swaps explained for frm/cfa level 1

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Agenda

• Introduction

• The Comparative Advantage Argument

• Interest rate swaps

• Valuation of swaps

• Currency swaps

• Credit risk

• Other types of swaps

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Introduction

• A swap is an agreement between two parties to swap cash flows in the future.

• The arrangement covers swaps on multiple dates.

• Futures or forwards can be considered as a simple example of a swap where there is a cash flow

exchange on one particular date.

• Most common swaps are interest rate swaps (IRS) and currency swaps.

• The legal agreement in which the two parties enter is called a confirmation, which covers the

termination date, calendar used, rates of payment, day count conventions etc.

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Agenda

• Introduction




• Currency swaps

• Credit risk


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)( FloatingFixed

• Take the example of two firms X and Y where:

– X wants to borrow floating

– Y wants to borrow fixed

• Table tells us that X can borrow fixed at 5% and Y can borrow fixed at 7%

• Also X can borrow floating at LIBOR and Y can borrow floating at (LIBOR+100bps)

• This implies that X has absolute advantage in borrowing over Y

• The point to note here is that the difference in fixed borrowing rates for X and Y( is not the same for

the floating borrowing rates.

• Combined benefit to both X and Y by using swap is which is 100 bps for X and Y.

Company Fixed Borrowing Floating Borrowing

X 5% LIBOR

Y 7% LIBOR+100bps

The Comparative Advantage Argument

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The Comparative Advantage Argument (Cont…)

X IB Y 5%

5.50%

Libor Libor

5.50%

Libor +

100

bps

• To reduce the borrowing rates X and Y enter into a swap shown below through the intermediary

which is usually an investment bank (IB).

• Assuming zero transaction charges for IB, X borrows at 5% and lends that money at 5.5% to Y

through an investment banker.

• Similarly Y borrows at LIBOR+100bps and lends to X at LIBOR.

• Therefore the net borrowing rate for X becomes (LIBOR-50bps) which is lower than the original rate

of LIBOR.

• Similarly the net borrowing rate Y becomes 6.5% which is 50bps less than the original rate of 7%

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Question – Comparative Advantage

XYZ IB ABC 10%

10.00%

LIBOR

+

100bps

LIBOR

+

250bps

10.50%

Libor +

100

bps

Following are the rates at which company ABC and XYZ can borrow from the market.

How can they benefit from Interest Rate SWAP?

Solution:

XYZ and ABC both benefit by 50bps while the IB makes 200bps profit

Fixed Rate Floating Rate

ABC 11% LIBOR+1%

XYZ 10% LIBOR+3%

+0.50%

+150bps

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Agenda

• Introduction




• Currency swaps

• Credit risk


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Interest rate swaps

• In the case of fixed-for-floating interest rate swaps two parties get into an agreement where one pays

interest on a floating rate to the other, while the other pays a fixed rate of interest on the same amount

• LIBOR is the most common reference rate of floating interest

• Notional principal is exchanged or basically no principal is exchanged

• IRS can be used for

– Changing a liability

– Transforming a liability

Party 1 Party 2

Fixed Rate

Floating Rate

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Changing a liability

• Party 1 avails a loan of 10% while party 2 avails a floating rate loan at LIBOR +0.3%

• Party 1 is receiving a fixed rate of 8% from party 2

• Party 1 pays floating interest rate

– Party 1’s effective cash flow:

• Net cash outflow is (LIBOR+2% )

– Party 2’s effective cash flow:

• Net cash outflow is 8.3 %

• Point to note here is that Party 1’s fixed liability is changed to floating liability after the swap.

• Party 2’s liability is changed from a floating liability to a fixed liability of 8.3%

LIBOR+0.3% 10% Party 1 Party 2

LIBOR

8%

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Financial intermediaries

• In the practical world most swaps are traded in the OTC market where financial institutions act as

market makers .

• In the diagram above you can see that the financial institution is making a 3 basis point spread on the

fixed payment of the transaction

• In such cases the bank has separate contract with party 1 and party 2.

• Party 1 and party 2 might not even know that they are on the other sides of the same swap.

• Bank creates a market by creating both bid and offer positions so that it can seek clients on either

side of the swap

• It is exposed to certain credit risks in case it is unable to find a counter party for a swap

LIBOR+0.3% 10% Party 1 Party 2

LIBOR

9.985

%

LIBOR

10.015

%

Financial

Institution

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Swap rates

• The swap rate is the average of

– The fixed rate a market maker is prepared to pay in exchange for a receiving LIBOR ( its bid rate)

– The fixed rate it is willing to receive in return for a payment of a floating rate ( its offer rate)

• Like LIBOR swap rates are not risk free rates but close to risk free rates

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Agenda

• Introduction




• Currency swaps

• Credit risk


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Valuation of swaps

• There are 2 ways to value a swap.

– Considering it as a difference of two bonds

– Considering it as a portfolio of FRAs

• Value using bonds

– Consider an example in which the swap lasts for n years. If the payments are made at the end of each

year then :

– If the principal is exchanged between the 2 parties at the end of the swap, then Party 1’s cash flow

suggests that it’s long a fixed rate bond and short a floating rate bond.

– Party 2 is short a fixed bond and long a floating rate bond.

– We can value the swap by looking at the pay offs of either party.

• Hence the value of the swap can be given as:

V = Bfix – Bfl

– Where,

• Bfix= PV of payments

• Bfl = (P+AI)e-rt

– Value of a floating bond is equal to the par value at coupon reset dates and equals to the Present Value

of Par values (P) and Accrued Interest (AI)

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Valuation of swaps

• Value using portfolio of FRAs

• In this case we assume that each payment at a future date is a forward rate agreement.

• For payment at time t, the rate used is the rate for the period between t-1 and t. This rate would be

FRA at t-1.

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Question

Calculate the fixed rate of interest on the swap.

Interest rate swap

We enter into a swap where we receive floating rates in return for fixed rate pay outs

Contract details as below

Notional Principal $5,000,000

Term (Years) 4

Settlement 6 monthly

Floating Rate LIBOR 6mo

LIBOR forward rates and spot rates given:

Time (Years)

6mo LIBOR Fwd

Rate

LIBOR Spot

Rate

0.00 2.8300 0.0000

0.50 3.1120 2.6768

1.00 3.2230 3.1135

1.50 4.5680 3.2950

2.00 4.1897 3.7953

2.50 4.3196 3.7441

3.00 3.9648 3.8523

3.50 5.0128 3.7997

4.00 4.0910

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Answer

Calculation of fixed rate

based on LIBOR forward rates we receive the following 8 cash inflows.

We discount each using the [LIBOR] spot rates.

Time (Years)

6mo LIBOR Fwd

Rate Cash Flow In

LIBOR

Spot Rate

Discount

Factor PV of Cash In

0.00 2.8300 0 0.0000 0 0

0.50 3.1120 $141,500 2.6768 0.9868 $139,631

1.00 3.2230 $155,600 3.1135 0.9696 $150,866

1.50 4.5680 $161,150 3.2950 0.9522 $153,441

2.00 4.1897 $228,400 3.7953 0.9276 $211,855

2.50 4.3196 $209,485 3.7441 0.9114 $190,932

3.00 3.9648 $215,980 3.8523 0.8918 $192,619

3.50 5.0128 $198,240 3.7997 0.8766 $173,771

4.00 $250,640 4.0910 0.8505 $213,157

$1,426,272

In no arbitrage case the PV of fixed payment should be:

$1,426,272 .

Hence,

$1,426,272 = annual payment * Sum ( Discountfactors )

$1,426,272 = annual payment* 7.3664

$193,619 = annual payment

Thus, the fixed interest rate is $193,619 / $5,000,000

3.87%

Total PV of Floating Payments

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Agenda

• Introduction




• Currency swaps

• Credit risk


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Currency swaps

• Currency swap involves exchanging principal and interest payment in one currency with the principal

and interest payments in other currency

• In this case the principal needs to be specified and it is exchanged in the beginning as well as the end

of the swap

• Consider a currency swap between party 1 and 2. In this case Party 1 is in India and can borrow in

INR and party 2 is in Australia and can borrow competitively in AUDs at 6%. Party 1 borrows Rs

380,000 at 12% and exchanges the principal with party2 for 100,000 AUDs (which it borrows in

Australia). The principal is exchanged back at the end of the life of the swap and the life of the swap is

5 years

• What is the net payout for party 1 and party 2?

6% AUD 12% INR Party 1 Party 2

5.1%

AUD

12%

INR

5% AUD

12.1%

INR

Financial

Institution

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• Which of the following statements is correct when comparing an Interest rate Swap with a Currency

Swap?

A. At maturity there is no exchange of principal between the counterparties in IRS and there is an

exchange of principal in Currency Swaps.

B. At maturity there is no exchange of principal between the counterparties in Currency Swaps and there is

an exchange of principal in IRS.

C. The counterparty in an IRS needs to consider fluctuation in exchange rates, while currency swap

counterparties are only exposed to fluctuations in interest rates.

D. Currency swaps counterparties are exposed to less counterparty credit risk due to offsetting effect of

currency risk and interest rate risk embedded within the transaction.

Questions

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Valuation of currency swaps

• Just like IRS this swap can be valued using bonds approach and FRA approach

• Valuation using bonds

– Party 1 is receiving payments in Rupees while paying in AUDs. Hence we can say that he is long a rupee

bond and short an AUD bond

– The value of the swap will be the difference in the PV of the bonds.

Vswap= BRs – S0BAUD

– Where,

• S0 is the current spot exchange rate between Rs and AUDs

• Valuation as a portfolio of forward contracts

– In this case we determine the forward exchange rate at each point when the swap payments occur

– The foreign currency is converted using the forward exchange rate

– In the example above the 1 year, 2 year, 3 year, 4 year forward rate for INR-AUD exchange is used for

converting AUD cash flows to INR every year

– This is then discounted back to the present value to give the value of the swap.

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Question

The US$ interest rate is 6% per annum and the INR rate is 8% per annum. Assume that the term

structure of interest rates is flat in the US and India. Assume current value of INR to be 0.02 US$.

Company ABC, under the terms of a swap agreement, pays 7% per annum in INR and receives 3% per

annum in US$. The principal in the US is $10million and that in India is 550million INR. Payments are

exchanged each year and the swap will last for 3 more years. Determine the value of swap assuming

continuous compounding in all interest rates.

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Solution

Valuation of currency swap in terms of bonds (millions):

Value of swap in million $ = 531.278*0.02 – 9.1519 = $1.4737 million.

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Agenda

• Introduction




• Currency swaps

• Credit risk


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Credit risk (Covered in detail in VaR later)

• A financial institution has a credit risk exposure from a swap only when the value of the swap is

greater than zero.

• Potential losses from a swap are much less than losses from defaults on a loan with the same

principal.

• Potential losses from a currency swap are much higher than losses from an interest rate swap.

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Agenda

• Introduction




• Currency swaps

• Credit risk


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Other types of swaps

• LIBOR is the most common floating rate in IRS; however there can be other floating rates like,

commercial paper (CP) rates.

• In floating for floating swaps: rates of one type (LIBOR) can be swapped with floating rates of

another type (CP)

• In an amortizing swap the principal amount reduces in a predetermined amortization rate

• In a step up swap the principal increases in a predetermined way

• In Credit default swaps (CDS) the buyer of the swaps pays premium to the seller of the swap till the

time the underlying does not default. If the underlying defaults then the seller of the swap makes a

payment to the buyer and the CDS is terminated.

• In a compounding swap the interest on one or both sides is compounded forward to the end of the

life of the swap and there is only one payment at the end of the contract.

• In a fixed for floating currency swap the fixed rate of interest in one currency is swapped for a

floating rate of interest in another currency

• An equity swap is an agreement to exchange the total returns (dividends and capital gains) from an

equity index for a fixed/floating rate of interest.

• In a puttable swap one party has the option of terminating the contract early.

• Swaptions are options on swaps which provide one party with the right at a future time to enter into a

swap where a predetermined fixed rate is exchanged for floating.

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• Which of the following achievable swap positions could be used to transform a floating-rate asset into

a fixed-rate asset?

A. Receive the floating-rate leg and receive the fixed-rate leg of a plain vanilla interest-rate swap

B. Pay the fixed-rate leg and receive the floating-rate leg of a plain vanilla interest-rate swap.

C. Pay the floating-rate leg and pay the fixed-rate leg of a plain vanilla interest-rate swap

D. Pay the floating-rate leg and receive the fixed-rate leg of a plain vanilla interest-rate swap

Questions

Five Minute Recap

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Party 1 Party 2

Fixed Rate

Floating Rate

Interest rate swaps:

Types of swaps:

•Credit default swaps

•Compounding swap

•Fixed floating currency swap

•Equity swap

•Amortizing swap

Value of the swap:

V = Bfix – Bflo

Here: Bfix= PV of payments

Bflo = (P+AI)e-rt

swaps explained for frm/cfa level 1

Education