UNIVERSITAS INDONESIA PRICING CREDIT DEFAULT SWAPS IN ...

UNIVERSITAS INDONESIA

PRICING CREDIT DEFAULT SWAPS IN THE ASIAN REGION PRE-CRISIS AND POST-CRISIS 2008

Proposed By: DENDI ANUGERAH PRATAMA SUHUBDY 0906525056

Proposed As One Of The Requirements To Obtain Bachelor Degree In Economics 2013

UNIVERSITAS INDONESIA FACULTY OF ECONOMICS DEPARTMENT OF ACCOUNTING ACCOUNTING MAJOR

APPROVAL OF THESIS

Name

: Dendi Anugerah Pratama Suhubdy

Student Number

: 0906525056

Major

: Accounting

Thesis title

: Pricing Credit Default Swaps in the Asian Region Pre-Crisis and Post Crisis 2008

Date

The Head of Department:

Dr. Dwi Martani, S.E., Ak.

of Accounting

Date

Thesis Supervisor:

Dr. Gede Harja Wasistha CMA

Table of Contents STATEMENT OF AUTHENTICITY ......................................................................... 4 EXECUTIVE SUMMARY.......................................................................................... 5 CHAPTER I ................................................................................................................. 6 INTRODUCTION ....................................................................................................... 6 1.1 Background ........................................................................................................ 6 1.2 Problem Identification ........................................................................................ 9 1.3 Research Objectives ........................................................................................... 9 1.4 Benefits of Research ........................................................................................... 9 I.5 Hypothesis ........................................................................................................... 9 Hypothesis 1 ......................................................................................................... 9 Hypothesis 2 ......................................................................................................... 9 I.6 Outline of the Thesis ......................................................................................... 10 CHAPTER II .............................................................................................................. 11 THEORETICAL FRAMEWORK ............................................................................. 11 2.1 Credit Default Swaps ........................................................................................ 11 2.1.1 Definition of Credit Default Swaps ........................................................... 11 2.1.2 History of Credit Default Swap ................................................................. 12 2.1.3 The Credit Default Swap Market ............................................................... 12 2.1.4 Payoffs of A Credit Default Swap Facing A Credit Events ...................... 13 2.1.6 Purposes of Entering A Credit Default Swap ............................................ 19 2.1.7 Valuation .................................................................................................... 20 2.2 Modelling Default Probabilities ....................................................................... 23 2.2.1 Types of Default Probabilities ................................................................... 23 2.2.4 Structural Approach to Default Prediction and Valuation ......................... 24 2.2.5 Reduced Form Models to Default Prediction and Valuation ..................... 25

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2.3 Arbitrage ........................................................................................................... 29 2.3.1 First Order Arbitrage ................................................................................. 30 2.3.2 Second Order Arbitrage: Value between Bonds and CDS as a Risk Free Rate ..................................................................................................................... 31 2.3.3 Third Order Arbitrage: RNPD of Bond, CDS, and Implied Equity (Fundamental) Values ......................................................................................... 32 CHAPTER III ............................................................................................................ 34 RESEARCH METHODOLOGY ............................................................................... 34 3.1 Hypothesis Testing ........................................................................................... 34 3.1.1 Second Order Arbitrage Test ..................................................................... 34 3.1.2 Third Order Arbitrage ................................................................................ 37 3.2 Asian Market .................................................................................................... 40 3.3 Data and Data Sources...................................................................................... 41 3.4 Results of Regression ....................................................................................... 41 3.5 Limitations of Research.................................................................................... 47 CHAPTER IV ............................................................................................................ 49 DATA ANALYSIS .................................................................................................... 49 4.1 Pre and Post Crisis ............................................................................................ 49 4.1.1 Second Order Arbitrage ............................................................................. 51 4.1.2 Third Order Arbitrage ................................................................................ 60 4.1.2.1 Prior Crisis .............................................................................................. 60 4.1.2.2 Post Crisis ............................................................................................... 62 4.2 Special Case: Sharp’s Bankruptcy ................................................................... 64 4.2.1 Prior Bankrupt............................................................................................ 66 4.2.2 Post Bankrupt ............................................................................................. 73 CHAPTER 5 .............................................................................................................. 80 5.1 Conclusion ........................................................................................................ 80 5.2 Implication of Research .................................................................................... 80 5.3 Suggestions to Further Research ...................................................................... 80 References .................................................................................................................. 82

Universitas Indonesia

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Appendix .................................................................................................................... 84 List of Companies .................................................................................................. 84 VBA Code to Obtain the Implied Volatility........................................................... 90 STATA Panel Data Analysis Results ..................................................................... 94 Overall Data Analysis ......................................................................................... 94 Prior dan Post Crisis Analysis .......................................................................... 102 Second Order Arbitrage Analysis ..................................................................... 102 Prior Crisis ........................................................................................................ 102 Post Crisis ......................................................................................................... 106 Third Order Arbitrage Analysis ........................................................................... 110 Prior Crisis ........................................................................................................ 110 Post Crisis ......................................................................................................... 111 Sharp Bankruptcy ................................................................................................. 113 Prior Bankrupt................................................................................................... 113 Summary ........................................................................................................... 114 Post Default....................................................................................................... 115 Summary ........................................................................................................... 116


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STATEMENT OF AUTHENTICITY Hereby, I declare Name

: Dendi Anugerah Pratama Suhubdy

Student Number

: 0906525056

Major

: Accounting

Hereby declare as follows: 1. Final works are titled: Pricing Credit Default Swaps in the Asian Region Pre-Crisis and Post-Crisis 2008 The research associated with this thesis is the result of my own work 2. Any ideas or quotation from the work of others in the form of publications or other forms in this thesis, has been recognized in accordance with the standard procedure in the reference disciplines. 3. I also acknowledge that this thesis can be generated thanks to the guidance and full support by my supervisor, namely: Mr. Gede Harja Wasistha If later on in this thesis found the things the show has done academic cheating by me, then I have an academic degree I would get drawn in accordance with the provisions of Accounting Degree Program, Faculty of Economics, University of Indonesia. Jakarta,

Dendi Anugerah Pratama Suhubdy


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EXECUTIVE SUMMARY The global financial crisis has been shredding credit default swaps into limelights. Since its first contract been introduced by JP Morgan in 1998, credit default swaps has been used as an intrument to protect investors from the risk of the exposure of default of a corporation or even a sovereign nation. The solution for the problem to price these esoteric intruments by a no-arbitrage assumption has been created by many financial economist, such as Hull, White and Predescu (2000). In their published paper they analyzed the linkage between the credit default swap pricing with its respected underlying bond and the riskfree rate. In the process, according to Taleb (1997) in a second-order arbitrage such as in a derivative with its underlying there must be a close significant relationship between the them. The author tries to expand this relationship within the third order arbitrage such the linkage between the risk-neutral probability (RNPD) to default of the bonds, CDSs, and equities (fundaental) values. The purpose of this arbitrage relationship seeking, other than to calculate the fair price for the credit default swap, but to indicate any price behavioural differences pre and post of the global financial crisis of 2008. In the dataset, the author also describes the process of Sharp’s bankruptcy in the end of 2012. The author obtaines that there are second but no third or arbitrage relationship between the corporate bond market, equity market and its respective credit derivative market. The author also obtains facts that the models that Fitch Equity Implied Rating does not work to predict the changes in Risk-Neutral Probability to Default in the case of Sharp’s bankruptcy. Keywork: arbitrage, credit default swap, risk-neutral probability to default


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CHAPTER I INTRODUCTION 1.1 Background According to Hull1 (2000) a credit default swap (CDS) is a financial contract that provides insurance against the risk upon the default of payments of a particular company. Should the company be insolvent in the range of the contract or default on specific bond payments (in the International Swap and Derivatives Associations’ term this is called the credit event, since it may not only be a default but also a restructuring on credit), the buyer of the CDS will have the right to sell the bond to the seller of the CDS at a value that is termed in the contract, which is commonly at the amount of par. The bond which is the underlying asset of the CDS is refering is called the reference obligation, and the total par value of the bond is called the notional principle. An entity which may be an insurer, a reinsurer, a bank, a hedge fund, or a corporation under certain regulations may be able to enter into a CDS deal with another entity which is called the counterparty. In simple terms, a CDS may be considered as a insurance against the default of a bond. Nevertheless it has several differences such as the buyer of CDS may not be obliged to hold the reference obligation to enter in such a contract. Thus, there are several reasons entities enter into a CDS deal: (1) arbitrage, (2) hedging, (3) speculation. First, an entity may buy a CDS to implement a strategy such as arbitrage of capital structure changes of the firm. Say the reference firm, the firm which issues the reference obligation or the bond, is in considering debt financing through issuing more bonds in the international capital market. Such increase in debt equity ratios 1

Valuing Credit Default Swaps I: No Counter Party Default Risk


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may change the reference firm ability to pay its current debt in the future, thus an arbitrageur could buy a CDS to protect against the increase in riskiness of holding the bond, while at the same time buying the bond and shorting the stock to lock an amount of profit within a certain range of time. This strategy will mainly be the discussion of my thesis. Second, an entity may enter a CDS deal to hedge againts the risk of default of a specific entity if it has bought the bond in the first place. Such strategy insures the bondholder, thus if a credit event occurs the bondholder receives minimum the initial investment on the bond. Third, an entity may not even have the bond, but it may speculate on a reference entity’s ability to pay its debt. If the ability to pay of the reference entity rises, then the CDS premia may decrease thus decreasing the value of the CDS and also vice versa (underspecific assumptions such as no change in the general macroeconomic condition). Since, Modigliani Miller theory on the capital of the firm, there has been significant amount of research on the capital structure of the firm. Several implications of these findings are the evidence on the link between stock prices and bond prices/yields2. If the performance of the firm decreases, it is more likely that insolvency increases, thus increasing the riskiness of holding a bond of the firm. Thus bond yields may increase, also at the same time when the market discounts the information on the performance of the firm, its stock would decrease. Thus, these has been underlying trading strategies of several risk arbitrage hedge funds, that may short the stock and the bond to obtain profit if it believes that such firm will decrease in performance and thus value.

2

study that clarifies this


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Since the introduction of the CDS by JP Morgan in 1996, it has been easier to implement for an asset managers to buy a CDS (pay the premium upfront to the CDS seller) rather than buying the whole bond, and also shorting the stock. This also has the same payoff structure, should the insolvency of the firm decreases. Thus, in the pasca-introduction of CDS and also credit derivatives generally, that there is an arbitrage value between stock prices, bond yields, and CDS premia. According to Taleb (1997)3 there are several types of arbitrage, mainly in the first, second, and third order. Each which has a degree of similarities between perceived values between two variables or characteristics in two financial instruments. A first arbitrage for example is the triangle arbitrage between three currencies, such as the EUR/USD, USD/IDR, and the IDR/EUR may only have a number in which the three of them hold constant relationships. A second order arbitrage may be on different instruments, but the same underlying assets, or on the same instruments, but on different underlying assets. The example of a second order arbitrage is bond arbitrage, and value trading. A third order arbitrage is just arbitrage on the price relationships or correlations on different instruments (behaves in a certain way). In the context of this thesis, the arbitrage that will be considered under my analysis is the second order arbitrage and third order arbitrage. The second order arbitrage has been tested by Hull and White (2000) for the a firm called Ashland in the US Stock, Bond and Derivaitve Market, while there has been no evidence of relationship testing between financial instruments in the Asian Pasific (APAC) Markets. The second order arbitrage is between the actual default probabilities obtained from accounting and equity information and risk-neutral probabilities obtained from CDS premia and bond yields. This arbitrage relationship has never been tested before in the Asian Pasific Region (APAC) market.

3

Dynamic Hedging: Managing Vanilla and Exotic Options


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1.2 Problem Identification Does the second arbitrage value between the CDS bond portfolio and the risk-free bond portfolio exist in the APAC financial market? Does the third arbitrage value between the actual default probabilities and the riskneutral probabilities exist in the APAC financial market?

1.3 Research Objectives There are two main objectives of this research which are: 

To obtain information on second order arbitrage opportunities between a CDS + bond portfolio and a risk-free bond portfolio



To obtain information on third order arbitrage opportunities between riskneutral probabilities to default (RNPD) between CDSs, bonds, and equities.

1.4 Benefits of Research I.5 Hypothesis Hypothesis 1 H0: There are no significant relationship between a CDS + bond portfolio and a riskfree bond portfolio H1: There are significant relationship between a CDS + bond portfolio and a riskfree bond portfolio Hypothesis 2 H0: There are no significant relationship between actual default probabilities and risk-neutral probabilities


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H1: There are significant relationship between actual default probabilities and riskneutral probabilities

I.6 Outline of the Thesis Chapter 1 explains about the background of why research in arbitrage in the Asian region, and also the research objectives. Chapter 2 explains about the literature review on the strudy on arbitrage and also on the development of credit default swaps, and default probability modelling. Chapter 3 explains on the methodology that is used to obtain variables, data, processing of variables to become default probability, and also the method to analyse. Chapter 4 explains about the result of my research. Last but not least is Chapter 5, which is the conclusion of my research.


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CHAPTER II THEORETICAL FRAMEWORK 2.1 Credit Default Swaps 2.1.1 Definition of Credit Default Swaps Credit default swaps are basically defined by several investment banks, practicioners, and academics such as: 

Investment Banks o Merrill Lynch (2006)4: Credit Default Swaps (CDS) are the most important and widely used instrument in the credit derivative market. In essence a default swap is a bilateral OTC agreement, which transfers a defined credit risk from one party to another. The buyer of the credit protection pays a periodic fee to an investor in return for protection against a Credit event experienced by a Reference Entity (i.e. the underlying credit that is being transferred). o Lehman Brothers (2003)5: A credit default swap (CDS) is used to transfer the credit risk of a reference entity (corporate or sovereign) from one party to another. In a standard CDS contract one party purchases credit protection from the other party, to cover the loss of the face value of an asset following a credit event. o Goldman Sachs (2007)6: A Credit Default Swap (CDS) is a bilateral overthe-counter derivative contract which transfers the risk of the loss of the face value of a reference debt issuer over a specified period between two parties (the protection buyer and protection seller).

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Credit Derivatives Handbook 2006 – Vol 1 & 2 Guides to Exotic Credit Derivatives – Lehman Brothers 2003 6 Goldman Sachs CDS 101, 2007 5


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

Practitioners o Okane (2003): A default swap is a bilateral contract that enables an investor to buy protection against the risk of default of an asset issued by a specified reference entity. Following a defined credit event, the buyer of protection receives a payment intended to compensate against the loss on the investment. More often, the fee is paid over the life of the transaction in the form of a regular accruing cash flow. The contract is typically specified using the confirmation document and legal definitions produced by the International Swap and Derivatives Association (ISDA). o Frank Fabozzi (2001): a credit default swap is probably the simplest form of credit risk transference among all credit derivatives. Credit default swaps are used to shift credit exposure to a credit protection seller.

2.1.2 History of Credit Default Swap In the early 1990s staff at Bankers Trust, later bought by Deutsche Bank, and JP Morgan developed the first credit default swaps as a way for the banks to protect themselves against their exposure to large corporate loans they made to their clients. From a relatively small market measured in the low hundreds of billions by the late 1990s, the product exploded during the 1990s and today their gross notional is reckoned to be close to $28 trillion (£17 trillion). 2.1.3 The Credit Default Swap Market All European credit default swaps are issued using the “master agreement” issued by the International Swaps and Derivatives Association (ISDA), a trade association of all the world’s leading investment banks and investors in so-called OTC [over-thecounter] derivatives. The term OTC is important, as CDS is not traded on a central exchange but as bilateral agreements between buyers and sellers, essentially investments banks and investors. Its current notional amount outstanding is $30 million.


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$70

Credit Default Swaps Outstanding

In Trillions USD

$60 $50 $40 $30 $20 $10 $0

Figure 1. Credit Default Swaps Outstanding Source: Goldman Sachs CDS 101 2.1.4 Payoffs of A Credit Default Swap Facing A Credit Events The CDS Contract Mechanics (No Credit Event) If no credit event happens then the protection buyer will keep paying an annual premium for protection on the reference entity to the protection seller until the CDS matures.


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Reference Entity (Bond)

Risk Transfer

Protection Buyer

Protection Seller CDS Premium Premium x bps per year

Figure 2. Mechanism of CDS no Credit Event Source: Credit Trading and Management The CDS Contract Mechanics (Credit Event Triggered) When a credit event is trigerred, for example a default occured on the reference entities bonds, the protection seller must pay the par amount of bond towards the protection buyer. The payment mechanism for these contracts are divided by two ways: (1) physical settlement, and (2) cash settlements. Physical Settlement In a physical settlement, the protection buyer will exchange the debenture of the bond with the 100 par cash amount by the protection seller.


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Bond or Loan Protection Buyer

Protection Seller

Par amount 100 Figure 3. Physical Statement CDS Trigger Source: Credit Trading and Management Cash Settlements In a cash settlement, the protection seller only pays the protection buyer by 100Recovery rate amount, which is payed in cash.

Protection Buyer

100 – Recovery rate

Protection Seller

Figure 4. Cash Settlement CDS Trigger Source: Credit Trading and Management 2.1.5 Credit Events 2.1.5.1 Default According to Rajan Singenellore, Yong Lee, Yufei Li, William Mann and Anurag Rajat (Bloomberg, 2012) a default event is defined as a the first of any of the following events that is subjected to an entity: failure to pay interest or principal on an interest bearing bond, bankruptcy filling or for banks, FDIC or government insurance program takeover.


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Once a firm enters a default phase, it may have to outcomes. One which the firm survives as in a successful restructuring process, and also a negative resolution which leads to a bankruptcy.

Figure 5. Timeline for A Firm to Default Source: Fitch Equity Implied Rating, Quantitative Methods for Credit 2.1.5.1 Restructuring According to Chaplin (2005), the definition of a restructuing is the event where the borrower rearranges the debt of the of the company, usually to detriment of the lenders but usually with their permission (the alternative – not giving, permission – being worse). This credit event may involve reducing the coupon rate, lengthening the debt, reducing the nominal, reducing the seniority, or otherwise replacing the debenture with a note with a lower value. Sovereign borrowers typically restruture, and it is also familiar for corporates to restructure. For example, when Consesco agreed a restructuring with its creditors, it was normal to trade CDSs with “original restructuring”. Currently, CDSs are trading with several clauses.


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1. No restructuring trigger 2. Original restructuring (US until 2001, EU until 2003/2004) 3. Modified restructuring (US 2001-2004) 4. Modified modified restructuring (EU and US 2004-present) Details on these restructuring clauses are explained below. Table 1 Types of Restructuring and Material Clause in ISDA Docummentation Type of CDS Restructuring Original Restructuring

Material Clause

1. A reduction in the rate or amount of interest or the amount of schedules interest accruals 2. A reduction in the amount of principal or premium payable at maturity or scheduled termination date 3. A postponement or other deferral or a date or dates for (a) payment or accrual of interest, or (b) payment or premium 4. A change in the ranking in priority of payments of any obligation causing the subordination of that obligation 5. Any change in the currency or composition of any payment of interest or principal where this results directly or indirectly from deterioration in the financial condition of the reference entity.

Modified The modified restructuring clause was created to lmit the cases restructuring (Mod when a restructuring could trigger a CDS contract and R) introduce a ‘restructuring maturity limitation’. On the occurence of a restructuring event only debt that has maturity on or before the earlier of a. 30 months after the restructuring date b. The latest maturity of the restructured debt c. Restructured facilities must have at least four creditors and need at least a two-thirds majority to approve d. ‘Consent not-required debt’ only is delivered, or is generally transferable (‘rule 144A, reg. S)


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e. Partial settlement is allowed Thus, modified restructuring changes two points to the above, to broad the scope of the deliverable debt a. Restructured debt with up to 60 months’ maturity is deliverable (other deliverable debt remains at 30 months) b. The deliverable obligation must be conditionally transferable These are several examples of corporate defaults and triggers of its CDSs. Table 2 Credit Events and Description Credit Event

Description

Example

Bankruptcy

Corporate becomes insolvent or is unable to pay its debts the bankruptcy event is, of course, not relevant for sovereign issuers

Delphi (DPH) Delta AirLines (DAL) Northwest Airlines (NWAC)

Failure to Pay

Failure to the reference entity to make due payments, taking into account some grace period to prevent accidental triggering due to administrative error

Argentina

Restructuring

Changes in the debt obligations of the reference creditor but excluding those that are not associated with credit deterioration such as a renegotiation of more favorable terms

Conseco Xerox Solutis


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2.1.6 Purposes of Entering A Credit Default Swap 2.1.6.1 Hedging For example, Goldman Sachs owns 5-year senior unsecured Singapore Telecommunication Ltd bonds within its proprietary portfolio, it may hedge its exposures towards the default of the bond by buying CDS protection. In the occurence of a credit event during the life of the CDS, the debt can be delieverd into the CDS and Goldman Sachs could receive the bond at par. Prior to default, for example the widening of the spread on SingTel bonds is likely be accompanied by widening of the CDS spread. Therefore, there is some spread hedging between the two, and precisely how much depends on the ‘delta hedge ratio’7 and the ‘basis risk’. The CDS therefore protects not only against the default risk but also against the mark-to-market change in value of bond arising from spread change. 2.1.6.2 Speculation If a hedge fund holds a view that spreads are going to narrow on General Motors, then it could buy GM debt and wait until its yield lowers, and it makes a profit from the trade. Alternatively, compared to go long GM debt, one could short the CDSs, referencing GM (for example at 100bps – 5 years). If the hedge fund is right, such as the spread narrows to 50bp per annum, he then could buyback the CDS and make a profit of 50 bps for 5 years.

7

The sensitivity of price of a derivative to the change in the price of its underlying (stocks, bonds, CDSs)


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2.1.6.3 Arbitrage If a Morgan Stanley for example takes a view that the there are differences between the bond spread rate and CDS rate on the current underlying bond (this will be explained more in Chapter 4) such that the bond spread is lower than the CDS rate8, one could make riskless profits by shorting the CDS, buying the bond, and shorting the T-Bill. This will be our main discussion throughout our analysis. 2.1.7 Valuation Several academics tried to create pricing or valuation models for CDSs under several no-arbitrage assumptions or risk-neutral settings such as Hull and White (2000), Turnbull (2000) and Duffie (2000). Basically the their valuation models are similar while the newest relax assumptions that are not realistic under trading conditions. 2.1.7.1 Under No Counterparty Risk In a paper named Valuing Credit Default Swaps I: No Counterparty Default Risk, Hull and White (2000) created a pricing model for the CDS assuming flat treasury curves.

s=

s *(1 R aR) (1 R)(1+ a*)

(1)

Where the constituent variables are s*

: par bond spread (between the underlying bond and the treasury)

R

: recovery rate

a

: coupon rate

8

under several assumptions


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a*

: average value of accruals from 0 < t < T

s

: premium on idealized CDS

Several assumptions that are made by Hull and White (2000) to simplify the valuation are: 

A flat treasury curve or a flat yield curve and constant interest rates. Stochastic interest rates make the no-arbitrage argument for the idealized CDS less than perfect, but do not affect valuations given assumptions that interest rates, default probabilities, and recovery rates that are independent.



A consequence of a non-flat treasury curve when pricing the CDS will lead to the par yield Treasury bond being worth less than the face alue plus accrued interest on average. Hull and White (2000) shows that when there is a upward slope in the curve then the premium becomes underestimated, and a downward sloping curve leads to and overestimating the spread on the CDS.

2.1.7.2 Under Counterparty Risk Hull and White (2000) relaxed the assumption of counterparty credit risk in its second paper of valuation of CDS. From several assumptions such as: 1. The probability of a counterparty default during the life of the CDS conditional on the reference entity defaulting during the life of the CDS is Prc/Qc. Hull and White (2000) assumes that there is a 50% chance that the counterparty default occurs before the reference entity defaults and a 50% chance that it occures after the reference entity defaults. Since discounting is ignored this implies that

P rc g = 0.5 Qr

(2)


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2. When a CDS is triggered, the payments by the CDS purchaser are half the average payments in the no-counter-party-default case 3. When both default with the counterparty defaulting first, the payments made by the purchaser are on third less than in the no-counterparty default case.

h=

Qc Prc + 2 3

(3)

1 g 1 h

(4)

This ultimately results in the valuation of

s = sˆ

,which relaxes the assumption of no-counterparty default risk in CDS valuations. Variables to define the pricing model of the premium of the CDS are Qr

: The probability of default by the reference entity between time 0 and T

Qc

: The probability of default by the counterparty between 0 and T

Prc

: The joint probability of default by the conterparty and the reference entity

between time 0 and T. This can be calculated from Qr, Qc, and the default correlation using equation 5. g

: The proportional reduction in the present value of the expected payoff on

the CDS arising from counterparty defaults h

: The proportional reduction in the present value of expected payments on the

CDS arising from counterparty defaults Snr

: The CDS spread assuming no counterparty default risk


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2.2 Modelling Default Probabilities 2.2.1 Types of Default Probabilities There are two types of default probabilities classified from the difference of extraction or computational methods to obtain them. 2.2.2 Actual Default Probabilities The first, which is the actual default probability or in financial economic terms is known as the real world default probability, is obtained from calculating historical default probabilities of a firm. It is also used extensively in banking regulations such as Basel II, and III for the purpose of stress testing. 2.2.3 Risk-Neutral Default Probabilities The second probability to default is obtained by extracting it from bond spread data using the equation

pd =

bondspread (1 R)

(5)

Where the constituent variables are Bondspread

: yield of corporate bond minus riskfree bond rate

R

: recovery rate

Pd

: probability to default

for the risk-neutral probability to default (abbreviation RNPD) from the bond and the equation


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pd =

cdspremium (1 R)

(6)

Cdspremium

: premium paid on every dollar default (in basis points)

R

: recovery rate

pd

: probability to default

2.2.4 Structural Approach to Default Prediction and Valuation Structural models of default are cause-and-effect models (Loffer and Posch, 2007). From an economic point of view, a structural approach defines conditions under which a firm is expected to default and then estimate the probability that these conditions will happen to estimate the default probability. 2.2.4.1 Altman Z-Score In 1968, Edward Altman was the first academic to study about the default probabilities of a corporation using accounting information. Based on reasoning that there are limits of a corporation between insolvency that can be detected within its financial statements and ratios. Several financial ratios that is used to obtain what is famously known as an Altman Z-Score are 1. Net working capital/total assets 2. Retained earnings / total assets 3. Earnings before interest and taxes / total assets 4. Sales / total assets Both are then inputed in a linear model from Altman and then determine the whether the Z-score obtained is within cuttoff point which is


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Z >= is classified as non-bankrupt Z < is classified as bankrupt 2.2.4.2 Ohlson Logit Model In 1980, James Ohlson published a paper entitled Financial Ratios and the Probabilistic Prediction of Bankruptcy in the Journal of Accounting Research9 which introduces a bankruptcy prediction modelling using the maximum likelihood estimation (conditional logit model). The dataset of the studies are from 1970-76 of several variables such as 1. Ohlonsize

: Log (total assets/GNP price-level index). The index assumes

a base value of 100 for 1968 2. TLTA

: total liabilities/total assets

3. WCTA

: working capital/total assets

4. CLCA

: current liabilities/total assets

5. OENEG

: 1 if total liabilities exceed total assets, 0 otherwise

6. NITA

: net income/total assets

7. FUTL

: funds provided by operations/total liabilities

8. INTWO

: 1 if net income was negative for the last 2 years, 0 otherwise

9. CHIN

: relative change in net income prior and this year in

percentage The result of Ohlson model is a number between 0 and 1 which is defined as the default probability. 2.2.5 Reduced Form Models to Default Prediction and Valuation

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Journal of Accounting Research, Vol. 18, No. 1 (Spring, 1980), pp. 109-131


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2.2.5.1 Black, Scholes on Valuing Corporate Debt using option pricing models As an further implication of its option pricing model, Black and Scholes (1978) found out that a common stock could be treated as a call option on the firms assets. Basically several assumptions that Black and Scholes (1978) made was 1. Consider a company that has common stock and bonds outstanding and whose only asset is shares of common stock of a second company 2. The bonds outstanding of the company are pure discount with no coupons, giving the holder the right to a fixed sum of money with a specified maturity 3. Suppose that the bonds contain no restriction on the company except a restriction that the company cannot pay any dividends until after the bonds are paid off 4. Suppose that the company plans to sell all the stock it holds (liquidation) at the end of the specified maturity, and payoff the bond holders, and pay remaining money to stockholders as a liquidating dividend. Basically Black and Scholes treats a common stock of a corporation as a European call option on a firms assets, and a bond as selling a European put option on the firms assets. Based on the famous Black-Scholes formula, the structural model to estimate the default probability of a firm is.

prob(default) = ( DD)

DD =

ln(At / L) + (r + 2 / 2)(T t) T t

(7)

(8)

Which one should be familiar since it is widely known as the d1 value for the BlackScholes option pricing model.


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2.2.5.2 Merton on Finding that debt valuation could be done by valuating a debt as an European call option Since, the development of the option pricing model under continous time assumptions. Robert Merton published a paper entitled On The Pricing of Corporate Debt: The Risk Structure of Interest Rates which mainly develops a pricing model for corporate bonds under the assumptions of optionality and relaxing assumptions for the Black-Scholes option pricing model which assumes a flat treasury curve and not a stochastic process. Several assumptions that are made under Merton’s corporate debt pricing: 1. There are no transaction costs, taxes or problems with indivisibilities of assets 2. There are a sufficient number of investors with comparable wealth levels so that each investor believes that he can purchase or unload securities as much as he can at the market price (liquidity assumption) 3. There exists an exchange market for borrowing and lending at the same rate of interest 4. Short-sales of all assets, with full use of the proceeds, is allowed 5. Continuous trading time 6. The Modigliani-Miller theorem that the value of the firm is invariant to its capital structure 7. The term-structure of interest rates is “flat” and known with certainty. A price of an asset is continuously compounded 8. The dynamics for the value of the firm, V, through time can be described by a diffusion-type stochastic process with the stochastic differential equation

dV = ( V C)dt + Vdz

(9)

Where the endogenous variables are a : the instaneous expected rate of return on the firm per unit of time


28

C : is the total dollar payouts by the firm per unit time to either its shareholders or liabilities-holders if positive Sigma : is the isntaneous variance of the return on the firm per unit time;; dz is a standard Gauss-Wiener process (Geometric Brownian Motion).

F[V, t] = Be rt { (d1)+

1 (d2)} d

(10)

2.2.5.3 Fitch Implied Equity Ratings: The Implementation of Barrier Option Pricing models as an improvement According to financial economists, such as Rubenstein and Reiner (1993), Rich (1994) and Stoll and Whaley derived another equation for debt and common stock modelling. Following the original work of Merton (1974), there has been widespread use of default probability models which employs the standard European call option framework for corporate debt valuation, which a firm can only default at the maturity date and not between. Nevertheless, a firm can default whenever their asset value fall below a default point – even if this occurs prior to the maturity of the option. In order to address this fact, previously develop models has been calibrated for a barrier, which is known as the barrier option framework for corporate debt. Figure 6: Barrier Default Probability Model


29

Source: Fitch Equity Implied Ratings (EIR), Fitch Quantitative Research 2007

2.3 Arbitrage According to Taleb (1997)

10

there are three types of arbitrage which is explained

below. Table 3: Arbitrage Orders Degree

Definition

Examples

First order

A strong-locked in Currency triangular arbitrage mechanical relationship in same instrument Location arbitrage Conversions and European options

reversals

“Crush” or “Crack”

10

Dynamic Hedging: Managing Vanilla and Exotic Options


for

30

Second Order

Different Instrument, same Cash-future arbitrage underlying securities Program trading Delivery arbitrage Distributional arbitrage (option spreading) Stripping

Second order

Different (but related) “Value” trading underlying securities, same instrument Bond arbitrage Forward trading Volatility arbitrage

Third order

Different securities, Bond against swap (the asset spread) different instruments, deemed to behave in Cross-market relationship related manner (correlation-based Cross-volatility plays hedging) Cross-currency yield curve arbitrage

Source: Dynamic Hedging: Managing Vanilla and Exotic Options 2.3.1 First Order Arbitrage A first order arbitrage is an arbitrage which is in the same financial instrument. For example, a triangular currency arbitrage which happens around a huge depreciation of a currency. Arbitrageurs could buy the currency that is not matched by the arbitrage assumption, and sell the currency that will fall in value.


31

Since the main discussion in this research is about the second and third arbitrage, the author will emphasize the explanaition of each artbirage. 2.3.2 Second Order Arbitrage: Value between Bonds and CDS as a Risk Free Rate The second order arbitrage is about an arbitrage between financial instruments that are different, but are linked because of the other instrument is an underlying of the other financial instrument. For example, risk arbitrage in option and underlying stocks. By replicating a portfolio of a stock and a riskfree bond, we could develop an arbitrage for options. In this case, the author is trying to emphasize on the second order arbitrage of a portfolio consisted of a bond and a CDS and a portfolio of a riskfree bond. In theory, there should be a direct arbitrage relationship such as

r=y s

(11)

For example if the yield on Unilever bonds are 4% and its CDS is 100bps, than the implied risk free rate from the portfolio of a bonds + CDS is 3%. Thus, the nearest riskfree-bond must have a yield of near 3% (adjusting for counterparty credit risk, and joint probability correlations to default, this may disperse in value). Should the riskfree rate is 3.5%, an arbitrageur may go long the riskfree bond, and short the bonds, and buy CDS protection at the same time until the yield of the securities converge. Although there are several assumptions and approximations made in this arbitrage argument (Hull White (2000)): 1. The argument assumes that market participants can short corporate bonds. Alternatively, it assumes that holders of these bonds are prepared to sell the bonds, buy the riskless bonds, and sell default protection when s > y - r.


32

2. The argument assumes that market participants can short riskless bonds. This is equivalent to assuming that market participants can borrow at the riskless rate (which rarely is the case) 3. The argument ignores the “cheapest-to-deliver bond” option in a credit default swap. Typically a protection seller can choose to deliver any of a number of different bonds in the event of default. 4. The arbitrage assumes that interest rates are constant so that par yield bonds stay par yield bonds. By defining the corporate bond used in the arbitrage as a par corporate floating bond and the riskless bond as a par floating riskless bonds we can avoid the constant interest rate assumption. Unfortunately, in practice par corporate bonds rarely trade. 5. There is counterparty default risk in the CDS 6. The circumstance under which the CDS pays off is carefully in ISDA documentation. The aim of the documentation is to match payoffs as closely as possible to situations under which a company fails to make payments as promised, on bonds, but the matching is not perfect. In particular, it can happen that there is a credit event, but promised payments are made. 7. There may be tax and liquidity reasons that cause investors to prefer a riskless bond to a corporate bond plus a CDS or vice versa. 8. The arbitrage assumes that the CDS gives the holder the right to sell the par bonds issued by the reference entity for its face value plus accrued interest. 2.3.3 Third Order Arbitrage: RNPD of Bond, CDS, and Implied Equity (Fundamental) Values Another unique part of arbitrage is the third order of arbitrage, which usually is not called an arbitrage but is called a pair trade. Several financial instruments have longrun stable relationships that one may notice that when A reduces in value, then B increases in value at the same time. This arbitrage may happen in different financial instruments such as what will be explained by this research.


33

Since there are structural models on estimating the default probability of the firm using the barrier model, the author would check whether there is a close relationship between the RNPD of the bond spread, and the RNPD from the CDS (assuming no counterparty credit risk).


34

CHAPTER III RESEARCH METHODOLOGY 3.1 Hypothesis Testing This research uses statistical inference to obtain conclusions for hypothetical testing on arbitrage relationship assumptions. There may or may not be an arbitrage based on the how strong the statistical relationship between variables. 3.1.1 Second Order Arbitrage Test Obtaining the Risk Free Bond for Derivative Traders In theory CDS spreads should be closely related to bond yield spreads. Define y as the yield on an n-year par yield riskless bond, and s as the n-year CDS spread. According to our previous literature review that there is a relationship articulated by the equation (10). The main problem in which we will discuss in the following is which type of riskfree rate should be the best benchmark for derivative traders and will the condition of recessions and bankruptcy distort the relationship between the instruments. 3.1.1.1 Under Generalized Conditions Under generalized condition, we assume that there are no macroeconomic or microeconomic condition that could distort the relationship between the CDS preimum, bonds yield, and riskfree yield. This is tested using the General Least Square (GLS) Linear Regression Method which has theoritical basis from Hull and White (2000).11

11

The Relationship between Credit Default Swap Spreads, Bond Yields, and Credit Ratings (Hull and White)


35

Y=

0

+

1 1

(12)

+

Utilization of Variables Y

: implied risk free rate, which is obtained from subtracting the bond yield

with its respected credit default swap premium A0

: intercept

A1

: slope of the linear curve

B1

: the comparable risk free rate which may be substituted by 

USD Treasury Rates o The United States T-Bill 1 month rate o The United States T-Bill 3 month rate



Great Britain Money Market Rates o The Great Britain Libor overnight rate o The Great Britain Libor 3 month rate



Swap Rates o United States 7 year Swap Rate o Great Britain 7 year Swap Rate

3.1.1.2 Under Recessions and Bankruptcy The author believes that there are the relationship may not fit due to counterparty credit risk (CCR), macroeconomic conditions, and a bankruptcy of a firm that denies the assumptio ceteris paribus. For counterparty credit risk adjustment, the author may not define inference statistically but the premium of differences between the two values are assumed to be


36

the premium of risk that has to be priced in by the derivative traders to adjust for sudden jump to default (which usually happens in the financial markets). There is a rare case that within samples of data, there has been a recent bankruptcy announcement from Sharp Corporation and gratefully the author could use the models to predict (backtest) the bankruptcy of Sharp Corporation.

Y=

0

+

1 1

+

2 rec

+

3 default

(13)

+


: implied risk free rate, which is obtained from subtracting the bond yield

with its respected credit default swap premium A0

: intercept

A1

: slope of the linear curve

B1

: the comparable risk free rate which may be substituted by 

USD Treasury Rates o The United States T-Bill 1 month rate o The United States T-Birll 3 month rate



Great Britain Money Market Rates o The Great Britain Libor overnight rate o The Great Britain Libor 3 month rate



Swap Rates o United States 7 year Swap Rate o Great Britain 7 year Swap Rate

Rhorec

: dummy variable, 1 if the firm’s dataset is between recession dates, 0

if it is not between recession dates


37

Rhodefault

: dummy variable, 1 if the firm’s is in default, 0 if it is not in default

3.1.2 Third Order Arbitrage The third order arbitrage will emphasize the relationship between the Risk-Neutral Probability to default implied by default spreads, credit default premiums, and the Risk Neutral Probability to Default from the Barrier Default Probability Model. 3.1.2.1 Obtaining the Default Probabilties from Accounting Information To obtain the default probability from accounting information, we used the adjusted barrier default probability to default model. 2r

H A(t)

E(t) = A(t)

(x + )

D(t) = A(t)

H ( x+ ) + A(t)

2

2r

+1

(y+ )

2r 2

e

r(T t )

K N(x )

H A(t)

2

1

(y )

2r

+1

(y ) + e +

r(T t )

K N(x )

H A(t)

2

(13)

1

(y )

(14)

which x+, x-, y+, y- constituents are 2

x± =

ln A(t) ln K + (r ± 12 T t

)(T t)

x± =

2 ln H ln A(t) ln K + (r ± 12 T t

(15)

2

)(T t)

(16)

Utilization of Variables


38

E (t)

: Market value of equity, which is also called the market capitalizatin of the company. Equals the total equity shares outstanding times the price per share.

D (t)

: Market value of debt, which is obtained from adding enterprise value with the cash and cash equivalent of the firm, and subtracting the market value of equity.

T

: Time horizon, which is the timeframe to default of a firm. The normal T that is used the the research is 1 years.

R

: Riskless interest rates, which is the USD 7 year swap rate at the given date.

A (t)

: Market value of the firms assets, which is equal to the enterprise value adding the cash and cash equivalent of a firm.

H

: Barrier of asset, which is the threshold of an asset that may trigger a default sue from the consortium of banks, for example the debt-toequity ratio below higher than a level may indicate a firms low solvency value.

K

: default point of the firm, the point where the if the asset falls below this level at the end of the time horizon, the bondholder may declare the firm in default.

Sigma (t)

: asset volatility, the standard deviation of asset changes throughout years. This is an estimated variable, from historical data or implied data.


39

Estimating Asset Volatility There are two ways to obtain asset volatility measures from literatures. 1. Historical Asset Volatility This method requires the historical total asset values for a set of years. For N, years the historical asset volatility is the standard deviation of the datasets. 2. Implied Asset Volatility Another method to obtain the asset volatility is to use equation 13 or 14, and then reverse the equation to obtain the asset volatility. Since we knew the value of the total market value of equity, market value of debt (barrier), book value of the firm’s debt (exercise), riskfree rate, the asset volatility is obtain from a numerical method called the Newton-Raphson method. For the Risk-Neutral Probability to Default implied by firm fundamentals (accounting information) we use this equation 2r

H PD(t) = ( x ) + A(t)

2

1

(y )

(17)

Utilization of Variables All of the variables that has been estimated above are then used to obtain the RiskNeutral Probability to Default using equation 17. 3.1.2.2 Obtaining the Risk-Neutral Default Probabilties from Bond Spreads To obtain the default probability from corporate bond spreads we use the following equation.

PD =

y r (1 R)

(18)


40

3.1.2.3 Obtaining the Risk-Neutral Default Probabilties from CDS Premiums To obtain the risk-neutral default probability from CDS premiums we can use the following equation.

PD =

s

(19)

(1 R)

3.1.2.4 Statistical Tests: Panel GLS Regression Model To obtain the statistical inference on the arbitrage relationship between these default probabilites, we use the General Least Square (GLS) regression method.

Y=

0

+

1 1

(20)

+


: there will be two test using two difference variables, which are the

risk-neutral probability of bond spreads, and would be tested again for the riskneutral probability of CDS spreads. B1

: the risk-neutral probability to default from equity (fundamental)

values

3.2 Asian Market Since there has been small evidence on the testing of arbitrage relationships between financial instruments in the derivative markets in the Asian region, there may be proof that there may be a arbitrage relationship between the markets of bonds, equities, and also credit default swaps. JELASIN LAGI TENTANG STRUCTURE MARKET MASING-MASING NEGARA, DAN OTC MARKET CREDIT DERIVATIF ASIA


41

3.3 Data and Data Sources The data that is used for this research is obtained from Bloomberg terminal from the range of 31/12/1999 until 12/10/2012 of Over-The-Counter CDS (of 120 companies) that are heavily traded in the Asia Pasific (APAC) region and its respective reference obligations (bonds) and also their accounting information. The data that were extracted included CDS premium, its reference obligation bond yields, and accounting information. 1. Enterprise Value 2. Cash and Cash Equivalent 3. Equity Price 4. Outstanding Shares 5. Book Value of Debt 6. Book Value of Assets 7. Book Value of Equities

3.4 Results of Regression 3.4.1 Hypothesis Testing 1 Our dataset includes 120 companies, with 131284 of datasets or daily observations of bond yield, CDS premium, USD 1 month T-Bill rate, USD 3 months T-Bill rate, LIBOR overnight rate, LIBOR 3 month rate, USD 7 year swap rate, and British 7 year swap rate over the period of 12 years, from 1th January 2000 until 12 October 2012. After conducting regressions on each risk-free rate with the implied risk free rate, we obtain results as follows.


42

R2

Riskfree Rate Type

A1

Significance

LIBOR Overnight Rate

11.79%

0.43

Not rejected within confidence interval 5%

LIBOR 3 Month Swap Rate

10.87%

0.40


USD 1 Month TBill Rate

11.89%

0.48


USD 3 Month TBill Rate

11.46%

0.48


USD 7 Year Swap 18.02% Rate (minus 10bps)

0.88


BP 7 Year Swap 17.09% Rate (minus 10bps)

0.85


According to the results, the most accurate benchmark for riskfree rate used to valuate credit derivatives especially credit default swaps are the USD 7 year swap rate minus 10 basis points. Compared to the previous research for linked between bond yields, CDS premium, and risk-free rates, which is conducted by Hull, White and Predescu, I found an interesting fact. Hull, White and Predescu’s findings were based on 31 companies, mainly US-based companies including Enron and Worldcom (at that current time has not declared default), with a dataset from 1 January 1998 until 15 July 2002. The


43

underlying bonds that are used in the findings are under several strict assumptions such as 1. The underlyings must not be puttable, callable, convertible or reverse convertible 2. The underlyings must be single currency (USD) bonds with fixed rate, semiannual coupons that are not indexed. Indexed bonds may induce overliquidity, and drive down yields. 3. The underlyings must not be subordinated or structured. 4. The issue must not be a private placement. Hull, White and Predescu results’ are summarize below. RiskFree Rate a Type

B

Std. Error of Adjusted R2 Residuals

Treasury Rate

0.12

1.10

0.25

94.1%

Swap Rate

0.09

0.972

0.203

96.1%

The regression results confirms Hull, White and Predescu (2000) findings that the USD 7 year swap rate is the best risk-free rate benchmark that is used by derivative traders. 3.4.2 Hypothesis Testing 2 Our dataset consist of 97553 observations between 13 April 2003 and 20 Desember 2012. This includes the data of Sharp at the time of default, thus highly skewing the data.


44

The regression results is summarize in the table below.


45

Risk-Neutral Probabilty to Default (RNPD) Type

b

R2

Standard Error

RNPD Bondspread 0.30 with Equity

0.01

0.14%

RNPD Premium Equity

0.03

1.96%

CDS 1.47 with

To adjust the data skewness caused by Sharp’s dataset, I eliminated the data to see the difference in results. Risk-Neutral Probabilty to Default (RNPD) Type

b

R2

Standard Error

RNPD Bondspread 0.13 with Equity

0.0003

0.86%

RNPD Premium Equity

0.02

2.47%

CDS 1.25 with


46


47

The results indicates that there are positive but small significant relationship between the RNPD of bond spreads and CDS premium with the RNPD of Equity. We could reject the H0 for hypothesis two, but there are two types of error that is prone to the results. 1. Equity values could hardly predict the changes in default probability of bond spreads and the default probability of CDS premiums 2. The model used to obtain default probability is wrong, and could not be used to compare RNPD of bond spreads and CDS premiums in the regression model.

3.5 Limitations of Research The author identifies several limitation of this research after conducting hypothesis testing from the data obtained. 

For hypothesis testing 1, the amount of dataset prior to crisis is only 29502, relatively small compared to the dataset post crisis. There may be a suspicion that the amount of dataset could not describe the phenomena explain prior crisis since the amount of data are not comparable. Although, this does not reduce the accuracy of the research.



For hypothesis testing 2, the amount of dataset prior to crisis is also only 23080, relatively small compared to post crisis. There also may be a suspicion that the amount of dataset could not describe the phenomena explain prior crisis since the amount of data are not comparable. Although, this does not reduce the accuracy of the research either.



For the utilization of variables in equation 17 to obtain the probability to default, the book value of debt that the author uses is the yearly value, and not the daily value since it is impossible to obtain a daily of the book value of debt. The only closes value to the daily book value of debt is the quarterly book value of debt, which is also unattainable.


48



The probability to default of the firm using fundamental values, which is used in equation 17, is very sensitive to asset volatility. There may be 3 values of asset volatility, the average weighted volatility of debt and equity, the implied asset volatility and also the historical asset volatility. The author implements the implied asset volatility and it implies a low value of asset volatility, which may underestimate the real asset volatility.


49

CHAPTER IV DATA ANALYSIS In this chapter, we will discuss in depth the regression analysis and its implications of the results in relations between the equity, credit, and derivative market. To further expand explanations, the author differenciates the analysis into several groups. 1. Prior and Post Crisis 2008 The regression mentioned in chapter 3 has lack of implications since its only explains the overall data, and not the behavior of arbitrage between different periods. The author divides the analysis and also the regression into two comparative periods, which are prior and post global financial crisis of 2008. Through comparative analysis, the author then compares the characteristics of financial instruments through different regimes, such as bond spreads, CDS premiums, and equity price relationship with the credit market. 2. Sharp’s Bankruptcy Suprisingly in 12 November 2012, Sharp Corporation had declared bankruptcy, thus obtaining a bankrupt firm in our dataset. The availability of such dataset allows the author to analyze the behavior of financial indicators of a firm prior and post bankrupt.

4.1 Pre and Post Crisis There has been significant changes in the credit markets prior and post crisis. According to Lando et all (2010), the subprime crisis caused a dramatic widening of coporate bond spread and disapperance of bond liquidity. Before the crisis hit, the liquidity was small for investment grade, ranging from 1 basis point (bp) for AAA to 4bp for BBB. The contributions of liquidity remains 5bp for AAA during the crisis,


50

which indicates a flight-to-liquidity. Moreover, the liquidity of BBB grade bonds increased to 93 bp, and for speculative grade rose from 58 to 197 bp, especially in the Lehman default and Bear Stearn takeover by JP Morgan.

According to the authors analysis, the are several permanent changes in the bond and its derivative markets, which is indicated by the implied risk free rate of corporate bonds, and several risk-free rate benchmarks, such as the USD 1 Month Treasury Bill rate, the USD 3 Months Treasury Bill rate, the LIBOR overnight rate, the LIBOR 3 Month rate, the British 7 year swap rate, and the United States 7 year swap rate.


51

4.1.1 Second Order Arbitrage USD 1 Month Treasury Bill Rate Prior to the crisis, as seen in figure 4.1 there is a gap between the 2.5% and 4% implied risk free rate, where almost all of the range in has a value except between those implied riskfree rate values. According to the regression analysis (see Appendix) and as seen in the figure 4.1 and 4.2 compared, the implied riskfree rate narrowed with the USD 1 Month Treasury Bill rate. This implies that the relationship between the USD 1 Month Treasury bill rate increases after the crisis of 2008. Period

Beta Coefficient

R2

Prior Crisis

0.08

1.17%

Post Crisis

0.54

2.88%

Figure 4.1 Implied Risk Free Rate vs USD 1 Month Treasury Bills Rate Prior Crisis


52

Figure 4.2 Implied Risk Free Rate vs USD 1 Month Treasury Bills Rate Post Crisis

USD 3 Month Treasury Bill Rate Prior to the crisis, as seen in figure 4.3 there is alsona gap between the 2.5% and 4% implied risk free rate, where almost all of the range in has a value except between those implied riskfree rate values. This phenomena also occured in the USD 1 Month Treasury. According to the regression analysis (see Appendix) and as seen in the figure 4.3 and 4.4 compared, the implied riskfree rate narrowed with the USD 3 Month Treasury Bill rate. This implies that the relationship between the USD 3 Month Treasury bill rate increases after the crisis of 2008, an implication also found in the USD 1 Month Treasury bill with its expected implied risk free rate. Period

Beta Coefficient

R2

Prior Crisis

0.083

1.15%


53

Post Crisis

0.49

2.35%

Figure 4.3 Implied Risk Free Rate vs USD 3 Month Treasury Bills Rate Prior Crisis

Figure 4.4 Implied Risk Free Rate vs USD 3 Month Treasury Bills Rate Post Crisis


54

LIBOR Overnight Rate As seen in figure 4.5, there is also a gap that is seen in the previous observation between the implied risk free rate and the LIBOR overnight rate. According to the regression analysis (see Appendix) and as seen in the figure 4.5 and 4.6 compared, the implied riskfree rate narrowed with the LIBOR Overnight rate. The quantitative proof of this narrowing spreads are indicated by the increase of beta coefficient 0.02 to 0.32 which means an increase correlation. Also the same as in the previous observations, this implies that there are increase relationship between the two financial spreads after the 2008 global financial crisis. Period

Beta Coefficient

R2

Prior Crisis

0.02

0.27%

Post Crisis

0.32

3.03%

Figure 4.5 Implied Risk Free Rate vs LIBOR Overnight Rate Prior Crisis


55

Figure 4.6 Implied Risk Free Rate vs LIBOR Overnight Rate Post Crisis

LIBOR 3 Months Swap Rate


56

Another gap phenomenon is also seen between LIBOR 3 Month Swap rate and the implied risk free rate. According to the regression analysis (see Appendix) and as seen in the figure 4.7 and 4.8 compared, the implied riskfree rate narrowed with the LIBOR 3 Month rate. The quantitative proof of this narrowing spreads are indicated by the increase of beta coefficient 0.02 to 0.49 which means an increase correlation. Also the same as in the previous observations, this implies that there are increase relationship between the two financial spreads after the 2008 global financial crisis. Period

Beta Coefficient

R2

Prior Crisis

0.02

0.24%

Post Crisis

0.49

2.35%

Figure 4.7 Implied Risk Free Rate vs LIBOR 3 Month Swap Rate Prior Crisis

Figure 4.8 Implied Risk Free Rate vs LIBOR 3 Month Swap Rate Post Crisis


57

British 7 Year Swap Rate Figure 4.9 illustrates, there is also a gap that is seen in the previous observation between the implied risk free rate and the British 7 Year Swap rate, similar to other 4 obeservations before. According to the regression analysis (see Appendix) and as seen in the figure 4.9 and 4.10 compared, the implied also riskfree rate narrowed with the British 7 year swap rate. The quantitative proof of this narrowing spreads are indicated by the increase of beta coefficient 0.32 to 0.73 which means a strong increase in correlation. Also the same as in the previous observations, this implies that there are increase relationship between the two financial spreads after the 2008 global financial crisis. Period

Beta Coefficient

R2

Prior Crisis

0.32

1.17%

Post Crisis

0.73

9.22%


58

Figure 4.9 Implied Risk Free Rate vs British 7 Year Swap Rate Prior Crisis

Figure 4.10 Implied Risk Free Rate vs British 7 Year Swap Rate Post Crisis

United State 7 Year Swap Rate


59

Finally the last United State 7 year swap rate which is the benchmark rate for our analysis, also contemplates the same results with all previous observations. Correlations improved from 0.45 to 0.89, a strong significant improve in correlations. Thus indicates that after the crisis, the implied risk free rate narrowed to the USD 7 year swap rate. Period

Beta Coefficient

R2

Prior Crisis

0.45

2.26%

Post Crisis

0.89

9.79%

Figure 4.11 Implied Risk Free Rate vs USD 7 Year Swap Rate Prior Crisis

Figure 4.12 Implied Risk Free Rate vs USD 7 Year Swap Rate Post Crisis


60

4.1.2 Third Order Arbitrage The third order arbitrage consist of the comparison of the risk-neutral probability to default (RNPD) between implied by equity (fundamental) values, CDS premiums, and bond spreads. A strong positive relationship implies a strong arbitrage value between the financial instruments, thus a trader may profit when each financial instrument diverts from its arbitrage value. 4.1.2.1 Prior Crisis Prior to the crisis, figure 4.13 is the scatter plot between the RNPD of equities and the RNPD of the corporate bond portfolio RNPD. The figure implies that the RNPD between equities and corporate bond portfolio are highly dispersed. Our regression analysis indicates that there is small predictability between the RNPD of Equity to the RNPD of Corporate Bond Portfolio, which is 0.34%. Figure 4.13 RNPD Equity vs RNPD Corporate Bond Portfolio Prior Crisis


61

There is also small predictabilty between the RNPD of equity and the RNPD implied by the CDS premium. Figure 4.14 RNPD Equity vs RNPD CDS Premium Prior Crisis


62

4.1.2.2 Post Crisis Post crisis of 2008, the author saw a change in dispersion of the dataset. Each RNPD of the corporate bond portfolio and the RNPD of the CDS premium is highly concentrated between the value of below 15%. The sudden surge in RNPD of corporate bond portfolio and RNPD of CDS premiums is the causality of a bankruptcy announcement of Sharp Corporation, which we will discuss in detail in 4.2 Sharp Bankruptcy. Despite this concentration, our analysis indicates a higher correlation of 0.43 and 1.23 for the RNPD of corporate bond portfolio and the RNPD of the CDS premium respectedly. Figure 4.15 RNPD Equity vs RNPD Corporate Bond Portfolio Post Crisis

Figure 4.16 RNPD Equity vs RNPD CDS Premium Post Crisis


63


64

4.2 Special Case: Sharp’s Bankruptcy At November 12th, 2012 the CEO of Sharp declared that the company is facing liquidity problems after a $4.9 billion dollar loss in its books. This jeopardized the market of Sharp’s equity, bond, and credit derivative. Bond yields of the corporation increased sharply to a high of 135% in the mid Desember 2012, the CDS premium of the corporation also increase dramatically to over 1000 basis points, and its market value also tanked from a share price of 600 Yen on the beginning of 2012, to a low value of 50 Yen a share. This event shows a close linkage between the equity, bond, and the credit derivative of the company. Thus, this should be an interesting object of research. Figure 4.17 Sharp Corp Bond Yield between 1 January 2009 and 28 Desember 2012

Sharp’s corporate bond yield is the cost in percentage of the riskiness of a bond that investors’ imply through the price of the bond. The price of the bond may fluctuate


65

by the change in supply and demand of bonds, thus also changing the yield of the bond. Figure 4.18 Sharp CDS Premium on Bonds between 1 January 2009 and 28 Desember 2012

Sharp’s CDS is the protection rate demanded by a third party insuer for the risk of default of Sharp’s bond. This protection rate is measured in basis points in reference to the par value of the bond. Figure 4.19 Sharp Equity Price (6753 JP Equity) between 1 January 2009 and 28 Desember 2012


66

Sharp’s equity price is measured in Yen and is traded at the Tokyo Stock Exchange under the famous Nikkei 225 average. 4.2.1 Prior Bankrupt Now we assess the behavior of Sharp’s bond yield, CDS premium, and also equity price in the event of bankruptcy. This could be reflected by the change in yield, CDS premium and also equity respected to each other. Figure 4.20 Return in Sharp Equity Price (6753 JP Equity) and Changes in Bond Yields Prior Crisis


67

According to our correlation analysis (see Appendix), the correlation between the return of equity with the change in yield is 0.06, which indicates a positif but weak correlation. Thus, if there is a 1% change in yield, assuming any other external variables are fixed, the change in equity may be 6.47%. Figure 4.21 Sharp Equity Price (6753 JP Equity) and Bond Yields of Sharp Corporation Prior Crisis


68

If we see the scatter plot of Sharp’s yield and its equity price before bankruptcy, we will see a scattered data with a concentration between the value of 600-1000 Yen for equity prices, and 0.25%-0.4% for its bond yields. We also consider the senstivity of equity prices to changes in CDS premiums. Through a scatter plot, we can see that there is a highly concentration of value between -2% - 2% changes in CDS premium and -1% - 1% changes in equity price. Our regression analysis shows that there is a correlation of -0.312 between changes in equity and changes in CDS premium. This indicates that the CDS premium and equity prices changes relationship are inversed. Figure 4.22 Changes in CDS Premium and Return of Equity of Sharp Corporation Prior Crisis


69

Figure 4.23 CDS Premium and Equity of Sharp Corporation Prior Crisis

This is also confirmed by the scatter plot of CDS premium and equity prices which has a negative slope downwards. The smaller the equity price the higher the CDS premium protection.


70

Figure 4.24 Changes in Yield and Changes in CDS Premium of Sharp Corporation Prior Crisis Pre default, Sharp sensitivity of yield changes to changes in CDS premium is 0.06, indicating a positive weak correlation. The values of changes in CDS premium and the changes in yield are concentrated between -20% - 20% and -15% - 15%.

Figure 4.25 Yield of Corporate Bond and CDS Premium of Sharp Corporation Prior Crisis


71

As seen above prior to bankruptcy, Sharp’s CDS premium and yield has a non-linear shaped curve while there is a cluster of dataset of CDS premium of 50 bps to a value of 0.25% - 1.25% of bond yield value. Figure 4.26 Risk-Neutral Probability to Default Implied by the Equity and CDS premium of Sharp Corporation Prior Crisis From the scatter plot below, dataset values are highly concentrated between 0 - 2.5% of RNPD of CDSs, while the RNPD of the equities are scattered. Our linear regression analysis indicates a low goodness of fit to the data which is 4.20%.


72

Figure 4.27 Risk-Neutral Probability to Default Implied by the Equity and Bond Spreads of Sharp Corporation Prior Crisis


73

The next linked values that is the interest of behaviour before bankruptcy is between RNPD of bond spreads with RNPD of equities. Through another regression analysis, there is a 16.96% goodness of fit with the data, adjusted to errors. 4.2.2 Post Bankrupt Since March 2008 to March 2012, company’s revenues had decreased by 28%. November 1st 2012, the company announced a statement that it is in such circumstances in which it is in doubt about the assumption of going concern. The assumption of going concern is an underlying assumption of financial statements and accounting that a company can operate within 12 months without any threat of liquidation. Figure 4.28 Return in Sharp Equity Price (6753 JP Equity) and Changes in Bond Yields Post Crisis


74

The scatter plot of equity prices returns and the changes in corporate yields shows that there is a mere difference with prior to default. The correlation prior to default was 0.06 while post crisis the correlation changed to -0.49, a significant change in correlations. This implies that there in Sharp’s bankruptcy case that a small increase in corporate bond yield changes, actually changes the return of equity prices in a significant amount. Figure 4.29 Sharp Equity Price (6753 JP Equity) and Bond Yields of Sharp Corporation Post Crisis

Compared with prior crisis, the dataset of Sharp bond yields and its equity prices imply that a high bond yield is followed by a low equity price. Although this could not reach us to a conclusion directly that high bond yields will ensure a low equity price value. Figure 4.30 Changes in CDS Premium and Return of Equity of Sharp Corporation Post Crisis


75

The concentration of changes in CDS premium to changes in equity prices are much dispersed after default, which a higher value of outlier datasets. There is an observation where 60% changes in CDS premium is followed by a 30% drop in equity price. The correlation between the changes in CDS premium and changes in equity prices -0.39, indicating a negative significant correlation. The data of CDS preimum and equity prices also confirms this. The concentration of low CDS premiums and high equity prices (a concentration of data in the left side of the graph) before default, changes into a lower equity prices while there is high CDS premiums. Figure 4.31 CDS Premium and Equity of Sharp Corporation Post Crisis


76

Prior to default, the correlation between the changes in yield with the changes in CDS premium was 0.06, while after event of default, the correlation spurred to 0.55 which indicates a high positive correlation. This implies that in case of bankrupt of Sharp, shift in the value of corporate bond yield will change CDS premiums by a high amount. Thus implying derivative traders compensation to hold Sharp’s risky bonds.

Figure 4.32 Changes in Yield and Changes in CDS Premium of Sharp Corporation Post Crisis


77

Figure 4.33 Yield of Corporate Bond and CDS Premium of Sharp Corporation Post Crisis


78

Prior to default, the curve of the plot between thte CDS premium and the yield values of the bonds of the corporation was non-linear. Suddenly, after default the plot was positively linear. The risk-neutral probability to default problem is one of the central findings of these research. Our method of determining the RNPD from equities are from a method proposed in Fitch’s Equity Implied Rating. A bad predictibility results of RNPD’s of equities towards RNPD’s of CDS premium and bond spreads implies that there may be mistakes in the model used by Fitch. Our resutls confirms this suspicion, since we obtained a very low goodness of fit, 2.33% between RNPD of equities towards RNPD of CDSs. This means that there is low predictability value of RNPD of equities for RNPD of CDSs, which also cast doubt on the implemented Fitch Equity Implied Rating. Figure 4.34 Risk-Neutral Probability to Default Implied by the Equity and CDS premium of Sharp Corporation Post Crisis


79

Figure 4.35 Risk-Neutral Probability to Default Implied by the Equity and Bond Spreads of Sharp Corporation Post Crisis For the relationship between RNPDs of Equities and bonds there is also a positive but weak goodness of fit of 3.05%. Since as seen below, the RNPD implied by the bond spread has jumpt to high levels while the RNPD of equity is still under 2%. Implying that there may be errors in the Fitch model that does not capture this default effect of sharp.


80

CHAPTER 5 5.1 Conclusion There are several conclusions that could be made from my research. First, that there is a strong positive arbitrage relationship between riskfree bond yields, bond yields, and credit default swap premium in the Asian equity, bond, and derivative market. Adding that to adjust for macroeocnomic and microeocnomic phenomenas such as recessions and bankruptcy, my finding confirms the distorition effects from those conditions. Second, that here is a positive relationship between the Risk-Neutral Probability to Default implied by bond spreads, credit default swap premium, and also equity (accounting) values but with a weak predictability. Thus, implying that there are the Equity Implied Rating of Fitch could not maintain consistency in predicting future values of Risk-Neutral Probability to Default.

5.2 Implication of Research Several implications of this research are 

The benchmark risk free rate that reflects most of the derivative trades is the USD 7 year swap rate. This implies that the benchmark risk free rate to be used in academic research and also practical trading that will have the lowest error rate is the USD 7 year swap rate.



The Equity Implied Model of Fitch, and also other rating agencies may be flawed and cannot ensure long-term predictability of bankruptcy. Thus, it must not be a base to predict firms into bankrupt because of the high error rate and the lowest goodness of fit.

5.3 Suggestions to Further Research The author suggest several improvements should any other researchers reproduce this research.


81



The test of other risk free rates such as other USD bond maturities, such as the 10 year Treasury bond and the 30 Year Treasury Bond.



Adjustment should be made on other bonds that trade in a different nation, even if is traded in USD nominal.



Adding other measures of default risk such as Moody’s KMV, that may reproduce a better comparison of bankruptcy models.


82

References Anonymous. 2012. The Corporate Bond Credit Spread Puzzle. FRBSF Economic Research. Brockman, Paul. Turtle, H.J. A barrier option Framework for Corporate Security Valuation. Journal of Financial Economics 67 (2003) 511–529 Duffie, Darell. Credit Swap Valuation. Financial Analyst Journal, February 1999. Hull, John and White, Allan. Predescu, Mirela. Bond Prices, Default Probabilities and Risk Premiums. 2000 Hull, John and White, Allan. Predescu, Mirela. The relationship between credit default swap spreads, bond yields, and credit rating announcements. Hull, John and White, Allan. Valuing Credit Default Swaps I: No Counterparty Default Risk. 2000. Hull, John and White, Allan. 2000. Valuing Credit Default Swaps II: Modelling Default Correlations. Liu, Bo. Kocagil, Ahmet. E. Gupton, Greg. M. Fitch Equity Implied Rating and Probability of Default Model. Quantitative Research Special Report. Merton, Robert. On Pricing of Corporate Debt: The Risk Structures of Interest Rate . The Journal of Finance, Vol. 29, No. 2, Papers and Proceedings of the ThirtySecond Annual Meeting of the American Finance Association, New York, New York, December 28-30, 1973. (May, 1974), pp. 449-470


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Murthy, Shashidhar. Market-Implied Risk-Neutral Probabilities, Actual Probabilities, Credit Risk and News. Financial and Control, Indian Institute Management Bangalore. 2011. Sundaram, K. Rangarajan. Merton/KMV Approach to Pricing Credit Risk. 2001. Taleb, N.N. Dynamic Hedging: Managing Vanilla and Exotic Options. John Wiley and Sons. New York. 1997.


84

Appendix List of Companies Company Name

CDS Ticker

Index

Equity Ticker

Bond Ticker

1 Woodside Petroleum Ltd

WPL AU EQUITY

USQ98229AC30 CORP

WPLAU CDS USD SR 5Y

ASX

2 Wesfarmers Ltd

WES AU EQUITY

XS0493491657 CORP

WESAU LTD CDS USD SR 5Y

ASX

3 Westpac Banking Corp

WBC AU EQUITY

XS0453410978 CORP

WESTPAC CDS USD SR 5Y

ASX

4 Telstra Corp Ltd

TLS AU EQUITY

XS0196578255 CORP

TLSAU CDS USD SR 5Y

ASX

5 Banking Group Ltd

ANZ AU EQUITY

XS0493543986 CORP

ANZ CDS USD SR 5Y

ASX

6 Rio Tinto Ltd

RIO AU EQUITY

US767201AC07 CORP

RIOLNTD CDS USD SR 5Y

ASX

7 QBE Insurance Group Ltd

QBE AU EQUITY

XS0454936013 CORP

QBEAU CDS USD SR 5Y

ASX

8 Qantas Airways Ltd

QAN AU EQUITY

USQ77974BA24 CORP

QANAU CDS USD SR 5Y

ASX

9 National Australia Bank Ltd

NAB AU EQUITY

XS0469028582 CORP

NAB CDS USD SR 5Y

ASX

LLC AU EQUITY

XS0269774104 CORP

LLCAU CDS USD SR 5Y

ASX

Australia & New Zealand

10 Lend Lease Group

CWO AU 11 SingTel Optus Pty Ltd

EQUITY

XS0457559838 CORP

SINGTEL CDS USD SR 5Y

ASX

12 Coca-Cola Amatil Ltd

CCL AU EQUITY

XS0262643751 CORP

CCLAU CDS USD SR 5Y

ASX

13 Australia

CBA AU EQUITY

XS0577454878 CORP

CBAAU CDS USD SR 5Y

ASX

14 BHP Billiton Ltd

BHP AU EQUITY

US055450AG50 CORP

BHPB CDS USD SR 5Y

ASX

15 Amcor Ltd/Australia

AMC AU EQUITY

XS0604462704 CORP

AMCAU CDS USD SR 5Y

ASX

16 Jemena Ltd

AGL AU EQUITY

USQ09680AR24 CORP

AGLAU CDS USD SR 5Y

ASX

US867232AB66 CORP

SUNAU CDS USD SR 5Y

ASX

USQ97012AB67 CORP

WESTFIELD CDS USD SR 5Y

ASX

AMP GROUP CDS USD SR 5Y

ASX

Commonwealth Bank of

8228789Z AU 17 Suncorp-Metway Ltd

EQUITY 2785254Z AU

18 Westfield Management Ltd

EQUITY 1415Z AU

19 AMP Group Holdings Ltd

EQUITY

AU3CB0171312 CORP

20 GPT RE Ltd

0277786D AU

AU300GPTM218 CORP GPT CDS USD SR 5Y


ASX

85

EQUITY 21 Vedanta Resources PLC

VED LN EQUITY

US92241TAD46 CORP

VEDLN CDS USD SR 5Y

FTSE

XS0458057352 CORP

SBI CDS USD SR 5Y

FTSE

920872Z LN 22 State Bank of India/London

EQUITY 8144729Z LN

23 JTI UK Finance PLC (EUR)

EQUITY

XS0269190533 CORP

JTI CDS EUR SR 5Y

FTSE

24 PCCW-HKT Telephone Ltd

PCCZ HK EQUITY

USG69552AA80 CORP

PCCW CDS USD SR 5Y

HANSENG

25 Hongkong Land Co Ltd

HLCZ HK EQUITY

XS0191426807 CORP

HKLSP CDS USD SR 5Y

HANSENG

26 CNOOC Ltd

883 HK EQUITY

US12615TAB44 CORP

AWILCO CDS USD SR 5Y

HANSENG

27 MTR Corp Ltd

66 HK EQUITY

XS0184198157 CORP

MTRC CDS USD SR 5Y

HANSENG

28 Wharf Holdings Ltd

4 HK EQUITY

XS0329230469 CORP

WHARF CDS USD SR 5Y

HANSENG

29 Swire Pacific Ltd

19 HK EQUITY

XS0247747081 CORP

SWIRE CDS USD SR 5Y

HANSENG

30 Sun Hung Kai Properties Ltd

16 HK EQUITY

XS0290534212 CORP

SUNHUN CDS USD SR 5Y

HANSENG

31 Hutchison Whampoa Ltd

13 HK EQUITY

USG4672UAA37 CORP

HUWHY CDS USD SR 5Y

HANSENG

32 Kazakhstan JSC

BRKZ KZ EQUITY

XS0179958805 CORP

DBKAZ CDS USD SR 5Y

KAZAKSHTAN

33 Tenaga Nasional Bhd

TNB MK EQUITY

USY85859AB54 CORP

TNBMK CDS USD SR 5Y

KLCI

34 Telekom Malaysia Bhd

T MK EQUITY

XS0200959384 CORP

TELMAL CDS USD SR 5Y

KLCI

35 Petroliam Nasional Bhd

PET MK EQUITY

USY68856AB20 CORP

PETMK CDS USD SR 5Y

KLCI

XS0200561180 CORP

GENTMK CDS USD SR 5Y

KLCI

USY5275KAP04 CORP

GSCCOR CDS USD SR 5Y

KOSPI

US50049MAA71 CORP

CITNAT CDS USD SR 5Y

KOSPI

USY3994MAN66 CORP

INDKOR CDS USD SR 5Y

KOSPI

Development Bank of

GENT MK 36 Genting Bhd

EQUITY GSCALZ KS

37 GS Caltex Corp

EQUITY 060000 KS

38 Kookmin Bank

EQUITY 024110 KS

39 Industrial Bank of Korea

EQUITY 017670 KS

40 SK Telecom Co Ltd

EQUITY

USY4935NAS37 CORP

SKM CDS USD SR 5Y

KOSPI

41 Korea Electric Power Corp

015760 KS

USY48406BA27 CORP

KORELE CDS USD SR 5Y

KOSPI


86

EQUITY 005490 KS 42 POSCO

EQUITY

XS0263366865 CORP

POHANG CDS USD SR 5Y

KOSPI

XS0216764620 CORP

HYNMTR CDS USD SR 5Y

KOSPI

005380 KS 43 Hyundai Motor Co

EQUITY 002860 KS

44 Hana Bank

EQUITY

US40963MAB81 CORP

HANABK CDS USD SR 5Y

KOSPI

45 Woori Bank Co Ltd

0003 KS EQUITY

US98105GAE26 CORP

WOORIB CDS USD SR 5Y

KOSPI

46 Nomura Securities Co Ltd

NCLZ JP EQUITY

XS0451558380 CORP

NOMURASE CDS JPY SR 5Y

NIKKEI

Tokyo Metropolitan

MOTZ JP

47 Government

EQUITY

XS0235389201 CORP

TOKYO CDS JPY SR 5Y

NIKKEI

48 Mizuho Corporate Bank Ltd

MIZC JP EQUITY

JP388575B486 CORP

MIZUHOB CDS JPY SR 5Y

NIKKEI

JP203000A647 CORP

IWATE CDS JPY SR 5Y

NIKKEI

EQUITY

JP367000A5B7 CORP

C A CDS JPY SR 5Y

NIKKEI

9509 JP EQUITY

JP385020A025 CORP

HOKKEL CDS JPY SR 5Y

NIKKEI

9508 JP EQUITY

JP324640A479 CORP

KYUSEL CDS JPY SR 5Y

NIKKEI

9503 JP EQUITY

JP322860BV49 CORP

KANSEL CDS JPY SR 5Y

NIKKEI

54 Inc

9502 JP EQUITY

JP352660A563 CORP

CHUBEP CDS JPY SR 5Y

NIKKEI

55 eAccess Ltd

9427 JP EQUITY

XS0605958288 CORP

EACCES CDS JPY SR 5Y

NIKKEI

56 All Nippon Airways Co Ltd

9202 JP EQUITY

JP342980A436 CORP

ANAIR CDS JPY SR 5Y

NIKKEI

57 Nippon Yusen KK

9101 JP EQUITY

JP375300A460 CORP

NIPYU CDS JPY SR 5Y

NIKKEI

58 Nippon Express Co Ltd

9062 JP EQUITY

JP372940A813 CORP

NIPEXP CDS JPY SR 5Y

NIKKEI

59 Kintetsu Corp

9041 JP EQUITY

JP326080B649 CORP

KINKI CDS JPY SR 5Y

NIKKEI

60 East Japan Railway Co

9020 JP EQUITY

JP378360B527 CORP

EJRAIL CDS JPY SR 5Y

NIKKEI

IWATEZ JP 49 Iwate Prefecture Citigroup Japan Holdings 50 Corp

EQUITY CTGJPZ JP

Hokkaido Electric Power Co 51 Inc Kyushu Electric Power Co 52 Inc Kansai Electric Power Co 53 Inc/The Chubu Electric Power Co


87

Sumitomo Realty & 61 Development Co Ltd

8830 JP EQUITY

JP340900A790 CORP

SUMIRD CDS JPY SR 5Y

NIKKEI

62 Fire Insurance Co Ltd

8751 JP EQUITY

JP357260C092 CORP

TOMARI CDS JPY SR 5Y

NIKKEI

63 Nomura Holdings Inc

8604 JP EQUITY

US65535HAB50 CORP

NOMURAH CDS JPY SR 5Y

NIKKEI

64 Daiwa Securities Group Inc

8601 JP EQUITY

JP350220B624 CORP

DAIWA CDS JPY SR 5Y

NIKKEI

65 ORIX Corp

8591 JP EQUITY

JP320045A525 CORP

ORIX CDS JPY SR 5Y

NIKKEI

66 Hitachi Capital Corp

8586 JP EQUITY

XS0495986530 CORP

HITCAP CDS JPY SR 5Y

NIKKEI

67 Jaccs Co Ltd

8584 JP EQUITY

JP338860B590 CORP

JACCS CDS JPY SR 5Y

NIKKEI

68 Co Ltd

8574 JP EQUITY

JP383375A363 CORP

PROMISE CDS JPY SR 5Y

NIKKEI

69 Acom Co Ltd

8572 JP EQUITY

JP310860A743 CORP

ACOMCO CDS JPY SR 5Y

NIKKEI

70 Resona Bank Ltd (USD)

8319 JP EQUITY

JP350060A626 CORP

RESONA CDS USD SR 5Y

NIKKEI

8318 JP EQUITY

USJ7771KNY93 CORP

SMBC CDS JPY SR 5Y

NIKKEI

72 UFJ Ltd

8315 JP EQUITY

JP358920E2A8 CORP

BOTM CDS JPY SR 5Y

NIKKEI

73 Shinsei Bank Ltd

8303 JP EQUITY

JP372900B534 CORP

SHNBK CDS JPY SR 5Y

NIKKEI

74 Aeon Co Ltd

8267 JP EQUITY

JP338820B560 CORP

JUSCO CDS JPY SR 5Y

NIKKEI

75 Takashimaya Co Ltd

8233 JP EQUITY

JP345600A775 CORP

TAKASH CDS JPY SR 5Y

NIKKEI

76 Toyota Tsusho Corp

8015 JP EQUITY

JP363500B665 CORP

TOYOTS CDS JPY SR 5Y

NIKKEI

77 ITOCHU Corp

8001 JP EQUITY

JP314360A6A3 CORP

CITOH CDS JPY SR 5Y

NIKKEI

78 Ricoh Co Ltd

7752 JP EQUITY

JP397340AA62 CORP

RICOH CO CDS JPY SR 5Y

NIKKEI

79 Mazda Motor Corp

7261 JP EQUITY

JP386840A7A9 CORP

MAZDA CDS JPY SR 5Y

NIKKEI

80 Nissan Motor Co Ltd

7201 JP EQUITY

JP367240B763 CORP

NSANY CDS JPY SR 5Y

NIKKEI

81 IHI Corp

7013 JP EQUITY

JP313480A762 CORP

ISHHAR CDS JPY SR 5Y

NIKKEI

82 Sanyo Electric Co Ltd

6764 JP EQUITY

JP334060B484 CORP

MATSEL B CDS JPY SR 5Y

NIKKEI

83 Sony Corp

6758 JP EQUITY

JP343500C593 CORP

SNE CDS JPY SR 5Y

NIKKEI

84 Sharp Corp/Japan

6753 JP EQUITY

JP335960B930 CORP

SHARP CDS JPY SR 5Y

NIKKEI

85 Seiko Epson Corp

6724 JP EQUITY

JP341475B5B7 CORP

SEIKOE CDS JPY SR 5Y

NIKKEI

Tokio Marine & Nichido

SMBC Consumer Finance

Sumitomo Mitsui Banking 71 Corp Bank of Tokyo-Mitsubishi


88

86 Fujitsu Ltd

6702 JP EQUITY

JP381800AV56 CORP

FUJITS CDS JPY SR 5Y

NIKKEI

87 NEC Corp

6701 JP EQUITY

JP373300B890 CORP

NECORP CDS JPY SR 5Y

NIKKEI

88 Toshiba Corp

6502 JP EQUITY

JP359220C6B4 CORP

TOSH CDS JPY SR 5Y

NIKKEI

89 Hitachi Ltd

6501 JP EQUITY

JP378860B583 CORP

HITACHI CDS JPY SR 5Y

NIKKEI

90 Mitsubishi Materials Corp

5711 JP EQUITY

JP390300A784 CORP

MITMAT CDS JPY SR 5Y

NIKKEI

91 Nisshin Steel Co Ltd

5407 JP EQUITY

JP367600A950 CORP

NISSTL CDS JPY SR 5Y

NIKKEI

92 Kobe Steel Ltd

5406 JP EQUITY

JP328980B721 CORP

KOBSTL CDS JPY SR 5Y

NIKKEI

93 JFE Steel Corp

5403 JP EQUITY

JP338603A976 CORP

JFE STEEL CDS JPY SR 5Y

NIKKEI

94 Metal Corp

5401 JP EQUITY

JP338100AT99 CORP

NIPPON STEEL CDS JPY SR 5Y NIKKEI

95 Taiheiyo Cement Corp

5233 JP EQUITY

JP344902B543 CORP

ONODA CDS JPY SR 5Y

NIKKEI

96 Oriental Land Co Ltd/Japan

4661 JP EQUITY

JP319890A816 CORP

ORILND CDS JPY SR 5Y

NIKKEI

97 Mitsubishi Chemical Corp

4010 JP EQUITY

JP389580A446 CORP

MIT CHE CDS JPY SR 5Y

NIKKEI

98 Sumitomo Chemical Co Ltd

4005 JP EQUITY

JP340140A462 CORP

SUMICH CDS JPY SR 5Y

NIKKEI

99 Nippon Paper Group Inc

3893 JP EQUITY

JP375430A754 CORP

NUNPC GRP CDS JPY SR 5Y

NIKKEI

100 Teijin Ltd

3401 JP EQUITY

JP354400B859 CORP

TEIJIN CDS JPY SR 5Y

NIKKEI

101 Kirin Holdings Co Ltd

2503 JP EQUITY

JP325800C839 CORP

KIRIN HLD CDS JPY SR 5Y

NIKKEI

102 Ltd

2264 JP EQUITY

JP392680A787 CORP

MOMILK CDS JPY SR 5Y

NIKKEI

103 Kajima Corp

1812 JP EQUITY

JP321020ABC8 CORP

KAJIMA CDS JPY SR 5Y

NIKKEI

104 Shimizu Corp

1803 JP EQUITY

JP335880AAC1 CORP

SHIMIZ CDS JPY SR 5Y

NIKKEI

105 Obayashi Corp

1802 JP EQUITY

JP319000B364 CORP

OBACRP CDS JPY SR 5Y

NIKKEI

106 Taisei Corp

1801 JP EQUITY

JP344360A751 CORP

TAISEI CDS JPY SR 5Y

NIKKEI

107 Zealand Ltd

TEL NZ EQUITY

NZTCND0027S1 CORP

TELNZ CDS USD SR 5Y

NZ

108 Reliance Industries Ltd

RIL IN EQUITY

US759470AC16 CORP

RILIN CDS USD SR 5Y

SENSEX

109 IDBI Bank Ltd

IDBI IN EQUITY

XS0530173987 CORP

IDBI CDS USD SR 5Y

SENSEX

Nippon Steel & Sumitomo

Morinaga Milk Industry Co

Telecom Corp of New

ICICIBC IN 110 ICICI Bank Ltd

EQUITY

USM5314BAE13 CORP

ICICI CDS USD SR 5Y

SENSEX

111 Bank of India

BOI IN EQUITY

XS0498932721 CORP

BOIIN CDS USD SR 5Y

SENSEX


89

1005Z IN 112 Export-Import Bank of India

EQUITY

XS0455479492 CORP

EXIMBK CDS USD SR 5Y

SENSEX

SDBC CDS USD SR 5Y

SENZEN

China Development Bank 113 Corp Export-Import Bank of

SDBZ CH EQUITY US16937MAB19 CORP EIBCZ CH

114 China

EQUITY

USY23862AD09 CORP

EXIMCH CDS USD SR 5Y

SENZEN

115 PTT PCL

PTT TB EQUITY

US69367CAA36 CORP

PTTTB CDS USD SR 5Y

SET

116 Telecommunications Ltd

ST SP EQUITY

US82929RAC07 CORP

STSP A CDS USD SR 5Y

STI

117 Noble Group Ltd

NOBL SP EQUITY USG6542TAE13 CORP

NOBLSP CDS USD SR 5Y

STI

STI

Singapore

263447Z SP 118 SP PowerAssets Ltd

EQUITY

XS0179020085 CORP

SPPOWER CDS USD SR 5Y

119 Foster's Group Pty Ltd

FBW GR EQUITY

USQ3748TAB54 CORP

FOSTERS CDS USD SR 5Y

XS0223450445 CORP

WANHAI CDS USD SR 5Y

Wan Hai Lines Singapore 120 Pte Ltd

0534162D TT EQUITY


90

VBA Code to Obtain the Implied Volatility Function dOne(Stock, Exercise, time, Interest, Volatility) dOne = ((Log(Stock / Exercise)) + ((Interest + ((Volatility * Volatility) / 2)) * time)) / (Volatility * Sqr(time)) End Function Function dTwo(Stock, Exercise, time, Interest, Volatility) dTwo = dOne(Stock, Exercise, time, Interest, Volatility) - (Volatility * Sqr(time)) End Function Function BSCall(Stock, Exercise, time, Interest, Volatility) BSCall = (Stock * ND(dOne(Stock, Exercise, time, Interest, Volatility))) (Exercise * Exp(-time * Interest) * ND(dTwo(Stock, Exercise, time, Interest, Volatility))) End Function Function BSPut(Stock, Exercise, time, Interest, Volatility) BSPut = BSCall(Stock, Exercise, time, Interest, Volatility) + Exercise * Exp(-Interest * time) - Stock End Function Function ND(z As Double) ND = Application.WorksheetFunction.NormSDist(z) End Function Function ImpliedVolatility(Stock, Exercise, time, Interest, target) High = 1 Low = 0 Do While (High - Low) > 0.0001 If BSCall(Stock, Exercise, time, Interest, (High + Low) / 2) > target Then High = (High + Low) / 2 Else: Low = (High + Low) / 2 End If Loop ImpliedVolatility = (High + Low) / 2 End Function Function Square(number) Square = number * number End Function Function power(number, powered)


91

power = Application.WorksheetFunction.power(number, powered) End Function Function xUp(assetval, strike, riskfree, vol, maturity, time) numerator = Log(assetval) - Log(strike) + (((riskfree + (0.5 * Square(vol))) * (maturity - time))) denominator = vol * Sqr(maturity - time) xUp = numerator / denominator End Function Function xDown(assetval, strike, riskfree, vol, maturity, time) numerator = Log(assetval) - Log(strike) + (((riskfree - (0.5 * Square(vol))) * (maturity - time))) denominator = vol * Sqr(maturity - time) xDown = numerator / denominator End Function Function yUp(barrier, assetval, strike, riskfree, vol, maturity, time) numerator = (2 * Log(barrier)) - Log(assetval) - Log(strike) + (((riskfree + (0.5 * Square(vol))) * (maturity - time))) denominator = vol * Sqr(maturity - time) yUp = numerator / denominator End Function Function yDown(barrier, assetval, strike, riskfree, vol, maturity, time) numerator = (2 * Log(barrier)) - Log(assetval) - Log(strike) + (((riskfree + (0.5 * Square(vol))) * (maturity - time))) denominator = vol * Sqr(maturity - time) yDown = numerator / denominator End Function Function EquityMV(barrier, strike, assetval, riskfree, vol, maturity, time) bracket1 = ND(xUp(assetval, strike, riskfree, vol, maturity, time)) ((power((barrier / assetval), (2 * riskfree) / (Square(vol) + 1))) * ND(yUp(barrier, assetval, strike, riskfree, vol, maturity, time))) bracket2 = ND(xDown(assetval, strike, riskfree, vol, maturity, time)) ((power((barrier / assetval), (((2 * riskfree) / (Square(vol))) + 1)) * ND(yDown(barrier, assetval, strike, riskfree, vol, maturity, time)))) EquityMV = (assetval * bracket1) - (Exp(-riskfree * (maturity - time)) * strike * bracket2) End Function Function DebtMV(barrier, strike, assetval, riskfree, vol, maturity, time) bracket1 = ND(-xUp(assetval, strike, riskfree, vol, maturity, time)) +


92

((power((barrier / assetval), (2 * riskfree) / (Square(vol) + 1))) * ND(yUp(barrier, assetval, strike, riskfree, vol, maturity, time))) bracket2 = ND(xDown(assetval, strike, riskfree, vol, maturity, time)) ((power((barrier / assetval), (((2 * riskfree) / (Square(vol))) + 1)) * ND(yDown(barrier, assetval, strike, riskfree, vol, maturity, time)))) DebtMV = (assetval * bracket1) + (Exp(-riskfree * (maturity - time)) * strike * bracket2) End Function Function ImpliedVolDebtBarrier(barrier, strike, assetval, riskfree, maturity, time, target) High = 1 Low = 0 Do While (High - Low) > 0.0001 If DebtMV(barrier, strike, assetval, riskfree, (High + Low) / 2, maturity, time) > target Then High = (High + Low) / 2 Else: Low = (High + Low) / 2 End If Loop ImpliedVolDebtBarrier = (High + Low) / 2 End Function Function ImpliedVolEquityBarrier(barrier, strike, assetval, riskfree, maturity, time, target) High = 1 Low = 0 Do While (High - Low) > 0.0001 If EquityMV(barrier, strike, assetval, riskfree, (High + Low) / 2, maturity, time) > target Then High = (High + Low) / 2 Else: Low = (High + Low) / 2 End If Loop ImpliedVolEquityBarrier = (High + Low) / 2 End Function Function ActualPD(barrier, assetval, riskfree, strike, maturity, time, vol, debtval) ActualPD = (ND(-xDown(assetval, strike, riskfree, vol, maturity, time))) + (power((barrier / assetval), (2 * riskfree / Square(vol))) * ND(yDown(barrier, assetval, strike, riskfree, vol, maturity, time))) End Function


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Function ImpliedVolBarrier(barrier, strike, assetval, riskfree, maturity, time, totalasset) High = 1 Low = 0 Do While (High - Low) > 0.0001 If (EquityMV(barrier, strike, assetval, riskfree, (High + Low) / 2, maturity, time) + DebtMV(barrier, strike, assetval, riskfree, (High + Low) / 2, maturity, time)) > totalasset Then High = (High + Low) / 2 Else: Low = (High + Low) / 2 End If Loop ImpliedVolEquityBarrier = (High + Low) / 2 End Function


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STATA Panel Data Analysis Results Overall Data Analysis Second Order Arbitrage summarize referenceobligation cdspreimum impliedriskfreerate libor3mswaprate liborovernightrate

usd3mtbills

usd1mtbills

usd7yearswaprateminus10bps

bp7yearswaprateminus10bps


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Second Order Arbitrage


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97


98

Adjustment for Crisis and Bankruptcy Status


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Third Order Arbitrage


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With Data Sharp Bankruptcy

Without Sharp Bankruptcy


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With Sharp Bankruptcy


102

Without Sharp Bankruptcy

Prior dan Post Crisis Analysis Second Order Arbitrage Analysis Prior Crisis


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Post Crisis


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Third Order Arbitrage Analysis Prior Crisis


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Post Crisis


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Sharp Bankruptcy Prior Bankrupt


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Summary


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Post Default


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Summary
