# Bonds and interest rates

FBL661 Corporate Finance

Lecture 6

• # 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
• Default risk free
• Shorts – redeemable within 5 years
• Medium –  redeemable within 5 – 15 years
• Long – redeemable over 15 years
• Undated

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)
• 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

Where:

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

Where:

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

expected

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

AFB

• 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

Where:

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
• 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’
• Prices are  ‘transparent’

• 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)

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

• 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