or a floor.

Zvi WienerFI - 1 slide 19 Inverse Floater Is usually created from a fixed rate security. Floater coupon = LIBOR + 1% Inverse Floater coupon = 10% - LIBOR Note that the sum is a fixed rate security. If LIBOR>10% there is typically a floor.

Zvi WienerFI - 1 slide 20 Price Quotes and Accrued Interest Assume that the par value of a bond is $1,000. Price quote is in % of par + accrued interest the accrued interest must compensate the seller for the next coupon.

Zvi WienerFI - 1 slide 21 Annualizing Yield Effective annual yield = (1+periodic rate) m -1 examples Effective annual yield = =8.16% Effective annual yield = =8.24%

Zvi WienerFI - 1 slide 22 Bond selling atRelationship ParCoupon rate=current yield=YTM DiscountCoupon rate<current yield<YTM PremiumCoupon rate>current yield>YTM Yield to call uses the first call as cashflow. Yield of a portfolio is calculated with the total cashflow.

Zvi WienerFI - 1 slide 23 YTM and Reinvestment Risk YTM assumes that all coupon (and amortizing) payments will be invested at the same yield.

Zvi WienerFI - 1 slide 24 YTM and Reinvestment Risk An investor has a 5 years horizon BondCouponMaturityYTM A5%39.0% B6%208.6% C11%159.2% D8%58.0% What is the best choice?

Zvi WienerFI - 1 slide 25 Bond Price Volatility Consider only IR as a risk factor Longer TTM means higher volatility Lower coupons means higher volatility Floaters have a very low price volatility Price is also affected by coupon payments Price value of a Basis Point = price change resulting from a change of 0.01% in the yield.

Zvi WienerFI - 1 slide 26 Duration and IR sensitivity

Zvi WienerFI - 1 slide 27 Duration

Zvi WienerFI - 1 slide 28 Duration

Zvi WienerFI - 1 slide 29 Duration Bonddurationprice impact of +1% YTM A3 yr B1 yr C10 yr D20 yr -3% -1% -10% -20%

Zvi WienerFI - 1 slide 30 Measuring Price Change

Zvi WienerFI - 1 slide 31 The Yield to Maturity The yield to maturity of a fixed coupon bond y is given by

Zvi WienerFI - 1 slide 32 Macaulay Duration Definition of duration, assuming t=0.

Zvi WienerFI - 1 slide 33 Macaulay Duration What is the duration of a zero coupon bond? A weighted sum of times to maturities of each coupon.

Zvi WienerFI - 1 slide 34 Meaning of Duration r $

Zvi WienerFI - 1 slide 35 Convexity r $

Zvi WienerFI - 1 slide 36 FRA Forward Rate Agreement A contract entered at t=0, where the parties (a lender and a borrower) agree to let a certain interest rate R*, act on a prespecified principal, K, over some future time period [S,T]. Assuming continuous compounding we have at time S:-K at time T: Ke R*(T-S) Calculate the FRA rate R* which makes PV=0 hint: it is equal to forward rate

Zvi WienerFI - 1 slide 37 ALM Duration Does NOT work! Wrong units of measurement Division by a small number

Zvi WienerFI - 1 slide 38 ALM Duration A similar problem with measuring yield

Zvi WienerFI - 1 slide 39 Do not think of duration as a measure of time!

Zvi WienerFI - 1 slide 40 Key rate duration Principal component duration Partial duration

Zvi WienerFI - 1 slide 41 Factors affecting Bond yields and TS Base interest rate - benchmark interest rate Risk Premium - spread Expected liquidity Market forces - Demand and supply

Zvi WienerFI - 1 slide 42 Taxability of interest qualified municipal bonds are exempts from federal taxes. After tax yield = pretax yield (1- marginal tax rate)

Zvi WienerFI - 1 slide 43 Do not use yield curve to price bonds PeriodAB 1-9$6$1 10$106$101 They can not be priced by discounting cashflow with the same yield because of different structure of CF. Use spot rates (yield on zero-coupon Treasuries) instead!

Zvi WienerFI - 1 slide 44 On-the-run Treasury issues Off-the-run Treasury issues Special securities Lending Repos and reverse repos

Zvi WienerFI - 1 slide 45 Forward Rates Buy a two years bond Buy a one year bond and then use the money to buy another bond (the price can be fixed today). (1+r 2 )=(1+r 1 )(1+f 12 )

Zvi WienerFI - 1 slide 46 Forward Rates (1+r 3 )=(1+r 1 )(1+f 13 )= (1+r 1 )(1+f 12 )(1+f 13 ) Term structure of instantaneous forward rates.

Zvi WienerFI - 1 slide 47 Determinants of the Term Structure Expectation theory Market segmentation theory Liquidity theory Mathematical models: Ho-Lee, Vasichek, Hull-White, HJM, etc.

Zvi WienerFI - 1 slide 48 What is the duration of a floater? What is the duration of an inverse floater? How coupon payments affect duration? Why modified duration is better than Macaulay duration? How duration can be used for hedging? Home Assignment