Bonds and interest rates

FBL661 Corporate Finance

Lecture 6

Bonds and interest rates

  • Outline

  • Government Bonds
  • Term Structure of Interest Rates
  • Floating Interest Rates
  • Managing Interest Rate Risk
  • Futures
  • Forwards
  • Swaps

Government Bonds

  • Gilt Edged Securities, Gilts, in the UK
  • Nominal value £100
  • Regular interest payments, coupon.
  • Fixed repayment date
  • Tradable
  • Default risk free
  • Shorts – redeemable within 5 years
  • Medium –  redeemable within 5 – 15 years
  • Long – redeemable over 15 years
  • Undated
  • Index linked

Term Structure of Interest Rates

Risks faced by Investors

  • Unexpected change in interest rates
  • Unexpected change in inflation
  • Default

Fixed Interest Investment

  • Known, fixed, interest (coupon) rate
  • Known time to maturity (fixed repayment date)
  • Tradable
  • Market value changes with change in market rates of interest

Relationship between changes in interest rates and market price

  • Price moves inversely to change in interest rate
  • Longer the maturity greater the price change
  • Price changes  increase with maturity but at a decreasing rate
  • Lower the coupon rate the greater the change in price

Term Structure of Interest Rates

P0    I    +       I      + ……. +   I + 100

(1+r)      (1+r)2                  (1+r)n

if you increase the interest rate the discounted cash-flow will decrease



P0 = current market price

I    = interest paid

r  = constant discount rate each year

Term Structure of Interest Rates

P0    I    +       I      + ……. +   I + 100

          (1+s1)    (1+s2)2                  (1+sn)n

this is more practical as every year you have different interest rates


P0 = current market price

I    = interest paid

sn  = spot interest rate for each year

s1   s2   sn

Spot Interest Rates

discount rate to use to discount any future rate, it is know now

  • The interest rate required to give a future cash flow its present value
  • Fair rate of return between now and period ‘n’
  • Different spot rates for different periods
  • Calculated by using Government Bonds
  • Plotted to give yield curve
today i will invest money, (spot rate)
UK Yield Curve – November 2010

Forward Interest Rates

estimation of the future interest rate


  • Required rate of return for an investment in period A that is repaid in period


  • Found from spot rates
  • To avoid arbitrage profits the return for a given period must equal the return for a shorter period followed by a reinvestment

Forward Interest Rates

calculation of forward rate from spot rates:

(1+SA)A*(1+AFB)B-A = (1+SB)B


SA    = spot rate for period A

SB    = spot rate for period B

AFB  = forward rate between periods A & B

Calculation of Spot & Forward Rates

Relationship between forward rates and future spot rates

  • Forward rates are best estimate of future spot rates
  • But are they biased?
  • Expectations
  • Liquidity premium <<
  • Inflation premium
  • Market segmentation, clientele effect <<

Floating Interest Rates

  • LIBOR <
  • London Inter Bank Offered Rate
  • Fixed daily for set periods – 6 months, 1 year, 1 month, overnight etc.
  • Average of 8, out of 16, leading London banks
  • LIBOR Rates – July 2010

Hedging interest rate risk

  • Hedging is important due to the size of the potential losses from adverse interest rate movements.
  • Interest rate risk depends on interest rate volatility, gearing and floating rate exposure.
  • Firms with significant floating rate debt are concerned about interest rate increases.
  • Firms with a lot of fixed rate debt may lose competitive advantage if interest rates fall.

Hedging techniques include:

  • Futures
  • Forwards
  • Swaps

Futures contracts

  • Futures are exchange-traded contracts to buy or sell a standard quantity of a financial instrument at an agreed price on an agreed date.
  • Company taking out futures contract places initial margin with the clearing house.
  • Contracts are marked to market so variation margin may be needed to meet the losses.
  • Hedging interest rate risk
  • Companies buy interest rate futures to hedge an interest rate fall and sell futures to hedge an interest rate rise.
  • Interest rate futures are priced by subtracting the interest rate from 100.
  • Gains and losses on interest rate changes are given in ticks (0.01% of contract price).
  • Futures position closed out by opposite trade.
  • Example of using interest rate futures
  • Company will borrow £0.5m for 3 months in 3 months time, interest rate now is 10%.
  • Company hedges by selling one £500 000 interest rate future at 90.
  • Assume interest rate in 3 months is 13% and that futures contract price has moved to 87.
  • Company closes out futures position by buying one interest rate future at 87.

Example of using interest rate futures

  • One tick = 500 000 × 0.0001 × 3/12 = £12.50
  • Tick movement = (90 – 87)/0.01 = 300 ticks
  • Gain on futures = 300 × 12.50 = £3750
  • This compensates for higher borrowing cost of 500 000 × 0.03 × 3/12 = £3750
  • Perfect hedge, since the contract price change mirrors the cash market change and the contract is equal to the borrowing amount and the period.


  • Returns ‘marked to market’
  • Readily tradable
  • Prices are  ‘transparent’
  • No up-front premium


  • Imperfect hedge due to over-or under-hedging
  • Cannot take advantages of favourable rates
  •  Allows borrower/lender to lock into an agreed interest rate at a future date for an agreed period
  • Short term, usually under 1 year
  • Start date and end date specified
  • An  FRA starting in 3 months and lasting for 3 months
  • Rate is determined from future rate
  • Over The Counter (OTC)


  • General definition of swap
  • An exchange of one stream of future cash flows for another stream of future cash flows with different characteristics.
  • Swaps are used extensively by banks and companies for hedging interest rate risk and exchange rate risk over long time periods.
  • Banks intermediate by warehousing swaps until counterparty is found.

Interest Rate Swaps

  • Started in 1980’s
  • Off balance sheet
  • Needed to find counterparty
  • Same principle and time period
  • OTC arrangement

Now arranged through bank

Interest Rate Swaps

  • Bank is counterparty – less risky
  • Any principle and time period
  • Bank will quote:
  • 5.25 – 5.62 against 6 month LIBOR
  • Company will either:
  • Pay bank 5.62% and receive LIBOR or
  • Pay bank LIBOR and receive 5.25%

Example of plain vanilla interest rate swap

  • Two companies A and B can borrow at:
  • Company A:     LIBOR   10% Fixed
  • Company B:      11% Fixed   LIBOR + 2%
  • A has a better credit rating than B
  • A wants floating rate debt, has comparative advantage in fixed rate debt
  • B wants fixed rate debt, has comparative advantage in floating rate debt.

Example of plain vanilla interest rate swap

  • A raises fixed rate loan at 10%
  • B raises floating rate loan at LIBOR + 0.2%
  • If servicing requirements are swapped, B is 1% better off and A is 0.2% worse off
  • Giving 0.2% of B’s 1% benefit to A makes A no worse off, giving half of remaining 0.8% benefit to A gives equal benefit to A and B
  • A pays LIBOR – 0.4%, B pays 10.6% fixed.

Interest Rate Swaps


  • Reduces cost of borrowing
  • Allows management of exposure to interest rate movements, hedging
  • Separates raising finance from cost of finance
  • Allows cash flows to be matched
  • Speculation


  • Swap locks company into agreed rates so cannot benefit from favourable rate changes.
  • Counterparty risk exists, as legal liability for interest payments stays with loan signatory.
  • Company exposed to interest and exchange rate risk if counterparty defaults.
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