Chapter 17 - Hedging Interest Rate Risk

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CHAPTE R 17 – HE DGING I NTE RE ST RATE R ISK

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FORWARD RATE AGREEMENT (FRA)

Definition:

– an agreement between a business and a bank that fixes an interest rate in the future

for a set period of time on a specified level of borrowing or lending.

EXAMPLE

A company wishes to borrow £100 million in three months time for a period of six months. Thecompany can borrow at LIBOR + 0.5% and LIBOR is currently at 3.5%. The company wishers to

protect the short-term borrowing from adverse movements in interest rates by entering a forward

rate agreement.

Show the outcome of the FRA if:

(a) LIBOR increases by 0.5%

(b) LIBOR decreases by 0.5%

FRA prices are:

3 v 9 - 3.85 – 3.80

3 v 6 - 3.58 – 3.53

6 v 9 - 3.55 – 3.45

Solutions:





INTEREST RATE FUTURES

Definition:

– is a binding contract between a buyer and a seller for delivery of an agreed interest

rate commitment on an agreed date and at an agreed price. The contracts aretraded on the LIFFE and the terms are standardised, with respect to the amounts,

dates and interest rates.

Terminology

• Contract size – standardised quantity of underlying item (interest rates)

• Delivery dates – settlement date on contract (March, June, September and December)

• Tick size – minimum price movement on futures contract

• Price – 100 – interest rate

• Buy or sell

Interest rate futures pricing

Futures price = 100 – interest rate

If interest rates are expected to be at 5.00% p.a. then the future will be quoted at 95.00 and a

person hedging against interest rate rises will sell at 95.00, conversely a person hedging against

interest rate falls will buy at 95.00

Interest rate futures position

A company hedging against a rise in interest rates in the future enters into a futures contract to

cover £10million of borrowing for a period of 3 months at 95.00 and closes out the contract at 93.50.

Buy now @ 95.00

Sell later @ 93.50

Loss 1.50





Interest rate futures contracts

The standard size of an interest rate futures contract is £500,000 and covers a period of three

months.

No. of contracts = Amt of cashdeposited/invested x No. of moths cashdeposited/invested for

Standard contract size 3 months

Example

A company wishes to borrow £60million in three months time for a period of two year. The

standard contract size on one three month sterling futures contracts is £500,000.

Calculate the number of contracts required.

Hedging imperfection

• Basis risk – difference between the market price and the futures price

• Number of contracts – difficult to achieve an exact number of contracts

Solutions:

1. Set up the hedge

2. Closing futures price

3. Closing spot price

4. Net outcome





EXAMPLE

The finance director of Popa plc has recently reviewed the company’s monthly cash budgets for the

next year and has revealed that the company is likely to need £60 million in three months’ time for a

period of two months. The market has been very volatile of late and the finance director is

concerned that short term interest rates could increase. He has therefore decided to protect againsta possible increase in interest rates using interest rate futures.

LIBOR is currently 6% per annum and Popaplc can borrow at LIBOR + 0.9%.

Derivative contracts may be assumed to mature at the end of the month.

Three month sterling futures (£500,000 contract size, £12.50 tick size)

December 93.870March 93.790

June 93.680

Illustrate how the short-term interest risk might be hedged if interest rates increase by 0.5%.

Assume that it is now mid-December.





INTEREST RATE OPTIONS (TRADED)

Definition:

provides the buyer with the right, but not the obligation to buy or sell the related interest rate

futures contract.

Solutions:

1.

Set up the hedge - buy/sell initially

- # of contracts

- tick size

- date

- premium

2. Closing futures price

3. Closing spot price

4. Net outcome

EXAMPLE

The finance director of Popa plc has recently reviewed the company’s monthly cash budgets for the

next year and has revealed that the company is likely to need £60 million in three months’ time for a

period of two years. The market has been very volatile of late and the finance director is concerned

that short term interest rates could increase. He has therefore decided to protect against a possible

increase in interest rates using interest rate futures.

LIBOR is currently 6% per annum and Popa plc can borrow at LIBOR + 0.9%.

Derivative contracts may be assumed to mature at the end of the month.

Three month sterling futures (£500,000 contract size, £12.50 tick size)

December 93.870

March 93.790

June 93.680





Options on three month sterling futures (£500,000 contract size, premium cost in annual

percentage)

Calls Puts

December March June December March June

93.750 0.120 0.195 0.270 0.020 0.085 0.180

94.000 0.015 0.075 0.115 0.165 0.255 0.335

94.250 0.000 0.030 0.085 0.400 0.480 0.555

Illustrate how the short-term interest risk might be hedged if interest rates increase by 0.5%.

Assume that it is now mid-December.





INTEREST RATE SWAPS

Definition:

a derivative in which one party exchanges a stream of interest payments for another party's stream

of cash flows. Interest rate swaps can be used by hedgers to manage their fixed or floating rates ofinterest.

Solution (vanilla swaps):

1. Calculate the gain

2. Split the gain and calculate the expected outcome

3. Demonstrate how the swap works





INTEREST RATE GUARANTEE (IRG)

Definition:

An interest rate guarantee (IRG) provides the right, but not the obligation, to pay or receive a fixed,

specified rate of interest for a defined period of time with a bank.





INTEREST RATE CAP

Option which gives the holder the right to a series of compensations if interest rates increase above

the exercise price at each interest fixing date or rollover date for the loan.

EXAMPLE

NTY a UK based company is arranging a loan of £15 million over a period of two years. Interest is

payable at six months LIBOR + 1.5%. The market has been very volatile and the company is

concerned about adverse movements in interest rate. The finance director has therefore decided to

buy an interest rate cap from a bank at an exercise price of 8% and a premium of 0.4%.

Calculate the effective rate of borrowing in each of the four interest periods assuming the six month

LIBOR rate for each period is as follows:

1st

interest period 10%

2n

interest period 7%

3rd

interest period 11%

4th

interest period 8%

INTEREST RATE FLOOR

Option which gives the holder the right to series of compensations if interest rates fall below the

exercise price at each interest fixing date or rollover date for the loan.

INTEREST RATE COLLAR

A combination of:

• Buying an interest rate cap and selling interest rate floor (borrowing)

Or,

• Buying an interest rate floor and selling interest rate cap (investing)

Note: both cap and floor must be for the same notional principal and maturity





EXAMPLE

BWT a UK based company is arranging a loan of £15 million over a period of two years. Interest is

payable at six months LIBOR + 1.5%. The market has been very volatile and the company is

concerned about adverse movements in interest rate. The finance director believes that interest rate

cap would be expensive and has therefore decided to use interest rate collars in which the capexercise price is 8% (premium 0.4%) and floor exercise price is 6% (premium 0.15%).

Calculate the effective rate of borrowing in each of the four interest periods assuming the six month

LIBOR rate for each period is as follows:

1st

interest period 9%

2nd

interest period 10%

3rd

interest period 7%

4t

interest period 5%





MACAULAY DURATION

“Weighted average time for the recovery of the payments and principal in relation to the current

market price of a bond”

•

Measures the number of years required to recover the cost of the bond

• Enables two different bonds to be compared

• Enables the value of a bond to be calculated for changes in interest rates

CALCULATION

1. Establish the cash flows arising at each future period

2. Calculate the present value of these future cash flows

3.

Calculate each year’s discounted cash flow as a proportion of the current value of the bond

4. Multiply the proportion calculated for each time period its time period and sum the

weightings

EXAMPLE

Seven years prior to the maturity of a bond with a 10% coupon, it is trading at a price of £95.01 per

cent and has a gross yield to maturity of 11.063%. Using the Macaulay duration method, you are

required to calculate the bond duration.

•

Changes in the value of a bond are inversely related to changes in the rate of return

• Long-term bonds have higher interest rate risk than shorter term bonds

• High coupon bonds have less interest rate risk than shorter term bonds

CONCLUSION

• Duration increases as maturity increases

• Duration decreases as the coupon rate increases

•

Duration will decrease as interest rates rise

Chapter 17 - Hedging Interest Rate Risk

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