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Specialist Masters Programme

Please list all names of group members: (Surname, first name) 1. Figueiredo, Joao 2. Xu, Mei 3. Gu, Xiangyun

4. Lemercier Jean 5. Ouyang, Chenjia 6. 7. GROUP NUMBER:

MSc in Finance

Module Code: SMM516

Module Title: Fixed Income

Lecturer: Alessandro Beber

Submission Date: 31st March 2014

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Group 15

Fixed Income Arbitrage in a

Financial Crisis: TED Spread

and Swap Spread in

November 2008

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Part I

Context Albert Mills is a former fixed-income strategist and trader at Morgan Stanley who has recently

joined one of his past colleague James Franey in the investment management company that

he founded - Kentish Town Capital (KTC). Mills’ knowledge about interest rate derivatives is the

main contribution to his new employer, and Mills has direct responsibility on $75 million (the

overall size of KTC is $300 million).

KTC’s strategy was to focus on fixed income relative value strategies, and had stayed away from

the mortgage market due to a lack of knowledge in this specific area of securities. As a result

the fund was clearly ahead of many competitors at the time of the case study (November

2008).

The economic environment at the time was the post Northern Rock’s and Lehman Brother’s

collapses and the subsequent turmoil in financial markets. Market volatility had increased

substantially across asset classes as Lehman’s counterparties had suddenly become exposed

to a great amount of market risk previously offset by their trades with Lehman and as a result

a flight to quality was taking place, with a very risk-averse sentiment ruling investors’ decisions.

Many investors had been closing positions and investing in Treasury bills alone, prime brokers

as KTC had increased collateral requirements to a point where it was almost impossible to hold

positions in anything but treasuries as well.

KTC’s profit had derived from selling short long-dated treasuries and going long in shorter-

dated treasuries, in duration-matched amounts (which is in some way a convergence trade).

As the fund betted on a steepening yield curve which had been triggered by the FED’s cut in

short-term rates, it had done well in spite of the crisis and Mills felt it was now time to exploit

opportunities in the market for U.S. dollar fixed-floating swaps.

At that precise date the thirty-year U.S. dollar fixed-floating spread had decreased from 30.25

to 6.25 basis points, having even been negative some days before this. The size of the swap

spread (6.25 basis points) was considerably low compared to the historical values that

averaged between 30 and 60 basis points, and Mills had never imagined that this value could

ever be negative. Given these values that he deemed “abnormally low” he felt that the current

low spreads presented a profitable trading opportunity.

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Part II

1. What is the swap trade that Mills is studying? The swap trade that Mills is studying is a “bet” on swap spreads widening from their current

level (0.0625% or 6.25 basis points) back to average historical values (30 – 40 – 50 basis points).

The trade in practice

Mills is long the swap –he pays a fixed rate and receives a floating rate (i.e. Libor). Meanwhile

he buys the corresponding amount of 30-year treasury (May 2038) in order to be neutral in

terms of market interest rates (the DV01 values are matched), using repo financing (see Q2).

Swap leg: Mills pays 2.128% every 6 months (4.2560% per annum), the fixed leg of the

swap, for the next 30 years. Mills receives the 3-month LIBOR rate (reset every 3

months), the floating leg, for the next 30 years.

Treasury leg: Mills receives 2.0965% every 6 months (4.193% per annum), the yield of

the May 2038 treasury. He used a repurchase agreement (“repo”) to finance the

purchase and hence pays the repo rate (0.15% annually).

Matching the bonds duration to become neutral to interest rate fluctuations

Mills is long the swap and shorts the treasury. If interest rates go up/down, the value of his

swap increases/decreases (he pays a relatively lower/higher interest rate compared to the

market rate, which is valuable). In order to hedge this interest rate exposure, he buys a bond

with the same maturity (May 2038) in the right proportion to match the duration:

The swap with fixed leg has a DV01 of $1.7 million for $1 billion notional – The May treasury

2038 has a $1.746 million DV01 for the same notional. Mills buys $0.97 billion of the thirty

treasury (1.7/1.746 = 0.973). The “dirty” price of the treasury $0.97 billion is $1.04 billion,

including the accrued interest ($2.13 per 100 face value).

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Turning the trade into a profit There is two ways the trade can be profitable:

Flows

The floating leg, in most cases, will be profitable as the repurchase rate is a

collateralized borrowing rate and as a result it should always be lower than the LIBOR

rate (unsecured borrowing rate between financial institutions).

On the fixed rate, Mills will pay the swap spread, currently 0.0625%; on aggregate the

flows will more or less cancel out as the negative payment of the fixed leg will be

matched by a positive payment on the floating rate. The effect on the value of the trade

should therefore be low.

Leg values

The position will benefit when the spread widen: the treasury yield (4.193%) decreases

and/or the swap fixed rate (4.2560%) increases. If the yield goes down, the treasury

will sell at a premium. This works the same way on the swap fixed leg if the swap rate

increases. This part of the trade is the most important to monitor.

2. How could Mills finance the trade? As mentioned in Q1, Mills will use a repurchase agreement to finance the purchase of the

treasury. He will pay the repo rate (0.15% annually) and will have a haircut of 2% (he will need

to post $21 million in capital to borrow the $1.04 billion needed to buy the bond).

3. What is the TED spread? The TED spread or Treasury-Eurodollar spread is the difference between the 3-month futures

contract for U.S. Treasuries and the 3-month contracts for Eurodollars having identical

expiration month. The spread measures the credit risk of the borrowers associated with

Eurodollar futures as Treasury bills had always been assumed to be risk free.

When the TED spread increases, default risk should also be increasing, which will in turn lead

investors preference to safe investments. Inversely, default risk is considered to decrease when

the TED spread falls.

How would you compute it empirically?

The Three-month TED spread is calculated as the difference between the 3-month LIBOR rate

and the 3-month Treasury bill yield. The 3-month Treasury bills which are originally quoted at

discount rate are converted into bond equivalent yields.

In this sense, the spread measures banks credit worthiness, reflecting the difference in

borrowing rates for an uncollateralized loan by banks and a safe loan to U.S. government.

Therefore, TED spread is often used to track the difference between the LIBOR and the

appropriate repo rate, as these are no more than loans secured by government bonds.

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4. What are the risks in the trade that Mills is about to put on? Risks can arise whether the swap spread narrows or widens as Mill anticipated.

[Narrowing spread] The yield on the 30-Year Treasury bond increases

An increase in yield on the 30-year Treasury bond has two implications. As the value of the

bonds decreases when the yield to m maturity increases, the broker might require KTC to post

additional cash collateral to compensate for the negative price change or ask to sell some

Treasury bonds which will have as a direct effect to reduce leverage. The liquidity of the 30-

year Treasury bond will then affect KTC’s ability to sell the bond. Therefore, it is important for

KTC to have sufficient capital reserve to meet cash requirements. Secondly, in the renewed

repo transaction, the broker might increase the haircut to reflect the risk for a drop in value of

the collateral.

[Narrowing spread] 30-year swap rate decreases

If Mills has been required to post initial margin against the swap, additional cash collateral may

also be required if the swap rate declines. Again, this will require KTC to have some cash

reserve.

[Widening spread] 30-year swap rate increases and effect on counterparty risk

Inherent in any OTC contract, the counterparty might not be able to fulfill the promised

payments. Particularly, when the market rate increases, the counterparty risk will increase as

the floating leg could have received more in exchange for paying the same amount.

The success of Mill’s trade will also depend on his ability to renew repo agreements every 3

months for 30 years (or until the spread widens).

Why is the spread so low? Can the spread turn negative? Why?

Higher yield on long-term Treasury bond In mid-October 2008, the US Treasury announced the purchase of preferred shares from nine

large financial institutions, which would mainly be financed by issuing long-term Treasury

bonds. The large increase in supply of Treasury bonds drove up their yield and hence imposed

a downside pressure on swap spreads.

The principal exchanged in a Treasury bond transaction is to be repaid at maturity (30 years

later in this case) whereas the principal is not exchanged in a swap transaction and the timely

payments are marked to market. In addition, the swap losses due to default of a counterparty

are only equal to the cost of replacing the position, when a default of a counterparty in bonds

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often means a loss of the principal. As such, the relatively riskier delivery method of Treasury

bond is reflected by a higher yield.

Lower 30-year swap rate After Lehman’s bankruptcy, investors sought for replacing hedges as their swaps with Lehman

had become void, which was an enormous market force. Fixed rate bond issuers, who have

timely fixed obligations would benefit from a steepen yield curve to pay the floating. Secondly,

sovereign debt managers also tend to reduce the duration of their outstanding debt (both ask

to receive the fixed rate in a swap). Thirdly, institutional investors wish to benefit from the

carry gain by entering in swap. Finally, commercial banks are less inclined to hedge their short

term variable rate deposits. As a result, there would be relatively more floating than fixed-rate

payers in the interest rate swap market. The swap rate thus decreased to reflect the higher

demand for the floating position.

From the fixed-payers’ perspective of view, another reason that might contribute to a lower

swap rate is the lower hedging cost of floating swap dealers. In addition, capital requirements

and regulation may induce investors to use swap instead of bonds, reducing the yield of swaps

(risk-weighted asset regulation for instance). Another explanation is the view of the market

that governments like any entities can default which drove up government bond yields.