Topic Seven Hedging exposures with swaps How do you convert a floating rate loan to a fixed rate...

Topic Seven

Hedging exposures with swaps

How do you convert a floating rate loan to a fixed rate loan, or a US dollar exposure to an Australian dollar exposure?

7.2

Topic Seven

Sub-Topics

Converting a floating interest rate to a fixed rate Adjusting the duration of a bond portfolio Converting the currency of a loan Diversifying an equity portfolio

7.3

Topic Seven

Student learning outcomesAfter completing this unit you should be able to do the following:

Demonstrate and explain the use of interest rate swaps to convert a floating rate to a fixed rate

Explain how to obtain the duration of an interest rate swap Use duration to explain why the conversion of a floating rate loan to a fixed rate

loan reduces the risk of the cashflows but increases the risk of the market value Demonstrate and explain the use of interest rate swaps to adjust the duration of

a bond portfolio Demonstrate and explain the use of currency swaps to convert the currency of a

loan Explain why a party to a currency swap would prefer fixed (floating) payments

over floating (fixed) payments Explain how a currency swap can create and manage a dual currency bond Demonstrate and explain the use of equity swaps to diversify an equity portfolio Demonstrate how an equity swap can be used to alter a portfolio’s asset

allocation Explain how cashflow and tracking error considerations differentiate equity

swaps

7.4

Topic Seven

References

Hull, J.C. (2011). Fundamentals of Futures and Option Markets. New Jersey: Pearson Education. Chapter 7.

7.5

Managing interest rate risk

A firm may be exposed to either or both of two forms of interest rate risk: The risk of borrowing and lending in the short-term

markets, which itself may be divided into: The risk of rates changing from the time a loan is anticipated

until it is actually taken out The risk associated with changes in interest rates once a

loan is taken out The risk associated with managing a bond portfolio

7.6

Managing interest rate risk

Forwards and futures are: best suited to managing the risk of an anticipated loan also well suited to changing the duration of a bond

portfolio Swaps are:

best suited to managing the risk of a series of cashflows on loans already taken out or in the process of being taken out

also used to change the duration of a bond portfolio

7.7

Converting a floating interest rate to a fixed rate

Swapping a floating rate for a fixed rate

As much of the funds banks receive are at a floating rate, banks prefer to lend at a floating rate of interest

Although a company may prefer to borrow at a fixed rate it is often only able to borrow at a floating rate

Companies preferring a fixed rate loan will often agree to a floating rate loan and convert it into a fixed rate loan via a interest rate swap contract

7.8



Example 7.1 IBP Corp typically borrows at a floating rate. It takes a

one-year $25 million loan at 90-day LIBOR plus 300 basis points. The payments will be made 2 Jun, 2 Sept, 1Dec and 1 Mar, about 91 days apart. The fixed rate on a one-year swap with quarterly payments at LIBOR is 6.27% pa (actual on 360).

Explain how IBP could convert the floating-rate loan to a fixed-rate loan using a swap.

Explain why IBP might be argued to still be exposed to the uncertainty of changing LIBOR.

7.9



Example 7.1 Explain how IBP could convert the floating-rate loan to a

fixed-rate loan using a swap. IBP borrows $25 million at a floating rate and enters into

a swap to pay a fixed rate of 6.27% and receive LIBOR. The notional principal on the swap is $25 million, equal

to the face value of the loan. The swap interest payments are to be made on the

same dates as the loan interest payments are to be made and are structured on an actual/360 day count consistent with that of the loan.

7.10



Example 7.1 Explain how the bank could convert the floating-rate loan

to a fixed-rate loan using a swap. On 2 Jun, 2 Sept, 1Dec and 1 Mar interest payments are

exchanged between the parties to the swap. IBP pays the swap counterparty:

IBP receives from the swap counter party:

IBP pays a net amount of interest equal to:

3600627025 Days.m$

36025 DaysLIBORm$

%.%.%. 279003276

7.11



Example 7.1 Explain why IBP might be argued to still be exposed to

the uncertainty of changing LIBOR. If interest rates fall IBP is still locked into 9.27% and will

not be able to take advantage of the lower cost of borrowing offered by a fall in interest rates.

Duration of the unhedged position:

Duration of the hedged position: 125.0200.025.0

625.075.00.1200.025.0

7.12


Calculate duration of a swap

A pay-fixed, receive-floating swap is equivalent to a portfolio containing a long position in a floating-rate bond and a short position in a fixed-rate bond

The duration of a pay-fixed, receive-floating swap is then equal to the duration of the long position in a floating-rate bond less the duration of the short position in a fixed-rate bond

The duration of a pay-fixed, receive-floating swap is negative, as this position would be expected to benefit from rising interest rates

7.13


Explain how swaps increase market risk

The duration of a fixed-rate loan is larger than the duration of a floating-rate loan for a given maturity

Converting a floating-rate loan to a fixed rate loan then increases the duration of the loan, which in turn increases the sensitivity of the market value of the debt instrument to a change in yields

However, converting a floating-rate loan to a fixed rate loan fixes the cashflows of the loan, subject to day count differences

7.14

Adjusting the duration of a bond portfolio

Adjusting duration of a bond portfolio

Adjusting the duration of a bond portfolio using swaps requires consideration of the following: Should the swap involving paying fixed, receiving

floating or paying floating, receiving fixed? To reduce duration pay fixed To increase duration pay floating

What are the terms of the swap? Trade-off payment frequency with notional principal

What is the notional principal of the swap?

D

DDPNP

*s

ptp

7.15


Adjusting duration of a bond portfolioExample 7.2

A $250 million bond portfolio has a duration of 5.50. The portfolio manager wants to reduce the duration to 4.5 by using a swap. Consider the possibility of using a one-year swap with monthly payments or a two-year swap with semiannual payments.

Determine the durations of the two swaps under the assumption of paying fixed and receiving floating. (Assume the duration of a fixed-rate bond is 75% of its maturity.)

Calculate the notional principal required under each swap.

7.16



Determine the durations of the two swaps under the assumption of paying fixed and receiving floating. (Assume duration of fixed-rate bond is 75% of maturity.)

Duration of a 1-year pay-fixed, receive floating swap with monthly payments is the duration of a 1-year floating-rate bond with monthly payments minus the duration of a 1-year fixed-rate bond with monthly payments.

Duration of a 2-year swap with semi-annual payments.

7080750200008330 ....

25175002200050 .....

7.17



Calculate the notional principal required under each swap.

One-year swap

Two-year swap

m$...

m$ 200251505504

250

m.$...

m$ 13537080505504

250

7.18

Converting the currency of a loan


Currency swaps are: designed for the purpose of managing exchange rate

risk Also for managing interest rate risk where exchange

rate risk is present

7.19



Example 7.3

A Japanese company issues a bond with a face value of JPY1.2 billion and a coupon rate of 5.25% pa. It decides to use a currency swap to convert this bond into a euro-denominated bond. The JPY/EUR exchange rate is 120. The fixed rate on euro-denominated swaps is 6% pa and the fixed rate on yen-denominated swaps is 5% pa. Payments are made annually.

Describe the terms of the swap. Identify all cashflows.

7.20



Example 7.3

Describe the terms of the swap. The company will enter into a swap with a notional

principal of EUR10m.

The company will pay a Yen denominated principal, receiving EUR, at initiation and receive a Yen denominated principal, paying EUR, at maturity.

The company shall receive Yen denominated interest payments and pay EUR denominated interest payments.

mEURm,JPY 101202001

7.21



Example 7.3

Identify all cashflows. At initiation:

Issuance of Yen bond: +JPY1,200m Swap -JPY1,200m AND

+EUR10m Annual Interest payments:

Bond -JPY63m Swap +JPY60m AND -EUR0.6m

At maturity: Issuance of Yen bond: -JPY1,200m Swap +JPY1,200m AND -

EUR10m

7.22


Explain preference for fixed or floating

A currency swap party’s preference for paying a fixed or floating rate will depend on its views about the direction of interest rate movements. Companies typically choose floating rates when they

think interest rates are likely to fall Companies typically choose fixed rates when they

think interest rates are likely to rise

7.23


Create a dual-currency bond

Firms may wish to raise the principal in the domestic currency and make the interest payments in a foreign currency, where they have sufficient foreign denominated income to make the interest payments but not to repay the principal

A dual-currency bond is equivalent to issuing an ordinary bond in one currency and combining it with a currency swap that has no principal payments

7.24


Construct a dual-currency bond Example 7.4

The USD/CHF exchange rate is 0.8000. Assume that the appropriate interest rate for a $20 million bond in USD is 5.5% and the appropriate fixed rates on a currency swap are 5.5% in USD and 5.0% in CHF.

From the perspective of the issuer, construct a synthetic dual-currency bond in which the principal is paid in US dollars and the interest is paid in Swiss francs. The face value will be $20 million, and the interest rate will be 5% in Swiss francs.

7.25




Issue $20m bond in US dollars, paying interest at 5.5%. Enter currency swap on US$20m notional principal, i.e.

CHF25m. The swap will involve the receipt of USD interest at 5.5%

and payment of CHF interest at 5.0%

7.26




The annual cashflows will be: On USD bond -US$1.1m On swap +US$1.1m AND –

CHF1.25m

7.27

Diversifying an equity portfolio


Equity portfolio managers frequently wish to realign the risk of their portfolios

Swaps can be used to diversify a concentrated portfolio achieve international diversification change the asset allocation between stocks and

bonds

7.28


Differentiate equity and other swaps

Equity swaps are distinctive due to: The fact that an equity index may show a negative

return which may mean that the fixed cashflow, in a swap exchanging a fixed payment for a variable receipt based on the return of an equity index, may not be fixed as it may increase if the index shows a negative return

Tracking error, where the returns of the portfolio are not reflected in the returns of the index underlying the swap, may also produce further cashflow problems

7.29


Diversifying an equity portfolio Example 7.5

CWF is a charitable organisation with an endowment of $50 million invested in diversified number of stocks. Samuel Zykes, a wealthy member of the community dies and leaves CWF a donation of stock in his company, ZYK, currently valued at $30 million. CWF does not want to sell the ZYK stock as it believes the Zykes family may make further donations in the future, however it is concerned about the concentration of the portfolio.

Advise CWF of a suitable swap strategy to increase the diversification of the portfolio.

Describe the issues facing parties to the equity swap.

7.30



Advise CWF of a suitable swap strategy to increase the diversification of the portfolio.

CWF enters a swap to pay the return on $30m of ZYK stock and receive the return on $30m of S&P 500 index.

The payments will be made quarterly. The maturity could be set for 5 years hence, assuming

CWF is expecting another grant might be forthcoming in 5 years time.

There is no exchange of notional principal. CWF will maintain possession of the ZYK stock and

voting rights.

7.31



Describe the issues facing parties to the equity swap. Cashflow problems:

CWF will have a net cash outflow if ZYK outperforms the S&P 500.

It is possible that CWF will pay the return on ZYK plus the return on the S&P 500, if ZYK has a positive total return and the index has a negative total return

Counterparty’s risk The counterparty will be long ZYK and short the

index. It could hedge this by shorting ZYK and buying the index.

7.32



A Canadian trust fund holds a portfolio of CAD300 million of Canadian equities. The manager would like to sell off CAD100 million and invest the funds in a pan-European portfolio. The manager arranges to do so using an equity swap in the domestic stock represented by the Toronto 300 composite and the Dow Jones Euro STOXX 50.

Advise the trust fund how to structure such a swap. Describe how tracking error could potentially interfere

with the success of the transaction.

7.33



Advise the trust fund how to structure such a swap. The trust should enter a swap to receive the return on

the DJ Euro STOXX 50 and pay the return on the Toronto 300.

7.34



Describe how tracking error could potentially interfere with the success of the transaction.

Tracking error is the failure of the derivative cashflow to match precisely the cashflow from the underlying portfolio. In this case tracking error means that the return actually earned on the domestic portfolio is not likely to perfectly match the Toronto 300 return. These returns are supposed to offset, but they are not likely to do so, certainly not with any accuracy. The return on the DJ Euro 50 does not present any tracking error concerns.

7.35


Altering the portfolio asset allocation Example 7.7

TMM wants to change the asset allocation on a $200 million portfolio. The portfolio allocations are as follows:

Current Desired Current Desired Trans

Equities 75% 90% $150m $180mLarge Cap 60% 65% $90m $117m

Mid Cap 30% 25% $45m $45m

Small Cap 10% 10% $15m $18m

Bonds 25% 10% $50m $20mGovernment 80% 75% $40m $15m

Corporate 20% 25% $10m $5m

7.36



Based on the S&P 500 index, the S&P Small Cap index, the Lehman Long Treasury Bond index and the Merrill Lynch Corporate Bond index, advise TMM on how to structure an equity swap to achieve its desired asset allocation.

7.37



Current Desired Current Desired Trans

Equities 75% 90% $150m $180mLarge Cap 60% 65% $90m $117m Buy $27m

Mid Cap 30% 25% $45m $45m None

Small Cap 10% 10% $15m $18m Buy $3m

Bonds 25% 10% $50m $20mGovernment 80% 75% $40m $15m Sell $25m

Corporate 20% 25% $10m $5m Sell $5m

7.38



Advise TMM on how to structure an equity swap to achieve its desired asset allocation.

Equity swaps Receive return on S&P500 on $27m Pay LIBOR on $27m Receive return on SPSC on $3m Pay LIBOR on $3m

Fixed-income swaps Receive LIBOR on $25m Pay return on LLTB on $25m Receive LIBOR on $5m Pay return on MLCB on $5m

7.39



Advise TMM on how to structure an equity swap to achieve its desired asset allocation.

Note that the overall position involves no LIBOR payments. The LIBOR payments can be eliminated and the equity and fixed-income swaps can be combined into a single swap with the following cashflows:

Receive return on S&P500 on $27m Receive return on SPSC on $3m Pay return on LLTB on $25m Pay return on MLCB on $5m

Topic Seven Hedging exposures with swaps How do you convert a floating rate loan to a fixed rate...

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