unit 7 - bonds and interest rate risk

Unit 7

Risk Assessment and Interest Rate Risk

Bonds

What is a bond?

I could borrow £1,000 from the bank at 6% for 5 years. That is a loan and is a form of debt.

Bonds

What is a bond?

I could borrow £1,000 from the bank at 6% for 5 years. That is a loan and is a form of debt.

Or I could issue a £1,000 bond @ 6% with a 5 year maturity. This would mean issuing 10 x £100 certificates. Let us assume that each bond is worth £100. So I would receive 10 x £100 = £1,000.

Then each year for 5 years I would pay the holder (“bearer”) of the bond £100 x 6% = £6. Each bearer has the right to sell the bond to another investor. As the borrower (“issuer”) it would make no difference to me. I would continue paying whoever are the bearers the annual interest and on maturity the £100 x 10.

Bonds

Let us look at the terminology:

A bond has a £100 nominal value, six year maturity and a coupon of 5%. The market yield to maturity for a similar bond is 7%.

Bonds

A bond has a £100 principal (or nominal) value, six year maturity and a coupon of 5%. The market yield to maturity for a similar bond is 7%.

The principal (or nominal) value is the amount upon which the interest is calculated. It is also the amount that will be repaid on maturity.

Bonds


The principal (or nominal) value is the amount upon which the interest is calculated. It is also the amount that will be repaid on maturity.

Note: the interest is calculated on the principal and NOT on the bond price.

[You can normally assume that the principal value is £100 in OU assignments and exams – this is because this is the usual denomination of UK bonds]

Bonds


The maturity is how long the bond will last before being repaid. In this case after six years the final interest payment will be made alongside the repayment of the principal (£100).

Note that the maturity is the total length of the bond – not necessarily the number of years left to run.

Bonds


The coupon is the amount of interest that is paid, as applied to the principal (not the price!)

So the interest will be 5% x £100 = £5 pa.

Bonds


The yield to maturity is the return including all interest payments and the repayment of the principal on maturity, that a particular type of bond is earning on the market.

By type we mean , for example, AA rated UK corporate bond with 7 years to maturity –similar risk and maturity.

Bond Price


Let us work out the price. It is simply the present value of the bond’s cash flows discounted using the YTM. So for the above bond:

Bond Price



0 1 2 3 4 5 6

Interest 5 5 5 5 5 5

Repayment 100

Total 5 5 5 5 5 105

DCF @ 7% 4.67 4.37 4.08 3.81 3.56 69.97 = £90.47

Bond Price



0 1 2 3 4 5 6

Interest 5 5 5 5 5 5

Repayment 100

Total 5 5 5 5 5 105

DCF @ 7% 4.67 4.37 4.08 3.81 3.56 69.97 = £90.47

So it would cost you £90.47 to buy this bond now, but you would still receive interest on £100. Note that this could have been the issue price – bonds do not have to be issued at £100.

Forwards and Futures

A forward contract is a contract obliging the parties to buy or sell a given commodity at a given price, at a given time, sometime in the future.

A futures contract is a forward contract that is standardised in order that it may be traded on an exchange ( in other words the futures contract itself can be bought and sold)

Forwards and futures can be used to “hedge” investment positions. Hedging means to remove or minimise uncertainty.

Futures

A farmer is expecting to harvest 100 tonnes of wheat in six months time. He can sell today a wheat six month future for £90 /tonne. He sells a contract for 100 tonnes.

Futures


In six months time the spot price of wheat is £88/t. So the farmer has “won” [ he could buy 100 tonnes for £8,800 and sell at £9,000 – or he could have sold into the market at £88/t instead he is selling at £90/t].

So the market will send him his profit of:

• 100 tonnes x (£90-88) = £200.

Futures


In six months time the spot price of wheat is £88/t. So the farmer has “won” [ he could buy 100 tonnes for £8,800 and sell at £9,000 – or he could have sold into the market at £88/t instead he is selling at £90/t].

So the market will send him his profit of:

• 100 tonnes x (£90-88) = £200.

• A future is a “contract of difference” – somewhere there is someone (“the counterparty”) who bought an equal and opposite contract (or one buyer bought 75 tons and another bought 25 tons – either way the total sell contracts will equal the total buy contracts)

Futures

Let us see how the hedge works.

The farmer goes to market and sells his wheat: 100 tonnes x £88 = £8,800.

So his total gain is £8,800 (market) + £200 (future) = £9,000. He has received £90 /tonne and so achieved his hedge

Futures

Let us see how the hedge works.

The farmer goes to market and sells his wheat: 100 tonnes x £88 = £8,800.

So his total gain is £8,800 (market) + £200 (future) = £9,000. He has received £90 /tonne and so achieved his hedge

Hedge achieved by combining a physical transaction alongside a derivative instrument

Futures

If instead in six months time the price of wheat is £95.

Now the farmer is a “loser” – he must sell wheat at £90 whereas it will cost him £95 to buy it in the spot market. So he must send to the futures market his loss:

100 tonnes x (£95-90) = £500. This is referred to as “closing out”

Futures

If instead in six months time the price of wheat is £95.

Now the farmer is a “loser” – he must sell wheat at £90 whereas it will cost him £95 to buy it in the spot market. So he must send to the futures market his loss:

100 tonnes x (£95-90) = £500. This is referred to as “closing out” – more later

So now he sells his wheat at market and gets 100 x £95 = £9,500.

So his total gain is:

£9,500 (market) - £500 (future loss) = £9,000 again he has hedged at £90/tonne

Hedge achieved by combining a physical transaction alongside a derivative instrument

Interest Rate Futures strategy

Let us assume that you can get a quote for £500,000 at 4% (96) for 3 months time . If you are borrowing money you wish to hedge against interest rates going up. If interest rates go up, the price of the future goes down.

So you wish to profit by the future going down in value. In which case you need to sell a future.

Futures strategy



If in 3 months the interest rate is 4.5% then the future will now trade at 95.5 so you sold at 96, you will now buy (“close out”) at 95.5, so your profit is [96-95.5%] x £500,000 x 3/12 = £625.

Futures strategy



If in 3 months the interest rate is 4.5% then the future will now trade at 95.5 so you sold at 96, you will now buy (“close out”) at 95.5, so your profit is [96-95.5%] x £500,000 x 3/12 = £625.

You pay your bank interest £500,000 x 4.5% = £5,625, but less your futures profit = £5,000 = 4%, your hedged rate.

Interest Rate Swaps

Sometimes it is possible to improve to get a more desirable interest rate by entering a swap.

Let us look at a very simple example.

Interest Rate Swaps



Company A can borrow at a fixed rate of 6.0% or a variable rate of Libor + 1.0%. It would prefer a variable rate.

Company B can borrow fixed at 6.2% or variable at Libor + 1.1%. It would prefer to borrow at a fixed rate.

Interest Rate Swaps



Company A can borrow at a fixed rate of 6.0% or a variable rate of Libor + 1.0%. It would prefer a variable rate.

Company B can borrow fixed at 6.2% or variable at Libor + 1.1%. It would prefer to borrow at a fixed rate.

If they enter their desired rates then the costs would be:

A L + 1

B 6.2

Total L + 7.2%

Interest Rate Swaps

Now assume they enter a swap agreement. A takes a fixed loan with its bank but agrees to pay Libor into the swap and receive 5.06% back.

B enters the same swap. It takes a variable loan with its bank but pays 5.06% into the swap and receives Libor from it.

So now:

A BPays bank 6%

Pays bank L+1.1%

Pays B Libor

Pays A 5.06%

Interest Rate Swaps

So A pays 6 + L and receives 5.06%, a total = L + 0.94% (L + 1%)

B pays 5.06 + L + 1.1% and receives L, a total = 6.16% (6.2%)

An overall total of L + 7.1% (7.2% before the swap)

A BPays bank 6%

Pays bank L+1.1%

Pays B Libor

Pays A 5.06%

The 2 companies have entered a swap agreement in addition to their individual bank agreements

Interest Rate Swaps

In practice a bank would set up the swap and be in the middle (getting a cut)

A BPays bank 6%

Pays bank L+1.1%

Pays new bank Libor

Pays new bank 5.08%Swap

bank

Pays A 5.03% Pays B Libor

Notice the bank makes a profit

Interest Rate Swaps

In practice a bank would set up the swap and be in the middle (getting a cut)

Now A pays 6 + L – 5.03 = L + 0.97 (L+1%)

B pays L + 1.1 + 5.08 – L = 6.18% (6.2%)

And the arranging bank gets 5.08% - 5.03% = 0.05%

A BPays bank 6%

Pays bank L+1.1%

Pays new bank Libor

Pays new bank 5.08%Swap

bank

Pays A 5.03% Pays B Libor

Notice the bank makes a profit

Next Time

We shall look at FX hedging and options from unit 8

unit 7 - bonds and interest rate risk

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