IRS Compression: Cleaning Books and Making Sense

IRS portfolio compression is built on a simple idea. As dealer firms continue to trade swaps with each other, trades can begin to be removed without impacting the interest rate risk profile of the swap portfolio.

For example, Dealer A may have written a swap with Dealer B such that it is receiving fixed rate cash flows from Dealer B with a maturity slightly longer or shorter than five years. Suppose a new swap is written for the same notional amount where Dealer A pays fixed rate cash flows to Dealer B for five years. In this case, the macro interest rate risks have been largely offset. Dealer B is paying fixed in the first swap while Dealer A is paying fixed in the second swap. The notional principal is the same. All the dealers need to do is determine the difference in value between the two swaps caused by the mismatch in dates and in the fixed rate payments. If the parameters for valuing these mismatches are agreed, there is no reason why the swaps cannot literally be torn up – this is what is meant by the term compression in a bilateral context.

This type of exercise had been going on in an ad hoc manner for years between dealers as a means of reducing notionals, cleaning up portfolios and reducing operational costs. ISDA reports that an exercise similar to compression was used in 1999 to tear up nearly $1 trillion of interest rate swaps at Long Term Capital Management.

The examples used in this appendix require dealers to tear up and rewrite swap contracts. It may sound simple in concept but it involves considerably more negotiation among dealers than the successful process currently in use managed by TriOptima.

Multi-Lateral Compression

The benefits of compression between two dealers are obvious. To achieve meaningful reductions in notional outstanding, however, bilateral compression is a cumbersome exercise. If applied across the dealer community, meaningful results for the industry would involve literally hundreds of compression exercises per currency. Multi-lateral compression, on the other hand, can produce tremendous results in a very efficient manner provided there is widespread acceptance by market participants. This is the approach adopted by TriOptima in its triReduce service.

Consider, for example, a closed world where there are only four dealers: A, B, C and D. Consider as well their interdealer swaps in five years are as follows

As can be seen, the total Net Amounts of Rs are 100 and the total Net Amounts of Ps are 100. This is a closed system. All the swaps among the four have to net to zero. In a bilateral compression world, the dealers will not be able to compress any trades because in this simple world they only have one swap with each other dealer.

In a multi-lateral compression world, all the work can be done at once. Dealer A needs to receive fixed for 25 and Dealer B needs to receive fixed for 75. C and D need to pay fixed for 50 each. The compression will result in A receiving 25 from C and B receiving 25 from C and 50 from D. We started with 400 of notional and are down to 100.

This was a very simple example but it shows the value of increasing participants in compression.

LIBOR RIGGGGGED!!!!!!!!

James Griffith, an officer working in  Financial crimes cell of London Police, was having business as usual over a cup of coffee in his office till he got a call from his senior which moved the earth beneath his feet and his eyes were about to pop out as he muttered in his bewilderment  ’Oh my!!!! Go..........d!” It was bigger than anything he had handled earlier and his imagination failed to gauge the impact of reason of this amazement. To quote very conservatively it is a 15 digit number; 350,000,000,000,000, precisely 350 trillion USD and this humongous amount was riding on a rigged benchmark. Yes, It was none other than LIBOR the most prominent benchmark used globally on which the best of Investment banks and Hedge funds quote their Floating rates and premier banks fix their lending rates. This did not happen anytime soon but as early as 2006. This was indeed scandalous than many other recent scandals!

Read the below:

These are some of the mails between traders who betted on LIBOR and submitters who submitted LIBOR to British bankers Association (BBA) daily.

“WE HAVE TO GET KICKED OUT OF THE FIXINGS TOMORROW!! We need a 4.17 fix in 1m (low fix) We need a 4.41 fix in 3m (high fix)” (November 22, 2005, Senior Trader in New York to Trader in London);

“You need to take a close look at the reset ladder. We need 3M to stay low for the next 3 sets and then I think that we will be completely out of our 3M position. Then its on. [Submitter] has to go crazy with raising 3M Libor.” (February 1, 2006, Trader in New York to Trader in London); 

“Your annoying colleague again … Would love to get a high 1m Also if poss a low 3m … if poss … thanks” (February 3, 2006, Trader in London to Submitter); 

“This is the [book's] risk. We need low 1M and 3M libor. PIs ask [submitter] to get 1M set to 82. That would help a lot” (March 27, 2006, Trader in New York to Trader in London);… 

“Hi Guys, We got a big position in 3m libor for the next 3 days. Can we please keep the lib or fixing at 5.39 for the next few days. It would really help. We do not want it to fix any higher than that. Tks a lot.” (September 13, 2006, Senior Trader in New York to Submitter)…” 

The fundamental principle underlying floating rates is to allow the market to determine borrowing costs. Customers who borrow on a floating-rate basis, if they are sensible, and institutions that loan money on a floating-rate basis, if they are ethical, therefore expect two things from a benchmark interest rate. First, the benchmark should reflect actual conditions in the financial markets. That means no random fluctuations -- money costs what it is worth. Second, the benchmark rate should not be easy to manipulate. No rational, informed borrower would borrow money at a variable rate of interest and then empower the lender to determine when and how the interest rate changed in the future.

So it is startling that Libor, the financial world's most important number, satisfies neither of these requirements. Libor is computed by the British Bankers' Association (BBA), a powerful trade association based in London that represents more than 250 financial institutions. These banks are located in 50 countries and have operations in just about every corner of the globe. But instead of using actual market rates, big banks estimate the interest rate that they think they would have to pay if they borrowed money from other institutions. That is different than reporting the actual interest rate at which they are really borrowing from other banks.

Each day, the BBA sets Libor rates for 15 loan maturities in ten different currencies. In the case of the dollar, 18 banks submit their hypothetical borrowing costs. The BBA discards the four highest and the four lowest submissions considered as outliers distorting the calculation, and then averages the remaining ten to come up with the Libor number. Thompson Reuters calculates all of these rates for the BBA, and then publishes the results, usually around 11:45 AM (CET).  

Rate setting desk were acceding to the traders request and sending the artificial low or high rates to BBA. A low rate quoted to BBA is aimed at keeping the rate so low that it’s taken as outlier and excluded from average rates. This resulted in a lower number forming part of average which would otherwise would have been excluded. Therefore the overall rate was lower than what it could have been with fair play. Though the average was impacted by few basis points, yet the mammoth magnitude of money riding on LIBOR made the outcome substantial.

There are plenty of reasons why banks would like to manipulate Libor rates. During the height of the financial crisis, regulators foolishly looked to Libor to determine the market's perception of the health of big banks. A big bank reporting a low Libor rate was thought to be able to borrow money from other banks cheaply and, therefore, was seen as a safe place to invest. Banks worried about attracting the attention of regulators may have submitted low Libor rates in order to try to deflect regulatory scrutiny. 

More nefariously, banks also manipulated Libor to make money or avoid losses on their trading portfolios. For example, when U.S. traders at Barclays wanted Libor to rise in order to draw a bigger profit on some of their financial products, they simply asked their colleagues at the rate-setting desk in London to push the numbers up or down to suit their needs. Barclays would then submit artificial bids and persuade their counterparts at other banks to do the same.

EURO ZONE CRISIS : NutShell

The euro zone is an economic and monetary union of 17 European Union member states that have adopted the euro (€) as their common currency. The euro zone currently consists of Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Malta, the Netherlands, Portugal, Slovakia, Slovenia, and Spain.
Monetary policy of the zone is the responsibility of the European Central Bank (ECB) which is governed by a president and a board of the heads of national central banks. The principal task of the ECB is to keep inflation under control.
Over the past few months, the European debt crisis has become more prominent and has been dominating headlines as the region’s sovereign debt issues continue to cause concern for the EU and potentially other global economies. The debt crisis basically came about because several Euro zone countries have lost control of their finances since the global recession, borrowing and spending more than they could realistically afford. The crisis was triggered by the worldwide financial collapse that began in 2008 and has been exacerbated by poor financial management.
The problem originated in Greece when it was realised that Greece’s deficit was twice as high as originally thought (12.7 per cent of GDP). It has since spread to other countries such as Spain, Ireland, and Portugal. Investors have since become less confident about Greece's ability to repay them and they demanded Greece pay higher interest rates on their bonds. This had a spiral effect as the more Greece had to pay bondholders in interest, the more it had to borrow, which in turn drove up interest rates even more. Greece's debt problems led investors who owned bonds issued by other peripheral Euro zone countries to lose confidence, especially because banks in France, Germany and the UK owned over $56bn worth of Greek government bonds. As a result of the crisis, other European countries have had to bail Greece out. This has cost billions of Euros. Greece was the first country to accept a bailout in May 2010, followed by Ireland and Portugal. However, before these bailouts were approved, the Governments of these countries had to agree to adopt 'austerity measures' to show they were doing what they can to tackle their economic problems themselves. This has led to mass public protests in Greece, with many people demonstrating against more job losses and tax rises as a result. A major concern is that if Greece is unable to keep repaying what it owes to other countries, the country could effectively go bankrupt which would have flow on affects on other countries. The uncertainty surrounding the Euro debt crisis has caused havoc in major world financial markets. This can be reflected in the CBOE volatility index. The Chicago Board of Options Exchange (CBOE) gives a standardised estimate of the market's expectation of future volatility. The index spiked upwards in August to the highest level since the global financial crisis. Over the past few weeks it has become more subdued as EU leaders begin to work out a possible solution to the EU debt crisis. In recent weeks, it appears that the Euro zone has inched closer to a resolution of its crisis. A debt-wracked Italy has come under pressure to introduce new reforms to tackle their own levels of debt. If Italy, the EU zone’s third largest economy, were to default, the bailout fund would become rapidly depleted and ineffective. Options are being explored on ways to scale up the EU’s 440 billion Euro war chest in the case that a larger economy such as Italy or Spain are dragged into the debt mire. One way of doing this is providing insurance to investors so that their losses would be recovered in the event of a debt default. Another option would be to create a separate fund and entice international investors and institutions to match EU commitments, thereby increasing the amount of cash available for potential future bailouts. By using such financial inventiveness, leaders hope to leverage the fund up to as much as a trillion Euros, which they hope will be enough to reassure volatile financial markets. In order to address the crisis, Greece's debt burden needs to be reduced so that the country can eventually stand on its own, banks need to raise more money so they can ride out the financial storm, and show that their European bailout fund is big and nimble enough to prevent larger economies from being dragged into the crisis. This criteria was met in the debt crisis plan which was unveiled in late October. A “Comprehensive” Debt Crisis Plan On the 27th October, 2011, the Euro zone leaders announced a “comprehensive and solid” response to the European debt crisis. The agreement has plans to: Begin negotiations on a nominal 50 per cent cut in bond investments to reduce Greece's debt burden by €100 billion. This would have the affect of cutting Greece’s debts from 160 per cent of GDP to 120 per cent of GDP by 2020. As well as the deal on deeper private sector participation in Greece, Euro zone leaders also agreed to scale up the European Financial Stability Facility (EFSF). The EFSF is Europe’s €440 billion bailout fund which was set up last year. The fund has already been used to provide help to other heavily in debt countries such as Portugal, Ireland and Greece, leaving around €290 billion available. An estimated €250 billion of that will be leveraged four to five times, producing a headline figure of around €1trillion, which will be deployed in a variety of ways. The EFSF will be boosted via both risk insurance and a special vehicle that will buy bonds. Further resources would come from co-operation with the IMF and sovereign wealth funds, including China. The fund would be tasked with ensuring financial stability in the Euro zone. These announcements have provided a degree of relief for international economies and share markets as it appears a tourniquet has been wrapped around the crisis for the time being. A recent announcement by the Prime Minister for Greece (George Papandreou) could undo a lot of the positive outcomes that came out of the debt crisis plan. The Prime Minister has called a referendum on accepting a second bailout plan. This move has renewed fears that Greece could default on its debt and that the Euro zone government debt crisis could deepen. This has shown that the debt crisis plan is only a movement in the right direction in trying to solve the crisis and that it is far from being laid to rest.

Differential Interest Rate Fix (DIRF)

DIFFERENTIAL INTEREST RATE FIX

DESCRIPTION

A Differential Interest Rate Fix (DIRF) is a contract that moves with reference to the SLOPE of a yield curve. The DIRF is meant for those who wish to profit from a steepening or flattening of one yield curve. The DIRF is customised with defined settlement dates, a defined value per basis point, and two defined points on the yield curve.

EXAMPLE

Assume an investor believes that the Italian yield curve will flatten over the next year more than that implied in the market. The client would enter into a flattening DIRF, say 2 years versus 7 years, for settlement in one year. The investor selects the amount per basis point they wish to transact, say ITL 1,000,000 per point. The DIRF price is given in terms of basis points. If at maturity the difference between the 2yr and 7yr ITL Swap rates has flattened below the DIRF level, the investor will receive ITL 1,000,000 for every basis point lower. If the difference is higher than the DIRF level, i.e. the curve has steepened, the investor will lose ITL 1,000,000 per basis point.

PRICING

The entry price is calculated by taking the difference between the implied forward rates for the two yield curve points chosen. This means in the above example, we calculate the one year forward 2yr rate and the one year forward 7 yr rate. The DIRF price is the difference. Investors who BUY the DIRF look to see the curve steepen, investors who SELL the DIRF look to see the curve flatten.

TARGET MARKET

This is a product for people who wish to take a position on the SLOPE of the yield curve without taking an outright position on a curve.

ADVANTAGES

·         Available in all major currencies

·         Can utilise any two points on the yield curve

·         Can be reversed at any time with reference to the then prevailing implied rates

·         Investor determines amount per point sensitivity

·         Settlement at maturity is against independent mid rate quoted on Telerate

·         No Exposure to parallel movement in yield curve

DISADVANTAGES

·         The attractiveness of DIRFs is dependent on the Implied Forward, rates not the spot rates, therefore expected movements can already be built in.

PRODUCT SUITABILITY

Simple Aggressiv

Credit Default Swap: Basics

A CDS is a contract that provides protection against the risk of a credit event by a particular company or country. The company is known as the reference entity and a default by the company is known as a credit event. The buyer of the insurance obtains the right to sell a particular bond issued by the company for its par value when a credit event occurs. The bond is known as the reference obligation and the total par value of the bond that can be sold is known as the swap's notional principal. The buyer of protection makes periodic payments to the protection seller until the occurrence of a credit
event or the maturity date of the contract, whichever is first. If a credit event occurs the buyer is compensated for the loss (possibly hypothetically) incurred as a result of the credit event.
A credit event usually requires a nal accrual payment by the buyer. The swap is then settled by either physical delivery or in cash. If the terms of the swap require physical delivery, the swap buyer delivers the bonds to the seller in exchange for their par value.
When there is cash settlement, the calculation agent polls dealers to determine the midmarket price, Q, of the reference obligation some specified number of days after the credit event. The cash settlement is then $(100 − Q)% of the notional principal.

The valuation of a credit default swap requires estimates of the risk-neutral probability that the reference entity will default at di erent future times. The prices of bonds issued by the reference entity provide the main source of data for the estimation. If we assume that the only reason a corporate bond sells for less than a similar Treasury bond is the possibility of default, it follows that:
Value of Treasury Bond - Value of Corporate Bond = Present Value of Cost of Defaults

By using this relationship to calculate the present value of the cost of defaults on a range of different bonds issued by the reference entity, and making an assumption about recovery rates, we can estimate the probability of the corporation defaulting at di erent future times. If the reference entity has issued relatively few actively traded bonds, we can use bonds issued by another corporation that is considered to have the same risk of default as the reference entity. This is likely to be a corporation whose bonds have the same credit rating as those of the reference entity and ideally a corporation in the same industry as the reference entity.
We start with a simple example. Suppose that a ve-year zero-coupon Treasury bond with a face value of 100 yields 5% and a similar ve-year zero-coupon bond issued by a corporation yields 5.5%. Both rates are expressed with continuous compounding. The value of the Treasury bond is
100 x e^(−0.05×5) = 77.8801
and the value of the corporate bond is 100 x e^(−0.055×5) = 75.9572. The present value of the cost of defaults is, therefore
77.8801 − 75.9572 = 1.9229
Define the risk-neutral probability of default during the five-year life of the bond as p. If we make the simplifying assumption that there are no recoveries in the event of a default, the impact of a default is to create a loss of 100 at the end of the five years. The expected loss from defaults in a risk-neutral world is, therefore, 100p and the present value of the expected loss is
100 x p x e^(−0.05×5)
It follows that: 100 x p x e^(−0.05×5) = 1.9229
so that p = 0.0247 or 2.47%.
There are two reasons why the calculations for extracting default probabilities from bond prices are, in practice, usually more complicated than this. First, the recovery rate is usually non-zero. Second, most corporate bonds are not zero-coupon bonds. When the recovery rate is non-zero, it is necessary to make an assumption about the claim made by bondholders in the event of default.

UCITS : Undertakings for Collective investment In Transferable Securities

Off late mutual funds are also showing the aggresion which was once idiosyncracy of hedge funds. Now they are also chasing alpha and craving for absolute returns. Thanks to UCITS, restirctions made easy and derivatives and OTC available as investment avenues.

Background
In simple terms, a UCITS is a mutual fund based in the European Union. UCITS stands for “Undertakings for Collective Investment in Transferable Securities” and UCITS funds can be sold to any investor within the European Union under a harmonised regulatory regime.
They have a strong brand identity across Europe, Asia and South America and are distributed for sale in over fifty countries as they have transparent, tried and tested regulation. The original Directive introducing the concept of a standard fund structure, “UCITS I”1, was adopted in 1985. However, due to differing cross border marketing restrictions in member states and the restricted range of asset classes permitted, the original Directive prevented UCITS from benefiting from the increasing range of investments that were available in the market. A second draft directive – UCITS II – was developed to rectify these issues, however extended political arguing between EU countries caused it to be abandoned.

UCITS III – development for change
It was not until 2003 that UCITS I was amended by a new Directive, UCITS III, which was itself made up of two directives: the Product Directive2 and the Management Directive3. The Product Directive expanded the type and range of investments that a UCITS could hold; The Management Directive sought to give a European passport to management companies of a UCITS fund to enable them to operate throughout the EU as well as tightening up risk management frameworks and increasing managers’ capitalisation requirements. The combined Directive was intended to widen consumer choice and consumer protection. It is this combined UCITS III Directive that fund managers now refer to when they talk about “UCITS-III-compliant” or “Newcits” funds. In general, they mean the fund is taking advantage of the wider investment powers. But there is a good deal more going on behind the scenes. One of the key benefits of the UCITS III Product Directive was the broadening of the investment powers available to mutual funds. This included derivatives for specific investment purposes and it has taken some years for the industry to realise that this enhanced breadth presents managers with the ability to offer a much fuller range of investment products than had previously been the case.
September 2010
ViewPoint
The Management Directive developed the existing concept of the “product passport”, on which BlackRock’s European Retail distribution model is based. Under the passport, a UCITS fund in one member state can be freely marketed to investors in another EU4 country, subject to a processing period of up to two months by the regulator in the other country.
The Management Directive also introduced new prospectus requirements as well as demanding that all UCITS funds use a “Simplified Prospectus” as a marketing document throughout the EEA. Permissions to allow managers to operate funds domiciled in other countries (the “management passport”) was not however a complete success and the new UCITS IV Directive, which will come into force in 2011, in part aims to rectify this.
BlackRock in the UK was one of the first firms to see the possibilities for UCITS III, with the launch in 2005 of UK Absolute Alpha. Since then, we have launched other funds and now offer a wide range of UCITS-III-compliant funds as well as seven “Newcits” funds to UK and European investors, investing in equity, fixed income and foreign exchange.
Regulatory change is constant, now more so than ever, but since UCITS III, further EU Directives, rules and guidance have been published, building on its base. This includes the Eligible Assets Directive5 which formally widened and clarified the scope of UCITS’ investments, the European Commission Recommendation for the use of financial derivative instruments for UCITS6 which introduced additional aspects and demands in risk monitoring and additional guidance by CESR7 on an assortment of matters.


Main Features of a UCITS
A UCITS can only invest in eligible assets. The original UCITS directive was restrictive in scope and effectively allowed only equity and bond funds.
UCITS III expanded the range of available investments to include derivatives for investment purposes, other UCITS and cash. This dramatically increased investor choice, allowing for cash funds, funds of fund, mixed asset funds.

UCITS must operate on a principle of risk spreading, which means that restrictions apply which limit the spread of investments, leverage and exposure. UCITS III, however, re-defined how derivative exposure can be measured.
A UCITS must be open-ended i.e. shares or units in the fund may be redeemed on demand by investors.
A UCITS must be liquid, that is, its underlying investments must be liquid enough to support redemptions in the fund on at least a fortnightly basis. In practice of course, the vast majority of UCITS funds are daily dealing.
Assets must be entrusted to an independent custodian or depositary and held in a ring-fenced account on behalf of investors.

The development of investment powers
Eligible Assets
As part of UCITS III then, the Product Directive expanded the type of available investments to allow a UCITS to invest in derivatives not only for efficient portfolio management “EPM” or hedging purposes but for investment purposes as well.
This has allowed a number of hedge fund strategies to be accommodated within the UCITS format such as equity long/short, relative value, etc. Some strategies, however, will not easily fit within a UCITS framework because the underlying asset class is not permissible (e.g. individual commodities or bank loans) or because of the lack of liquidity (e.g. distressed debt). The eligible assets that a UCITS can invest in include:

Transferable securities – effectively, publicly traded equities or bonds, listed on mainstream stock exchanges. Broadly, this was the range of assets allowed under UCITS I. Under UCITS III, choice has become wider after 2003.
Deposits and Money Market instruments (MMIs) – Cash deposits with “credit institutions” (i.e. banks) can now be held as investment assets, together with MMIs. These might include treasury and local authority bills, certificates of deposit or commercial paper. Thus pure cash funds can now be UCITS.

Other mutual funds – UCITS have always been able to invest in other funds, although this was tightly restricted. UCITS III relaxed this restriction, with further ability to invest in other open-ended mutual funds where those are other UCITS or non-UCITS funds with UCITS-like traits. This has allowed the development of UCITS funds of funds.

Financial Derivative Instruments – under UCITS I, derivatives could only be used for hedging and EPM (i.e. to reduce risk or cost, or to replicate a position that could otherwise be achieved through investing in the underlying asset). With the advent of UCITS III, UCITS are able to use derivatives for investment purposes, using exchangetraded or over-the-counter (“OTC”) instruments, with some limitations. The underlying of a derivative must be:
• an eligible asset of the type mentioned above
• interest rates
• foreign exchange rates and currencies
• financial indices (e.g. S&P 500).
Physical short selling is not permitted. However, the same economic effect can be achieved and is allowed through the use of derivatives such as Contracts for Difference (“CFDs”). Firms must have systems and controls in place that can measure the derivative risk and provide an appropriate level of cover, which can mean that on the opposite side of the exposure there must be cash, a similar asset or balancing derivative giving an opposite exposure to a similar underlying asset to cover the original derivative exposure. It can also mean that some UCITS III funds may have high levels of gross exposure.

Ineligible assets – certain assets remains out of scope:
Real estate
Bank loans
Physical metals such as gold (although certain securities based on metals are permitted)
Commodities (although derivatives on financial indices such as commodity indices are eligible)

Risk spreading and concentration rules
A UCITS must be properly diversified. There are a number of different limits, all of them in place since UCITS I, but the best known is the 5/10/40 Rule. This states that a UCITS cannot invest more than 5% of its assets in securities issued by a single issuer. However, this limit can be increased up to 10% provided that where the 5% limit is exceeded, the exposure to these issuers, when added together, does not exceed 40% of the fund’s assets. There are also rules round the proportion of a company that a UCITS may hold in that it might gain significant influence over its management. Rules exist too regarding the amount of a company’s debt or non-voting shares that can be held.

Valuation of IRS using zero /discount curve.

What affects Swap Value?

From a valuation perspective swaps are not much different from customized notes and bonds. The fixed cash flows in a swap are akin to the interest payments on a high quality fixed rate note, while swap floating cash flows are like the interest payments on a floating rate note. Market variables that affect swap pricing include changes in the level of interest rates, changes in swap spreads, changes in the shape of the yield curve, and FX rates (for currency swaps). Key transaction-specific variables that affect swap valuation include notional principal amount and amortization, time to maturity, swap payment frequency, and floating rate reference index.

Mechanics of Swap Pricing

Measuring the current market value of an interest rate swap involves four distinct elements:

1.	Constructing a zero coupon* yield curve
2.	Extrapolating a forecast of future interest rates to establish the amount of each future floating rate cash flow
3.	Deriving discount factors to value each swap fixed and floating rate cash flow
4.	Discounting and present valuing all known (fixed) and forecasted (floating) swap cash flows.

While this may sound complicated, the curve building and discounting techniques are the same techniques used to establish the theoretical market value of any interest bearing security.

Constructing a Yield Curve

The first step in swap valuation is to build a yield curve from current cash deposit rates, eurodollar futures prices, treasury yields, and interest rate swap spreads. These known market rates are “hooked” together to form today’s coupon yield curve. The coupon curve is the raw material from which a zero coupon yield curve is constructed, usually using a method called “bootstrapping”. This involves deriving each new point on the curve from previously determined zero coupon points (hence the phrase, “bootstrapping”).

Zero rates are higher than coupon rates when the yield curve is positively sloped and lower when the curve is inverted. The gap is widest at the far end of the yield curve. When rates are low and the yield curve flat the difference between coupon and zero rates will be minimal, but when rates are high and the curve steep, the difference is significant.

Because the cash flow dates of the swap to be valued rarely exactly match the dates for which zero curve points have been developed, interpolation between data points is needed to solve the problem. While this sounds simple, some extremely complicated algorithms have been developed to minimize the errors that can arise from interpolation.

Forecasting Future Short-Term Rates

One half of the cash flows in a simple swap are floating rate. What makes the floating leg of the swap hard to price is the uncertainty of the forward rates—only today’s floating rate is known for certain. A forecast of future floating rates — a forward yield curve of short term interest rates—is needed before prospective floating rate cash flows can be generated. In fact, the forward curve is just an extension of the zero coupon yield curve; once the zero curve has been developed, it easily transforms into the forward curve needed to generate the swap’s floating rate cash flows.

Deriving Discount Factors

Discount factors, used to present value each swap cash flow, are developed as part of the process of bootstrapping the zero coupon yield curve. Like forward interest rates, discount factors are just a transformation of zero coupon rates. In fact, there is a simple formula for converting one to the other**.

Valuing the Swap

With all the calculations concluded, the only step remaining is to apply the discount factors to find the present value of fixed and floating swap cash flows. These values are then netted to determine the swap’s current market value. This value can be positive, zero, or negative, depending on how market interest rates have changed since the swap was created. For a floating to fixed swap, higher market rates will create a gain for the hedger, lower rates a loss. In the example below, a swap with a remaining term of 2 years is valued at a point when market interest rates have risen 1% across the yield curve from the time the swap was put into place.

Simple Rule of Thumb for estimating the sentivity of a Swap's Value to changes in Market interest rates results in Change in Value

While understanding the basics of swap valuation should make senior financial officers more comfortable with the balance sheet implications of the firm’s hedging activity, a quick and dirty way to estimate a hedge’s value and rate sensitivity can also prove useful.

A Simple Rule of Thumb for Estimating the Sensitivity of a Swap’s Value to Changes in Market Interest Rates While understanding the basics of swap valuation should make senior financial officers more comfortable with the balance sheet implications of the firm’s hedging activity, a quick and dirty way to estimate a hedge’s value and rate sensitivity can also prove useful. DV ’01—the change in dollar value of a swap for a one basis point change in market interest rates— is a simple measure for benchmarking how the value of an interest rate swap changes as interest rates change. However, because the DV ’01 changes as market rates go up and down and the shape of the yield curve changes, it can only be used to estimate the change in a swap’s value for small shifts in rates.

The chart below describes the DV ’01 for a $25 million interest rate swap with maturity between 2 and 10 years. These values are based on today’s yield curve (May, 1999). The values needed to estimate the potential gain or loss on a hedge include the actual fixed rate on the swap, the market fixed rate for a swap of equal remaining life, and the DV ’01 of the swap.

For example, ***Company ABC has a two month window in which to execute a five-year swap program covering $25 million of its bank debt. The company could hedge the debt today at a fixed swap rate of 5.90%, but it hopes that the market will improve over the next few weeks. Using the DV ’01 value, the company can estimate how much it stands to gain or lose from delaying the hedge. From the chart, the DV ’01 of a 5 year $25 million swap is $9,375. A 25 basis point change in rates (a not uncommon occurrence over a two month period), would trigger an opportunity gain or loss around $234,375 ($9,375 X 25 basis points). With an available estimate now of how much is at risk, the company can decide how confident it is in its interest rate forecast.

Summing Up

Hedgers have typically been concerned with the actual market value of interest rate swaps only at financial reporting dates or when considering the early termination of a hedge. However, as active hedge management increases and accounting ground rules change, understanding the basic concepts underlying swap valuation takes on more importance.

* Zero coupon rates are associated with instruments that pay no interest until maturity. The zero coupon curve is used in securities valuation because it requires no assumptions about reinvestment rates on intermediate cash flows.

** Discount factors can be derived from zero coupon rates using the formula 1/(1+r)^n where r is the periodic rate and n is the number of periods. Where zero rates are derived on a continuously compounded basis (the usual method), the formula becomes 1/e rt where e is the natural log, r is the zero rate and t is the term in years.