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Contribution Details

Type Bachelor's Thesis
Scope Discipline-based scholarship
Title The negative basis trade: How to measure the CDS basis adequately
Organization Unit
Authors
  • Fabian Kunz
Supervisors
  • Chris Bardgett
  • Markus Leippold
Language
  • English
Institution University of Zurich
Faculty Faculty of Economics, Business Administration and Information Technology
Date 2010
Zusammenfassung The following thesis describes the problem of measuring the basis in credit risk markets in general and presents the three measures introduced in the theoretical section empirically for selected companies such as Daimler, Kraft Food or Coca Cola. A basis in general is defined to be a difference between two prices and is supposed to move within certain boundaries so that no arbitrage opportunities arise. In the financial markets, a wide range of bases are known, such as the ones in the futures markets for equity, commodities or rates and can be generally defined to be the difference between the cash and the derivative form of the same asset. Taking the German DAX Index as an example, you will see the spot trading around 3-5 points lower than the shortest futures contract, due to cost of carry, time value of money and other reasons. In credit risk however, the simple cost of carry no arbitrage argument does not hold, as the derivative and the cash form of the same asset, namely credit risk, differ in more than the point of time of delivery. The purest form of credit risk is traded within the so called Credit Default Swap, a contract that swaps the default risk of a third counterparty between the two counterparties in the swap. The protection seller agrees to pay a certain amount to the protection buyer in case of a credit event, which may be defined as default, restructuring or only a delay of payment. For this “insurance”, the protection buyer pays regular fees to the seller, the so called Credit Default Swap spread (which is actually not a spread, but an absolute value). At the inception of the swap it has (as most swap contracts) a present value of 0 which means that both legs, the one of the fixed spread payments that are known in advance, and the one dependent on a credit event, unknown in advance (time, size, happens at all) are of equal value. On the other hand, the cash of this credit risk is traded in various forms of bonds issued by the third party. Having bought one of these bonds, the investor will directly face the credit risk of the issuer and receive regular coupon payments as a compensation for this risk. Essentially, if two forms of the same asset do not trade within the no arbitrage range, either an arbitrage or (dependent on several assumptions such as the non default of the protection seller) a relative value opportunity arises that will be exploited by market participants. The difficulty in this work was to find out exactly, how the two forms of the same asset (the risk of default of a company) should be measured and compared. As a fundament, for both forms, the cash and the derivative one, some vehicles were introduced and explained. Consequently, pricing was explained. Using the main literature by Schoenbucher and Choudhry, the different forms ways to measure the basis were explained in detail:  Asset Swap basis defined as the asset swap spread – 5y CDS spread  Z-Spread basis defined as the bond’s Z-Spread – 5y CDS spread  Adjusted Z-Spread basis defined as the bond’s Z-Spread – adjusted Z-Spread, that is the Z-Spread of a theoretical bond. To find this theoretical bond, the original bond is priced using the default probabilities implied by the CDS curve. As the CDS are extremely liquid and traded over any time horizon from 6m to 10y or even further, one can calculate a specific default probability for every future cashflow and thus calculating the CDS implied bond price using a binomial tree of default/no default in each single period until maturity. The following data for 19 names was collected:  CDS curve using tenors 1y, 2y, 3y, 4y, 5y, 7y and 10y for the period from 02.01.2007 - 15.12.2009 (all data on daily basis)  the prices of one straight bond for each reference entity, paying coupon once a year, with maturity between 01.01.2011 and 31.12.2013, denominated in the same currency as the respective term structure of CDS for the same period as above  Swap curves as proxy for the risk free interest rate For each future payment, the exact linear interpolated values of all inputs were used. For this, the days to go were calculated using the 30/360 daycount convention, and having this, the exact swap rate to discount and the exact CDS spread could be used. This has the advantage that the full term structure of CDS and interest rate can be worked into the calculation, especially any form of curvature is represented one by one. Calculating a riskless bond price (discounting the future cashflows using the swap rates only), enabled to work a Z-Spread into the calculation, for the original market bond price and the theoretical CDS based bond alike. For this, MS Excel’s goalseek algorithm was used. These could be compared so calculate the Adjusted Z-Spread basis. The simple Z-Spread basis was easily calculated using the Z-Spread and the 5y market CDS spread. The Asset Swap Basis was calculated using a formula from the literature, based on the simple yield-to-maturity of the bond also easily calculated using the same algorithm. The procedure takes about 5 minutes for each bond to calculate 2265 values (3 spreads for each day, 755 days), and from then on the 2265 bases (on a 3y old Lenovo laptop). The difficulties of the calculation were in the small details: how to calculate the clean bond prices (as the market prices from the Thomson Data Stream were clean) correctly, how to calculate the default probabilities from the CDS, which assumptions to make and which not and so on. All in all, the work showed that only for extremely distressed values the Adjusted ZSpread method shows significant deviations from the two traditional measures. However, it is extremely interesting to see in which state of financial turmoil the system was during the crisis, as all tested companies lose their equilibrium of a basis of 0. For the more conservative values, the basis turns negative, probably implying sellers of cash bonds due to risk reduction (flight to quality), though no risen level of default probability, so no additional demand in the CDS. On the other hand, distressed companies such as automakers get positive bases due to strongly higher demand in the CDS. For all values, it becomes clear the markets have calmed down until end of 2009 as all bases reached the normal level of 0.
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