FRM swaps

Swaps

Swaps• A swap is a financial transaction in which two counterparties agree

to exchange streams of payments over time. • A swap is an agreement between two parties to exchange sequences

of cash flows for a set period of time.

• All swaps involve exchange of a series of periodic payments between two parties, usually through an intermediary which is normally a large financial institution which keeps a “Swap Book”.

• Swaps are customized contracts traded in the OTC market. Firms and financial institutions are the major players in the swaps market.

• Since swaps are OTC products, the risk of a counterparty defaulting is quite high and this is one of the major drawbacks of swap related product.

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Swaps• The market primarily consist of financial institutions and corporations who

use the swap market to hedge more efficiently their liabilities and assets.

• Many institutions create synthetic fixed- or floating-rate assets or liabilities with better rates than the rates obtained on direct liabilities and assets.

• A swap is an exchange of cash flows, CFs. It is a legal arrangement between two parties to exchange specific payments.

• In case of “Plain Vanilla” type of interest rate swap there would be exchange of cash flow for conversion of floating interest rate to fixed interest rate for a notional principal.

• Thus, there would be swap of floating and fixed interest rate payments.

• Since swaps are customized contract products, interest payments may be made annually, quarterly, monthly, or at any other interval determined by both the parties.

Swaps: TypesThere are four types of swaps:

1. Interest Rate Swaps: Exchange of fixed-rate payments for floating-rate payments

2. Currency Swaps: Exchange of liabilities in different currencies

3. Cross-Currency Swaps: Combination of Interest rate and Currency swap

4. Credit Default Swaps: Exchange of premium payments for default protection

Plain Vanilla Interest Rate Swaps: Terms1. Parties to a swap are called counterparties. There are two

parties:– Fixed-Rate Payer– Floating-Rate Payer

2. Rates:– Fixed rate is usually a T-note rate plus basis points.– Floating rate is a benchmark rate: LIBOR

3. Reset Frequency: Semiannual4. Principal: No exchange of principal5. Notional Principal (NP): Interest is applied to a notional

principal; the NP is used for calculating the swap payments.• Trade Date: It is the date on which the interest rate swap

contract signed.• Effective Date: It is the date on which the interest rate swap

contract is operationalised. On this date onward the interest payment is estimated.

Example

July 31, 2010, Company A and Company B enters into a 3 year swap with the following terms:

• Company A pays to Company B an amount equal to 5.50%(fixed interest rate) every 6 month on a notional principal of $ 10Mn.

• Company B pays to Company A an amount equal to 6 month LIBOR on the same notional principal.

Effective date March 1st and Sept 1st every year.

Decide the pay off for both the parties.

Plain Vanilla Interest Rate Swap: Example

1 2 3 4 5 6Effective Dates LIBOR Floating-Rate Fixed-Rate Net Interest Received Net Interest Received

Payer's Payment* Payer's Payment** by Fixed-Rate Payer by Floating-Rate PayerColumn 3 - Column 4 Column 4 - Column 3

9/1/Y1 5.00% 2,50,000₹ 2,75,000₹ - 25,000₹ 25,000₹3/1/Y2 5.50% 2,75,000₹ 2,75,000₹ 0₹ 0₹9/1/Y2 6.00% 3,00,000₹ 2,75,000₹ 25,000₹ - 25,000₹3/1/Y3 6.50% 3,25,000₹ 2,75,000₹ 50,000₹ - 50,000₹9/1/Y3 7.00% 3,50,000₹ 2,75,000₹ 75,000₹ - 75,000₹

* (LIBOR/2)($10,000,000)** (.055/2)($10,000,000)

Interest Rate Swap: Point

Points:• If LIBOR > 5.5%, then fixed payer receives the

interest differential.

• If LIBOR < 5.5%, then floating payer receives the interest differential.

Interest Rate Swaps’ Fundamental Use

• One of the important uses of swaps is in creating a synthetic fixed- or floating-rate liability or asset that yields a better rate than a conventional or direct one:

– Synthetic fixed-rate loans and investments

– Synthetic floating-rate loans and investments

Swaps as Bond Positions• Swaps can be viewed as a combination of a fixed-

rate bond and flexible-rate note (FRN).

• A fixed-rate payer position is equivalent to – Buying a FRN paying the LIBOR – Shorting a fixed-rate bond at the swap’s fixed

rate.• A floating-rate payer position is equivalent to

• Shorting a FRN at the LIBOR • Buying a fixed-rate bond at the swap fixed rate

Swaps as Bond Positions• From the previous example, the fixed-rate payer’s

swap’s CFs can be replicated by: Fixed Rate Payers– Selling at par a 3-year bond, paying a 5.5% fixed

rate and a principal of $100Mn. – Purchasing a 3-year, $100Mn FRN with the rate

reset every six months at the LIBOR.

Floating Rate Payers– Selling a 3-year, $100Mn FRN paying the LIBOR – Purchasing 3-year, $100Mn, 5.5% fixed-rate bond

at par

Size Problem: Multiple CounterpartiesParty A wanted to convert its 5.75% fixed interest carrying exposure $50,000,000 through a swap deal. The swap dealer matched the same with two floating for fixed swaps with Libor payment semi-annually.

Swap Market Structure

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m50$NP

AParty

m25$NP

BParty

PayerRateFixed

PayerRateFloating

BankSwapPayerRateFixed

PayerRateFloating

m25$NP

CParty

PayerRateFloating

PayerRateFixed

Swap Market Price QuotesSwap spread: Swap dealers usually quote two different

swap spreads– One for deals in which they pay the fixed rate– One in which they receive the fixed rate

Swap spread of 80/86 dealer buys at 80bps over T-note yield and sells at 86 over T-note yield.

• Take the fixed payer’s position at a fixed rate equal to 80 bps over the T-note yield and

• Take the floating payer’s position, receiving 86 bps above the T-note yield.

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Swap Market Price Quotes

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Swap Maturity Treasury Yield Bid Swap Spread (BP) Ask Swap Spread (BP) Fixed Swap Rate Spread Swap Rate2 year 4.98% 67 74 5.65% - 5.72% 5.69%3 year 5.17% 72 76 5.89% - 5.93% 5.91%4 year 5.38% 69 74 6.07% - 6.12% 6.10%5 year 5.50% 70 76 6.20% - 6.26% 6.23%

Swap Rate = (Bid Rate + Ask Rate)/2

Swap Bank Quote OfferingsExample:

Swap Valuation• At origination, most plain vanilla swaps have an

economic value of zero. This means that neither counterparty is required to pay the other to induce that party into the agreement.

• An economic value of zero requires that the swap’s underlying bond positions trade at par—par value swap.

• If this were not the case, then one of the counterparties would need to compensate the other. In this case, the economic value of the swap is not zero. Such a swap is referred to as an off-market swap

• In general, the value of an existing swap is equal to the value of replacing the swap—replacement swap.

Swap Valuation

• Formally, the values of the fixed and floating swap positions are:

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KS = Fixed rate on the existing swapKP = Fixed rate on current par-value swapSVfix = Swap value of the fixed position on the existing swapSVfl = Swap value of the floating position on the existing swap

NP)K1(

KKSV

M

1ttP

SPfix

NP)K1(

KKSV

M

1ttP

PSfl

where:

Advantages of Swaps• Company rating generally plays vital role in case of

market borrowing.

• A good rating reduced the cost of borrowing significantly.

• It may also happen that a company may be good in getting funds at lower floating rate and another company may be getting fund at lower fixed rate.

• Hence there are many possibilities for arrangement of interest rate swaps.

Comparative Advantage

• Swaps are often used by corporations and financial institutions to take advantage of arbitrage opportunities resulting from capital-market inefficiencies.

• To see this consider the following case.

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Case:– ABC Inc. is a large conglomerate that is working on raising

$300,000,000 with a 5-year loan to finance the acquisition of a communications company.

– Based on a BBB credit rating on its debt, ABC can borrow 5-year funds at either

• A 9.5% fixed –a spread of 250 bp over a 5-year T-note yieldOr • A floating rate set equal to LIBOR + 75

– ABC prefers a fixed-rate loan.

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Comparative AdvantageSuppose:

• The treasurer of ABC contacts his investment banker for suggestions on how to obtain a lower rate.

• The investment banker knows the XYZ Development Company is looking for 5-year funding to finance its $300,000,000 shopping mall development.

• Given its AA credit rating, XYZ could borrow for 5 years at either – A fixed rate of 8.5% (150 bp over T-note) Or – A floating rate set equal to the LIBOR + 25 bp

• The XYZ company prefers a floating-rate loan.21


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bp50bp100SpreadCredit

Floatingbp25LIBOR%5.8XYZ

Fixedbp75LIBOR%5.9ABC

preferenceRateFloatingRateFixed


• The Investment banker realizes there is a comparative advantage. – XYZ has an absolute advantage in both the fixed and

floating market because of its lower quality rating, but it has a relative advantage in the fixed market where it gets 100 bp less than ABC.

– ABC has a relative advantage (or relatively less disadvantage) in the floating-rate market where it only pays 50 bp more than XYZ.

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• Thus, it appears that investors/lenders in the fixed-rate market assess the difference between the two creditors to be worth 100 bps, whereas investors/lenders in the floating-rate market assess the difference to be 50 bps.

• Arbitrage opportunities exist whenever comparative advantage exist.

• In this case, each firm can borrow in the market where it has a comparative advantage and then swap loans or have the investment banker set up a swap.

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Note: • The swap won’t work if the two companies pass

their respective costs. That is:– ABC swaps floating rate at LIBOR + 75bp for

9.5% fixed – XYZ swaps 8.5% fixed for floating at LIBOR +

25bp

• Typically, the companies divide the differences in credit risk, with the most creditworthy company taking the most savings.

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• Given total savings of 50 bp (100 bp on fixed – 50bp float), suppose the investment banker arranges an 8.5%/LIBOR swap with a NP of $300,000,000 in which ABC takes the fixed-rate position and XYZ takes the floating-rate payer position.

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ABC XYZ%5.8RateFixed

LIBORRateFloating

BankSwap%5.8RateFixed

LIBORRateFloating

Example

Jan 1, 2010, Company A and Company B enters into a 10-year interest rate swap with the following terms:

– Company A pays Company B an amount equal to 11%(fixed interest rate) per annum on a notional principal of $200,000 .

– Company B pays Company A an amount equal to one-year LIBOR + 4% per annum on a notional principal of $200,000


Answer

Diagram below indicates the cash flows between the parties, which occur annually.

Fixed Rate: 11%

Floating Rate: LIBOR+4%

Company A Company B

AnswerAs on Jan 1, 2011:• Company A will pay to Company B

– $200,000 * 11% = $22,000 • Let us assume as on Jan 1, 2011, one-year LIBOR is

6.50%. Therefore, Company B will pay Company A – $200,000 * (6.50% + 4%) = $21,000.

• The settlement takes place through the net payment, that is Company A would pay US$ 1000 to Company B. At no point does the principal change hands, which is why it is referred to as a "notional" amount.

• If LIBOR in Jan 2012 becomes 7.15%, then Company B would pay to Company A at the rate 11.25% and Company A would pay Company B at the rate of 11%. In this case Company A would be profitable.

Synthetic Swap: Fixed -Loans and Deposits

• A Libor linked floating rate deposits of $100mn was accepted by a bank for a period of 3-year. On the same deposits, the bank has created a 5.50% semi-annual interest payment 3- year loan. Using the synthetic swap concept estimate the minimum Yield on the fixed rate loan, if the floating rate deposits convert to fixed rates.

Synthetic Swap: Fixed -Loans and Deposits

Deposits Payment

Fixed Interest

received on Loan Libor

Floating Interest Paid on Deposits

Swap Fixed received for

Floating Libor Deposit

Swap Net Received by

Bank

Total Interest paid

by Bank

Annualised Effective Loan

Yield100 2.75 4.50% 2.25 2.75 0.50 1.75 3.50%100 2.75 5.00% 2.50 2.75 0.25 2.25 4.50%100 2.75 5.50% 2.75 2.75 0.00 2.75 5.50%100 2.75 6.00% 3.00 2.75 -0.25 3.25 6.50%100 2.75 6.50% 3.25 2.75 -0.50 3.75 7.50%100 2.75 6.30% 3.15 2.75 -0.40 3.55 7.10%

Currency Swaps

Foreign Currency Swap• The first currency swap transaction took place in 1982 between

the World Bank and IBM. • A plain vanilla currency swap involves exchanging principal

and fixed interest payments on a loan in one currency for principal and fixed interest payments on a similar loan in another currency.

• The parties to a currency swap will exchange principal amounts at the beginning and end of the swap.

• Currency swaps are generally resorted to by parties who need a different currency for financing assets but can raise resources in a different currency, in a different market on more competitive terms and with comparative advantage.

• Because of their market share and pre-dominant position, a company may be better known in one market and can raise resources at lower cost

Steps involves in Currency Swap Transactions

• Exchange of equivalent amounts of different currencies.

• Exchange of periodic interest payments during the life of swap.

• Re-exchange of principal amount at a pre-determined rate on the maturity of swap.

Example

A Japanese Company wanted to raise US$ loan but it is not getting good response in US market. At the same time, a US based company wanted to set up a manufacturing plant in Japan is not getting Japanese Yen at competitive rate in Japan. US-based Company can raise US$ at 5.5% from US market and the Japanese Company can raise Yen loan at 3.75% from Japanese market.

Illustrate with diagram the transaction of Currency Swap between the two Companies.

AnswerThese companies can raise resources in their respective markets and then exchange those currencies to fund their requirements and this can be accomplished through a “Currency Swap”.

The principal can be swapped as per the following diagram.

US$ Principal US$ Principal

Yen Principal Yen Principal

US-based Company

Intermediary Bank

Japan-Based Company

US$ Loan Yen Loan

Answer• The regular interest payment can take place as per following

diagram.

US$ at 5.50% US$ at 5.50%

Yen at 3.75% Yen at 3.75%

US-based Company

Intermediary Bank

Japan-Based Company

US$ Loan 5.5% Interest rate

Yen Loan 3.75% Interest rate

Example

Company A, a U.S. firm, and Company B, a European firm, have 5 years debt exposures equivalent to $50 million. As on January 1, 2010, the exchange rate is $1.25 per euro. The dollar-denominated interest rate is 7.25%, and the euro-denominated interest rate is 4.5%. Arrange a Currency Swap and decide the payment after one year if, the exchange rate is $1.40 per euro as on Jan 1, 2011.

Answer• Company A, the U.S. firm, and Company B, the

European firm, need to enter into a five-year currency swap for $50 million. First the principal will be exchanged.

• Since the exchange rate, at the time of swap arrangement, is $1.25 per euro, Company A pays $50 million, and Company B pays Euro 40 million (50/1.25).

• Company A will borrow from US market US$50 at a rate of 7.25% and Company B would borrow from Euro market Euro 40 million at the rate of 4.5%. This satisfies each company's need for funds denominated in another currency, which is nothing but currency swap.

Answer

Principal Exchange Arrangement

US$50million

Euro 40 million

Company A of US Market

Company B of Euro Market

AnswerPeriodic Interest Payment • Company A would mobilize US$ at a cost of 7.25%

annually and Company B would mobilizes Euro at a cost of 4.5% annually. Since both of them exchange their currencies, cost of borrowing would be also be exchanged by them.

• Company A would bear the Euro cost of borrowing and Company B would bear the US$ cost of bearing.

• US$ annual borrowing cost: US$ 50 million @7.25% : US$ 3.625million

• Euro annual borrowing cost Euro 40 million @ 4.5% : Euro 1.80 million.

Answer

• As on Jan 1, 2011, exchange rate is US$ 1.40 per Euro and hence Euro 1.80 million is equivalent to US$ 2.52 million.

• Hence the interest payment would be :– Company A would pay US$ 2.52 million to Company B– Company B would pay US$3.625 million to Company A– Hence the net US$ 1.105 million would be paid by

Company B to Company A • At the end of the swap of period both the parties re-

exchange the original principal amounts. • These principal payments are unaffected by exchange rates

at the time.

Jan 1, 2012, Company A and Company B enters into a 10-year interest rate swap with the following terms: – Company A pays Company B an amount equal to 9%

(fixed interest rate) per annum on a notional principal of Rs. 10 lakh .

– Company B pays Company A an amount equal to one-year LIBOR + 3.50% per annum on a notional principal of Rs.10 lakh.


Examples• Using following information, estimate the WACC

for IBM in US$– Out of total debt of US$100 million, it has $50 million

US$ yield 8% and US$ 50 million is Yen-denominated debt yield 2% in Yen.

– Debt represent 25% of IBM’s Capital and effective tax shield of IBM is 33%

– Risk-free rate in US$ is 6% while in Yen it is 2%

– IBM’s equity portfolio beta is 0.85

– Global Market Risk-premium is 4%

Solution• For estimating WACC for IBM in US$ we need to find out the cost of

yen-denominated debt in US$, given that its yield in Yen is 2%. The return on Yen-denominated debt to a US investor is equal to the debt’s yield in Yen plus the % change in the foreign exchange price of the Yen.

• Cost of Yen-denominated debt in US$

= Cost of Yen debt in Yen + % change FX value of Yen

K ¥d = K¥¥d + E(x $/¥)

• As per Unbiased Interest Rate Parity Hypothesis, the expected change in foreign currency value is the risk-free interest differential between the two countries.

• Hence, % change FX value of Yen against US$

= Risk-free rate in US( 6%) less Risk-free interest rate in Yen (2%) = 4%

Cost of Yen-denominated debt in US$ = K¥¥d + E(x $/¥) = 2%+ 4% =6%

Solution• Estimation of IBM’s Cost of Debt Capital• Kd = Cost of US$ Debt *Weight + Cost of Yen Debt *Weight

= 8% *50% + 6%*50% =7%• Estimation of IBM’s Cost of Equity Capital

Ri = Rf + βiUS (RUS – Rf) where

Global Market Risk-premium : 4% Risk-free interest rate in US: 6%• Equity betas: IBM: 0.85 RIBM = 6% + 0.85 *4% = 9.40%

• Estimation of IBM’s WACC• Kw = WdKd(1-t)+WsKs Where

Kd : Before tax cost of debt : 7%Ks : cost of equity : 9.40%t : Effective corporate tax rate: 33%Wd : weight for debt capital : 25%Ws : Weight for equity capital: 75%

Kw = 25%*7%*(1-33%) +75%*9.40% =8.22%

Credit Default Swaps• It is a financial agreement that the seller of the

CDS will compensate the buyer in the event of a loan default or other credit event.

• The buyer of the CDS makes a series of payments, known as CDS fee or spread to the seller and in exchange receives a payoff if the loan defaults.

• A default is often referred to as a "credit event" and it includes events as failure to pay, restructuring and bankruptcy, or even a drop in the borrower's credit rating.

Credit Default Swaps• CDS contracts on sovereign obligations also usually

include as credit events repudiation, moratorium and restructuring.

• Size of CDSs are in the $10–$20 million range with maturities between 1yr and 10 yr.

• The payoff is generally the principal amount of the loan.

• The compensation for the buyer of CDS is the face value of the loan.

• In the event of default, the seller takes possession of the defaulted loan.

Credit Default Swaps• Anyone can purchase a CDS, even buyers who do

not hold the loan instrument. • CDS contracts outstanding auction in the market

and anybody can purchase it. • CDSs are not traded on an exchange and there is

no required reporting of transactions to a government agency.

• Recent financial crisis expose the lack of transparency of CDS market and it became a concern to regulators as it increased the systemic risk.

Credit Default Swaps• The "spread" of a CDS is the annual amount the

protection buyer must pay the protection seller over the length of the contract, expressed as a percentage of the loan amount.

• For example, if the CDS spread of 50bps , then an investor buying $10 million worth of protection must pay $50,000 to the CDS seller.

• Payments are usually made on a quarterly basis, in advance. These payments continue until either the CDS contract expires or loan defaulted.

Average Cumulative Default Rate (%) 1970-2010

Grade/Time 1 2 3 4 5 7 10 15 20Aaa 0 0.013 0.013 0.037 0.104 0.244 0.494 0.918 1.09Aa 0.021 0.059 0.103 0.184 0.273 0.443 0.619 1.26 2.596A 0.055 0.177 0.362 0.549 0.756 1.239 2.136 3.657 6.019Baa 0.181 0.51 0.933 1.427 1.953 3.031 4.904 8.845 12.411Ba 1.157 3.191 5.596 8.146 10.453 14.44 20.101 29.702 36.867B 4.465 10.432 16.344 21.51 26.173 34.721 44.573 56.345 62.693Caa 18.163 30.204 39.709 47.317 53.768 61.181 72.384 76.162 78.993

Table Interpretation• Moody’s Credit rating of Baa has a 0.181% of defaulting at

the end of 1st year, 0.581% of chance of defaulting at the end of 2nd year and so on.

• Probability of Baa would default during 2nd year is 0.581%-0.181%.

• Probability of Caa would default during 3rd year is 39.709%-30.204%. It is an unconditional probability.

• Probability of Caa would survive until the end of 2nd year is 100-(39.709%+30.204%).

• Probability of Caa would default during 3rd year with condition it has not defaulted in the earlier years is {Probability of default during 3rd year/ Probability of survive till 2nd year }. (39.709%-30.204%)/(100%-30.204%)

Table Interpretation• The conditional probability for a short-time

period is known as hazard rate or default intensity. Probability of default at the end of ‘t’ year is {1- exp(-βt)}, where β is the average hazard rate between the time 0 and ‘t.’

• Credit Default Spread (CDS), recovery rate and hazard rate are linked in the following manner:β = CDS spread/ (1-Recovery Rate)

Problem• Suppose the hazard rate is 1.5% per year and

it remains constant. What is probability it would be defaulted by the end of 1st year, 2nd year, 3rd year and 4th year. Estimate the unconditional probability that it would be defaulted during 4th year. What is the probability that it would be defaulted in the 4th year with condition that it has not defaulted earlier.

Solution• Defaulted by the end of • 1st year : 1- exp(-1.5%*1)=0.0149• 2nd year: 1- exp(-1.5%*2)=0.0296• 3rd year : 1- exp(-1.5%*3)=0.0440• 4th year: 1- exp(-1.5%*4)=0.0582• 5th year: 1- exp(-1.5%*5)=0.0723• Default during the 4th year:0.0582-0.0440=0.0142• Unconditional probability that it has defaulted in the

4th year and not defaulted earlier : 0.0142/(1-0.0440)

CDS Deal : Practical Calculation• Basic Features• One year term• Premium is c% (e.g., .02 or 2%)• Notional value is N (e.g., $10,000,000)• Premiums paid quarterly at times t1, t2, t3, t4. • Default, if occurs, it happens at one of these times.• Quarterly premium payment = Nc/4 paid at the end

of the quarter. (Nc/4=$50,000)• Recovery rate is R (e.g., .50 or 50%). • If defaults, payment would be N(1-R)

CDS Deal : Practical Calculation

• Basic Features• Probabilities of no default looking ahead from

time t=0 are P1, P2, P3, P4. These depend on the credit rating of CDS Purchaser.

• Discount rates for computing present values of cash flows to be received 1, 2, 3, and 4 periods in the future, δ1, δ2, δ3, δ4.

CDS Deal : How the Contract Ends

Time t0

Time t1

Time t2

Time t3

Time t4

Joint Probabilities – Contract Ends Default@ T2

Prob(Default at T1) =P(D1)

Prob(Not Default at T1) =P(ND1)

Prob(Default at T2|ND1) =P(D2|ND1)

Prob(Not Default at T2|ND1) =P(ND1)

P(Default at T2 and Not Default at T1) = P(D2|ND1)P(ND1) = P1(1-P2)

PV of Cash Flows

Sum = Expected PDV of Sum to obtain Expected PresentPremium Payments Discounted Value of Default Payment

Expected Present Value

Price DecisionNotional value is N The probabilities p1, p2, p3, p4,The discount rates, δ1, δ2, δ3, δ4The recovery rate, R

All known.

Set PV = 0.

The only unknown is c, which is the price.

There is a Solution

1

2

3

4

1

1 2

1 2 3

1 2 3 4

0 implies

(1 1)

1(1 2)4(1 )

1 2(1 3)

1 2 3(1 4)

1(1 2)

1 2(1 3)( )

1 2 3(1 4)( )

1 2 3 4( )

PV

p

p pR

p p p

p p p pc

p p

p p p

p p p p

p p p p

CDS Deal : Problematic Aspect

• There is no reserves creation to ensure payment, if actual default happens.

• No regulations to define what actually constitute credit events.

• Proper valuation of underlying mortgage assets.

• Sudden rating migration lead to increase in CDS spread and conversion of even good mortgage assets into toxic assets.

Documents

FRM swaps