FIBI

1
Fixed Income Instruments 1

• Zvi Wiener
• 02-588-3049
• mswiener_at_mscc.huji.ac.il

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

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

4
Plan

• Active Bond Portfolio Management
• Indexing
• Liability Funding Strategies
• Bond Performance Measurement
• Interest Rate Futures
• Interest Rate Options
• Interest Rate Swaps, Caps, Floors

5
Characteristics of a Bond

• Issuer
• Time to maturity
• Coupon rate, type and frequency
• Linkage
• Embedded options
• Indentures
• Guarantees or collateral

6
Sources

• Fabozzi, Bond Markets, Analysis and
  Strategies, Prentice Hall.
• P. Wilmott, Derivatives, Wiley.
• Hull, White, Manuscript.

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

8
Basic terms

• Principal
• Coupon, discount and premium bonds
• Zero coupon bonds
• Floating rate bonds
• Inverse floaters
• Deferred coupon bonds
• Amortization schedule
• Convertible bonds

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

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

11
Major risks

• Interest rate risk
• Default risk
• Reinvestment risk
• Currency risk
• Liquidity risk

12
Time Value of Money

• present value PV CFt/(1r)t
• Future value FV CFt(1r)t
• Net present value NPV sum of all PV

13
Term structure of interest rates
Yield IRR
How do we know that there is a solution?
14
Price-Yield Relationship

• Price and yield (of a straight bond) move in
  opposite directions.

price
yield
15
General pricing formula
16
Accrued Interest

• Accrued interest interest due in full period
• (number of days since last coupon)/
• (number of days in period between coupon payments)

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

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.

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 LIBORgt10 there is typically a floor.

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.

21
Annualizing Yield

• Effective annual yield (1periodic rate)m-1
  examples
• Effective annual yield 1.042-18.16
• Effective annual yield 1.024-18.24

22

• Bond selling at Relationship
• Par Coupon ratecurrent yieldYTM
• Discount Coupon rateltcurrent yieldltYTM
• Premium Coupon rategtcurrent yieldgtYTM
• Yield to call uses the first call as cashflow.
• Yield of a portfolio is calculated with the total
  cashflow.

23
YTM and Reinvestment Risk

• YTM assumes that all coupon (and amortizing)
  payments will be invested at the same yield.

24
YTM and Reinvestment Risk

• An investor has a 5 years horizon
• Bond Coupon Maturity YTM
• A 5 3 9.0
• B 6 20 8.6
• C 11 15 9.2
• D 8 5 8.0
• What is the best choice?

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.

26
Duration and IR sensitivity
27
Duration
28
Duration
29
Duration

• Bond duration price impact of 1 YTM
• A 3 yr
• B 1 yr
• C 10 yr
• D 20 yr

-3 -1 -10 -20
30
Measuring Price Change
31
The Yield to Maturity

• The yield to maturity of a fixed coupon bond y is
  given by

32
Macaulay Duration

• Definition of duration, assuming t0.

33
Macaulay Duration
A weighted sum of times to maturities of each
coupon.

• What is the duration of a zero coupon bond?

34
Meaning of Duration
35
Convexity
36
FRA Forward Rate Agreement

• A contract entered at t0, 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 KeR(T-S)
• Calculate the FRA rate R which makes PV0
• hint it is equal to forward rate

37
ALM Duration

• Does NOT work!
• Wrong units of measurement
• Division by a small number

38
ALM Duration

• A similar problem with measuring yield

39

• Do not think of duration as a measure of time!

40

• Key rate duration
• Principal component duration
• Partial duration

41
Factors affecting Bond yields and TS

• Base interest rate - benchmark interest rate
• Risk Premium - spread
• Expected liquidity
• Market forces - Demand and supply

42
Taxability of interest

• qualified municipal bonds are exempts from
  federal taxes.
• After tax yield pretax yield (1- marginal tax
  rate)

43
Do not use yield curve to price bonds

• Period A B
• 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!

44

• On-the-run Treasury issues
• Off-the-run Treasury issues
• Special securities
• Lending
• Repos and reverse repos

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).

(1r2)(1r1)(1f12)
46
Forward Rates

• (1r3)(1r1)(1f13) (1r1)(1f12)(1f13)
• Term structure of instantaneous forward rates.

47
Determinants of the Term Structure

• Expectation theory
• Market segmentation theory
• Liquidity theory
• Mathematical models Ho-Lee, Vasichek,
  Hull-White, HJM, etc.

48
Home Assignment

• 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?