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
P_{0} = I + I + ……. + I + 100
(1+r) (1+r)^{2} (1+r)^{n}
if you increase the interest rate the discounted cashflow will decrease
Where:
P_{0} = current market price
I = interest paid
r = constant discount rate each year
Term Structure of Interest Rates
P_{0} = I + I + ……. + I + 100
(1+s_{1}) (1+s_{2})^{2} (1+s_{n})^{n}
this is more practical as every year you have different interest rates
Where:
P_{0} = current market price
I = interest paid
s_{n} = spot interest rate for each year
s_{1} _{ } s_{2} s_{n}
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)
Forward Interest Rates
estimation of the future interest rate
expected
 Required rate of return for an investment in period A that is repaid in period
_{A}F_{B}
 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+S_{A})^{A}*(1+_{A}F_{B})^{BA} = (1+S_{B})^{B}
Where:
S_{A} = spot rate for period A
S_{B} = spot rate for period B
_{A}F_{B} = 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 exchangetraded 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.
Advantages
 Returns ‘marked to market’
 Readily tradable
 Prices are ‘transparent’
 No upfront premium
Disadvantages
 Imperfect hedge due to overor underhedging
 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)
Swaps
 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
Advantages:
 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
Disadvantages
 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.