Bond Analysis

1
Bond Analysis

• PRM Handbook I.B.1 I.B.2
• Rickard Brannvall
• http//finance.groups.yahoo.com/group/jPRMIA_study
  /

2
Compounding methods

• These include annual, semi-annual, quarterly and
  continuous methods.
• The amount of interest payable for a given rate
  is dependent on the day count convention and
  compounding frequency used
• Hence 10 semi-annual on a 30/360 day count is a
  different amount of interest payable than 10
  annually on an actual/actual day count convention.

3
Compounding methods

• The equivalent interest rates according to the
  frequency of payment of interest can be derived
  by a simple formula.
• Different markets such as bonds and loans have
  different conventions.
• E.g. US treasuries semi-annual while Eurobond
  market has annual convention
• Continuous compounding is most often used in
  financial modelling as it makes manipulation of
  equations much easier.

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Key things you should know

• How to calculate interest payments depending on
  compounding frequency and day count convention
• How to convert from one convention to another
• Standard money market and bond market conventions

5
Study Question

• Q. A bond pays interest of 10 semi-annually on
  an actual/actual convention, what is the rate of
  interest on an annual actual/actual basis?

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Answer

• A. The day count convention is the same so we do
  not have to worry about converting this, payment
  of 10 semi-annually means payment of 5 each
  half year, so this equates to (15)(15)(110.
  25) i.e. 10.25 on an annual compounding basis.

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Bond Characteristics

• The most classical fixed-income instruments are
  straight bonds, which, against payment of a
  principal, provide a regular coupon (interest)
  and a redemption payment.
• Bonds are issued by companies to raise money to
  finance their business and are issued via Banks
  to investors.
• Bonds are a type of tradable loan that are
  characterised by a face or notional amount for
  each bond and a coupon (interest rate) payable.

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Bond Characteristics

• Bonds can have fixed or floating interest rates,
  the later known as FRNs (floating rate notes).
• Zero coupon bonds does not pay coupon only
  redemption amount.
• Inflation indexed bonds are popular to hedge
  inflation risk.

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Bond Characteristics

• Asset backed bonds draw income and principal
  payments from pool of collateral e.g. mortgages,
  credit card obligations, car loans
• Physical property, tax-receipts, securities etc
  can also work as collateral for bonds
• Structured bonds can reference stock-index or
  commodity prices to determine floating coupon

10
Bond Characteristics

• The prices of bonds usually quotes as a
  percentage of face (or notional) value e.g. 101.
• Clean price quoted in markets. Dirty price is
  what is paid and includes accrued interest
• Embedded options issuer right to call, investor
  put, convertible bond

11
Bond valuation

• Price equals present value of future cashflows
  for bonds without embedded options
• Use appropriate discount curve for target market
  and credit
• For fixed coupon bond with N periods

12
Yield Measures

• Current yield tells how much return the present
  coupon give as from market price
• Yield to maturity one discount yield that
  equals price with discounted cashflows
• Yield to maturity is the r that solves below
  equation

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Key things you should know

• What the terms face value, notional, coupon,
  redemption, maturity and principal mean
• How bonds are used to raise capital
• How bonds are traded between investors via
  dealers
• The inverse relationship between bond price and
  yield
• Simple concepts of yield to maturity
• Credit spreads
• Liquidity spread

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Study Question

• Q. A fixed-income instrument will pay 12-month
  Libor on a 1,000 Swiss Francs (CHF) face value
  two times one year from today and two years from
  today (no principal payment). The rates are set
  in arrears (payments at the end of a year reflect
  the Libor rate at the beginning of the year).
  What is the price of this instrument if the
  (zero-coupon) two-year CHF swap curve is a 3 for
  all maturities?
• a) CHF 57.4
• b) CHF 1000
• c) CHF 106
• d) CHF 67.6

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Answer

• A. Swap rates are quoted against LIBOR (floating
  rate index) and a flat swap curve implies that
  forward LIBOR is constant over the curve and
  equal to the swap rate.
• The cash flows are, for the first year, 3 on
  1000 CHF payable in two instalments, and the same
  for the second year 60 CHF in total. As there is
  no principal repaid, b) and c) are out of the
  question.
• As these payments are discounted (as coming later
  than today), 57.4 is the only possible solution
  a)

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Duration and convexity

• Duration and convexity are measures of
  sensitivity of a bond price to changes in yield.
• Duration is the first derivative and convexity is
  the second derivative
• Convexity is the rate of change of duration with
  changes in yield.
• Convexity is correction to duration

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Duration and convexity

• Used as a risk measure for interest rate
  sensitivity
• Determine hedging of interest rate risk
  (immunization)
• There are several different definitions of
  duration Macaulay duration (D)and modified
  duration (MD)
• Differ by factor of (1yield)
• Zero-coupon long-dated bonds have the highest
  duration.

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Key things you should know

• Macaulay cash flow weighted average maturity
• modified duration change in price
• Calculation of duration
• Interpretations of duration
• Graphical representation
• Convexity adjustment

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Study Question

• Q. When does the duration of a bond equal its
  maturity?

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Answer

• A. Duration being the weighted average of the
  maturity of (discounted) cash flows, duration and
  maturity equate when there is only a final cash
  flow to be received at maturity (in other words,
  for a single cash flow, or a zero-coupon bond).

21
Floating rate notes

• FRNs are fixed-income instruments (bonds)
  providing a coupon fluctuating with a given
  interest rate index (Libor) and a redemption
  payment.
• FRN typically trade close to par (100) price
  since the interest rate they pay is usually equal
  to LIBOR plus a spread appropriate to the
  issuers credit risk.

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Key things you should know

• How the coupon payment is calculated.
• How the floating index reference (e.g. LIBOR
  rate) is determined.
• How price of the FRN is effected by changes in
  interest rate and credit worthiness of the issuer.

23
Study Question

• Q. A company issues an FRN at par, which pays
  LIBOR plus 125 b.p., quarterly. Overtime the
  credit rating of the firm declines from AA to
  BBB, how would this effect the price of this FRN?

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Answer

• A.The spread to LIBOR represents the extra return
  for assuming the credit risk of the issuer of the
  bonds.
• If the creditworthiness of the issuer declines
  the market will require a higher return for
  assuming this risk, i.e. they require a higher
  spread than 125 b.p.,
• so they will pay less for this FRN and it will
  trade at a price below par (100).