ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 20: Interest rate risk
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When interest rates change, there might be a general increase or fall in interest rates
across the entire length of the yield curve. A general increase or fall in the yield
curve for all maturities is often called a general shift in the yield curve.
More often, however, some parts of the yield curve rise or fall when other parts of
the yield curve remain unchanged. For example, short-term interest rates might rise
but longer-term rates might remain unchanged. (Sometimes when this happens, the
yield curve changes from normal to inverse.)
Sometimes interest rates on one part of the yield curve might rise or fall sooner than
they rise or fall on a different part of the yield curve. For example, interest rates on
maturities up to two years might increase by 0.5%, and interest rates on maturities
over two years might not rise until several months later.
Two important factors affecting changes in interest rates are:
interest rate policy decisions by the government or central bank
the effect of supply and demand for bonds or loans.
Central bank action
In some countries, short-term interest rates are managed by the central bank on
behalf of the government. Changes in short-term interest rates can be used to
influence the condition of the economy, such as the rate of inflation and possibly the
level of unemployment. Interest rates are managed by the central bank or central
government, for example, in the US, the eurozone countries and the UK.
When a central bank raises short-term interest rates, which it is able to do through
its activities in lending to the banking system or its activities in the money markets,
all short-term interest rates will normally be raised by the banks. For example, if the
Bank of England raised its interest rate by 0.25%, all UK commercial banks would
immediately raise their LIBOR rates and base rates, probably by 0.25%. There would
be no immediate effect on long-term interest rates, although these might go up in
time.
Similarly, when a central bank reduces its short-term lending rate to commercial
banks, the banks will normally reduce their own interbank lending rates. (However
this is not always the case: during the ‘banking crisis’ in 2007 - 2008, banks in the UK
did not reduce their LIBOR rates in response to reductions in lending rates to the
banks from the Bank of England.)
Supply and demand for bonds
Interest yields on bonds affect the market price of issued bonds. Higher yields mean
lower bond prices, and lower yields result in higher market prices for bonds in
issue.
Yields (bond prices) are affected by the supply and demand for bonds in the market.
There are different views about what factors affect the demand of investors for
bonds. Three explanations of interest rates and changes in interest rates are:
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expectations theory
liquidity preference theory
market segmentation.
2.3 Expectations theory
Expectations theory is a theory stating that long-term interest rates can be used to
predict investor expectations of future short-term interest rates. Put another way,
long-term interest rates are derived from current short-term interest rates and
expectations of what short-term rates will be in the future, up to the end of the
longer-term interest period.
Some simplified examples might help to illustrate the theory.
Example
The current one year interest rate is 5.50% and the current six-month interest rate is
5.25%.
If expectations theory is correct for short-term interest rates, we would be able to
identify investor expectations of what the six-month rate will be in six months time.
This is because investors will be indifferent about whether to invest money now for
12 months, or whether to invest for six months and then re-invest the returns from
the six-month investment for a further six months. If either of these options
provided a bigger return, investors would choose it in preference to the other.
Let the six-month rate at the end of month 6 be r.
Since investing for 12 months will provide the same return as investing for six
months and then another six months:
[1 + (0.0525) × 6/12] [1 + (r × 6/12)] = 1.0550.
1.02625 × (1 + r/2) = 1.0550
(1 + r/2) = 1.0550/1.02625 = 1.0280
r/2 = 0.0280
r = 0.0560 = 5.6%.
Investors expect the six-month rate to have risen to 5.6% at the end of month 6.
Example
The current one-year interest rate is 6%. Investors expect the one-year rate to fall to
5.75% by the end of Year 1, 5.50% by the end of Year 2 and 5.4% by the end of Year
3.
If expectations theory is valid, the total return from investing for 12 months now,
then again at the end of year 1, year 2 and year 3 should be the same as the total
return form investing now for four years.
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The current four-year interest rate can be calculated as follows:
Let the current four-year interest rate be r.
(1.0600)(1.0575)(1.0550)(1.0540) = (1 + r)
4
1.246463 = (1 + r)
4
(1 + r) = 1.0566 = 5.66%.
Expectations theory and changes in interest rates
If expectations theory is correct, changes in investor expectations about what
shorter-term interest rates will be in the future will result in changes in current
longer-term interest rates.
For example, suppose that the central bank raises short-term interest rates by 0.25%.
If investors expect these changes in rates to continue in the future, their expectations
about future short-term interest rates will change. This will lead to changes in
longer-term interest rates, which will increase to allow for investor expectations of
higher shorter-term rates.
There is a strong rational justification for expectations theory, and to a certain extent
the theory is probably valid. If longer-term rates did not reflect investor
expectations of future short-term rates, investors should be able to make profits by
investing in either shorter-term or longer-term bonds.
However, it is unlikely that expectations theory on its own explains interest rates
and changes in interest rates. The Bank of England commented (Bank of England
Quarterly Bulletin, May 1995): ‘In practice for a number of reasons it is unlikely that
expectations theory holds exactly: long-term interest rates are unlikely to be simply
the average of actual and expected future short-term rates.’
2.4 Liquidity preference theory
Liquidity preference is the preference that people have for holding cash rather than
investing it. Liquidity preference theory states that in order to overcome this
preference of individuals for holding cash, borrowers must offer interest.
Individuals might have cash in the bank on which they earn no interest but for
which they have no immediate use: they could be persuaded to invest this cash by
the attraction of interest on the investment.
The theory also states that investors also prefer short-term interest-yielding
investments rather than long-term interest-yielding investments. This is because
there is greater risk with longer-term investments than with shorter-term
investments.
Example
If there is no expectation of future changes in interest rates, liquidity theory states
that investors would prefer to invest in one-year bonds at 6% than to invest in four-
year bonds at 6%.
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The reason they would prefer one-year bonds at 6% over four-year bonds at 6% is
that there is more investment risk in the four year bonds. The value of the one-year
bond is based on interest for one year at 6% and the guaranteed redemption value of
the bond after one year. If interest rates went up unexpectedly, their investment
would lose some value but not much.
The value of the four-year bond is based on interest for four years at 6% ($24 on
$100 bonds over four years) and the redemption value of the bonds at the end of
Year 4. If interest rates went up unexpectedly, their investment would lose more in
value than the one-year bond, because more of the bond’s value is in the future
interest income.
Liquidity preference can therefore be described as a risk aversion of investors.
Given no difference in interest yields, they will prefer shorter-term investments to
longer-term investments.
To persuade investors to overcome their liquidity preference and invest in longer-
term investments, it is therefore necessary to offer higher yields on longer-dated
bonds.
Liquidity preference theory therefore states that yields on longer-dated bonds are
higher than would be predicted by basic expectations theory, because investors
must be offered a higher yield to overcome their risk aversion and liquidity
preference.
2.5 Market segmentation
Market segmentation theory differs from expectations theory and liquidity
preference theory. It disagrees with the view that the yield curve can be seen as
interest rates for different maturities in a single investment market.
It states that the market for bonds and other interest-yielding investments is not a
single market. The market is divided into different segments, and interest yields in
each segment of the market are determined by factors within that segment. Many
investors focus on just one segment of the market: for example an investment
institution might deal exclusively in bonds with maturities of five to ten years, and
not deal at all in bonds with maturities below five years or over ten years. In
contrast, pension funds might choose to invest heavily in long-dated bonds, to
match their pension liabilities that are also long-dated.
Since the market is segmented, the theory states that there is no reason why interest
rates in different segments of the market should be related to each other.
Investors specialising in a certain segment of the market will stay in this segment
whatever the expectations of interest rates in other segments of the market. This can
lead to anomalies in the shape of the yield curve.
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Example
Pension funds are major investors in the bond markets. These funds have long-term
liabilities, because they will be required to pay pensions to members of their pension
scheme for many years into the future. Pension fund managers are therefore
attracted to very long-term bonds, such as government 30-year or 50-year bonds.
The strong demand for long-dated bonds has exceeded the supply of the bonds in
the past, and the long-dated bond market has been a separate segment of the bond
market. Heavy demand for the bonds has kept the yields on long-dated bonds low,
even when yields on shorter-dated bonds, say 10 – 15 year bonds, have been higher.
Lower yields on very long-dated bonds are inconsistent with the predictions of
expectations theory or liquidity preference theory.
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Hedging interest rate risk: FRAs
Hedging methods
Matching and smoothing
Asset and liability management
Forward rate agreements (FRAs)
The features of an FRA agreement
How an FRA works
3 Hedging interest rate risk: FRAs
3.1 Hedging methods
Some organisations might wish to hedge their exposures to interest rate risk. They
might also want to take advantage, if possible, from any favourable movements in
interest rates. There are several ways in which risks can be hedged and
opportunities to benefit from interest rate changes can be exploited. These include:
matching and smoothing
asset and liability management
forward rate agreements or FRAs
3.2 Matching and smoothing
Matching and smoothing are ‘internal’ methods of hedging interest risk.
Matching involves setting off interest income against interest payments, so that the
interest rate exposure is to the net amount of interest payments (or net interest
income). This method of interest rate hedging might be difficult for companies to
achieve as interest payments on loans are likely to be much higher than interest
payments on deposits or investments. Matching is likely to be more practicable for
financial institutions such as banks.
Smoothing is where companies have a balance of fixed and floating rate debt. For
example a company might choose to have 50% of its debt capital in the form of fixed
interest liabilities and the other 50% in floating rate liabilities. If interest rates rise
the disadvantage of higher variable interest rates will be offset by the comparatively
low fixed rates. If interest rates fall the disadvantage of the fixed rate will be offset
by a lower variable rate.
3.3 Asset and liability management
Asset and liability management in the context of financial management means
managing risk in financial assets and liabilities. In banks for example, asset and
liability management involves monitoring risk, such as interest rate risk and credit
risk, in a bank’s portfolio of assets and liabilities.
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Where possible, assets (e.g. loans to customers) are matched with liabilities (e.g.
borrowings by banks) in order to control risk arising from gap exposures and basis
risk etc.
3.4 Forward rate agreements (FRAs)
Forward rate agreements (FRAs) are used extensively by some companies to hedge
exposures to short-term interest rate risk.
A forward rate agreement (FRA) is a forward contract for an interest rate. FRAs are
negotiated ‘over-the-counter’ with a bank. In some respects, an FRA is similar to a
forward exchange rate. It is a contract arranged ‘now’ that fixes the rate of interest
for a loan or deposit period starting at some time in the future. For example, an FRA
can be used to fix the interest rate on a six-month loan starting in three months’
time.
How are banks able to offer fixed rates of interest for future lending periods?
Banks are able to quote forward rates for interest rates because there is a large and
active money market, and banks are able to borrow and deposit funds short-term.
As a result, if a bank can borrow for nine months at one rate of interest and deposit
funds for three months at another rate of interest, it can work out a rate to quote to a
customer that wants to borrow between the end of month 3 and the end of month 9.
A ‘forward rate’ can be fixed now that will guarantee the bank a profit on the
transaction.
A numerical example might help to illustrate this point.
Example
A bank can borrow dollars for nine months at 5% and can deposit dollar funds for
three months at 4.75%. Suppose that it borrows $1 million for nine months and
places them on deposit for three months.
After nine months, it will have to repay $1 million + ($1 million × 5% × 9/12) =
$1,037,500. The loan repayment is $1,000,000 and interest payable is $37,500.
After three months, its dollar deposit will grow to $1 million + ($1 million ×
4.75% × 3/12 = $1,011,875. The interest received is $11,875.
To break even by lending to a customer from the end of month 3 to the end of
month 9 (six months), the bank would need to earn interest of $25,625 ($37,500 –
$11,875) on its end-of-month 3 investment of $1,011,875..
The (annual) interest rate on the month 6-month lending would therefore have
to be:
25,625
1,011, 875
×
12
6
×100% = 5.06%
This is not what banks would do in practice, but the example is intended to show
that banks are able to use spot money market rates (which are rates for borrowing or
depositing funds ‘now’) to derive interest rates for a future interest period, knowing
that they will make a suitable profit.
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3.4 The features of an FRA agreement
An FRA, like a forward exchange contract, is a binding agreement between a bank
and a customer. It is an agreement that fixes an interest rate ‘now’ for a future
interest period.
An FRA for an interest period starting at the end of month 3 and lasting until the
end of month 9 is a 3v9 FRA or a 3/9 FRA.
Similarly, an FRA for a three-month period starting at the end of month 2 is a
2v5 FRA or a 2/5 FRA.
The interest rate period is a money-market term – less than 12 months. Similarly the
interest rate that is fixed is a money market (i.e. short –term) rate of interest.
Notional principal
An FRA is an agreement that fixes a forward interest rate on a notional amount of
money or ‘notional principal’.
A forward exchange contract for currency is an agreement to buy and sell currency
at a future date, when there will be an exchange of currencies between the bank and
its customer. An FRA is different. It is not an actual agreement to take out a loan or
to make a deposit. An FRA is an agreement that fixes a future interest rate, and it
does this by stating the amount of a notional loan or deposit. The size of the notional
amount of principal (the notional loan or deposit) is specified in the FRA agreement.
This idea might seem unusual: an FRA is a contract on a future rate of interest; it is
not a contract to provide an actual loan or deposit.
For example a company might want to fix an interest rate now on a three-month
loan starting in two months’ time, with a 2v5 FRA.
It will arrange the FRA with one bank, and this effectively fixes the future three-
month borrowing rate.
The actual three-month loan at the end of month 2 can be obtained from a
different bank. The loan does not have to be arranged with the bank with which
the FRA contract was made.
Buying and selling FRAs
FRAs are bought and sold.
If a company wishes to fix an interest rate (cost) for a future borrowing period, it
buys an FRA. In other words,
buying an FRA fixes an effective forward rate for
short-term borrowing.
If a company wishes to fix an interest rate (income) for a future deposit period, it
sells an FRA. Selling an FRA fixes a forward rate for a short-term deposit.
The counterparty bank sells an FRA to a buyer and buys an FRA from a seller.
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FRA rates
A bank trading in FRAs will publish indicative rates. For example, prices for sterling
FRAs might be quoted as follows:
3 v 6 5.27 – 5.23
4 v 7 5.32 – 5.28
5 v 8 5.39 – 5.34
9 v 12 5.63 – 5.56
3 v 9 5.40 – 5.36
4 v 10 5.45 – 5.41
6 v 12 5.50 – 5.45
A bank will always apply the rate to an FRA agreement that is more favourable to
itself. For example, a company wanting to fix the interest cost with a 6 v 12 FRA,
using the rates in the table above, would be quoted a rate of 5.50% for the FRA. This
is because a ‘lending’ rate of 5.50% is more favourable to the FRA bank than a rate
of 5.45%.
3.5 How an FRA works
An FRA works by comparing the fixed rate of interest in the FRA agreement with a
benchmark rate of interest, such as LIBOR. The comparison takes place at the
beginning of the notional interest period for the FRA.
If the FRA rate is higher than the benchmark rate (LIBOR), the buyer of the FRA
must make a payment to the seller of the FRA, in settlement of the contract
If the FRA rate is lower than the benchmark rate (LIBOR), the buyer of the FRA
receives a payment from the seller of the FRA, in settlement of the contract.
The amount of the payment is calculated from the difference between the FRA rate
and the benchmark rate (LIBOR rate), applied to the notional principal amount for
the FRA and calculated for the length of the interest period in the agreement.
Example
Suppose that a company knows that it will need to borrow $10 million in three
months’ time for a period of six months. (Alternatively, suppose that a company has
a floating rate loan of $10 million, with interest payable every six months, and the
next interest period due to start in three months’ time.)
The company can hedge its exposure to the risk of a rise in the six-month interest
rate by buying a 3 v 9 FRA for a notional principal amount of £5 million. If the
bank’s FRA rates for 3 v 9 FRAs are 5.40 – 5.36, the rate applied to the agreement
will be 5.40%. The benchmark rate of interest, or ‘
reference rate’, will be the six-
month dollar LIBOR rate.
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Settlement of the FRA
Suppose that at the end of month 3, six-month LIBOR is 6.25%. The FRA rate is
lower than 6.25%. The actual interest rate for borrowing is 6.25% but the FRA has
fixed a rate of 5.40%. The FRA rate is settled by a payment from the bank to the
buyer of the FRA.
The difference between the FRA rate and LIBOR is 0.85%. The payment to settle
the FRA will therefore be based on an interest difference of: 0.85% × $10 million
× 6/12 = $42,500.
The actual payment will actually be less than this, because the FRA is settled
immediately, at the beginning of the notional interest period, and not at the end
of the period. The $42,500 is therefore discounted from an end-of-interest period
value to a start-of-interest period value, using the reference rate of interest as the
discount rate. This PV is the amount received in settlement of the FRA.
Suppose that at the end of month 3, six-month LIBOR is 4.75%. The FRA rate
(5.40%) is higher than the spot rate. The actual borrowing rate in the money market
is 4.75% and the FRA has fixed a rate of 5.40%. Therefore the FRA rate is settled by a
payment from the buyer of the FRA to the bank. The difference between the FRA
rate and LIBOR is 0.65%.
The payment to settle the FRA will therefore be based on this interest rate
difference: 0.65% × $10 million × 6/12 = £32,500.
Again, because the payment is at the beginning of the interest period and not at
the end of the period, the $32,500 should be discounted to a present value at the
reference rate of interest. This PV is the amount of the payment in settlement of
the FRA.
How an FRA fixes a forward interest rate
Continuing the example, the company will presumably want to borrow $10 million
for six months from the end of month 3. It will do so by arranging an ordinary
short-term loan with a bank. The interest rate on the loan might be set at US dollar
LIBOR + 1%.
Suppose that at the end of month 3, six-month dollar LIBOR is 6.25%. The
company will therefore borrow for six months at 7.25% (= LIBOR + 1%). It will
receive a payment from the FRA of 0.85%, so that the net cost of borrowing will
be 6.40% (7.25% – 0.85%). This net effective interest rate is equal to the FRA rate
of 5.40% plus the margin of 1% above LIBOR for the borrowing. The company
has therefore been able to fix LIBOR at 5.40% with the FRA.
Suppose that at the end of month 3, six-month LIBOR is 4.75%. The company
will therefore borrow for six months at 5.75% (= LIBOR + 1%). However, it must
also make a payment of 0.65% to settle the FRA, bringing the total cost of
borrowing for the six months to 6.40% (5.75% + 0.65%). Again, this total effective
rate is equal to the FRA rate of 5.40% plus the 1% margin, and the FRA has
therefore fixed the effective LIBOR rate at 5.40%.