Jul 14

FRM 2008 Episode #9: Credit C (Credit Derivatives)

by David Harper, CFA, FRM, CIPM

FRM |

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In this issue

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About Episode #9 (Credit Risk: Credit Derivatives)

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Please find links to earlier episodes (#1 to #8) at the end of this note. We are following the sequence of GARP's 2008 FRM Study Guide.

This latest episode (Credit C) concludes the Credit Risk discipline. This episode has a 100+ page PowerPoint you can download and comes in two parts (1 hour + 45 minutes). This episode reviews credit derivatives. As usual I would like to offer a few tips in regard to this episode.

Structural model

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The structural approach is thematic in the credit risk discipline of the FRM. Structural refers to the balance sheet structure of the firm or bank: loan assets on the left-hand side of the balance sheet are funded by capital sources (senior debt, subordinated debt, equity) on the right-hand side.

The Stulz reading (Chapter 18) focuses on this structural view: the value of these three capital classes, on the right hand side, are a function of asset values on the left hand side. Specifically, in a contingent claim approach:

  • Equity is a call option on the firm's assets. If shareholders pay off the debt (i.e., exercise their option where the strike price is the face value of the debt), they own the firm.
  • The values of the capital classes are partly a function of firm value; e.g., if firm value is high, subordinated debt looks more like senior debt. If firm value is low, subordinated debt looks more like equity.

Credit risk approaches

  

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This structural approach finds employment in the Moody's KMV approach to default prediction (PD). On the member page, I've uploaded a spreadsheet that, following de Servigny, computes a poor man's version just to illustrate: it is pretty much the Black-Scholes model.

We contrast this structural approach (i.e., the probability of default is a function of the distance of the firm value from some level of liabilities) to the estimation of PD with reduced-fom approaches. Reduced-form approaches ignore the firm's balance sheet as a cause of default, instead treating the default process as random variable to be directly modeled.

Portfolio Models

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In regard to the credit risk models, you do not need to know the detailed mechanics of each model. Rather, you need to know the conceptual "stuffing" that goes into the model and, importantly, the pros and cons. Just as Jorion does in the handbook, de Servigny slices up the models along key dimensions:

  • Is it a simulation or analytical?
  • What definition of risk is modeled? This is key, note that three definitions of credit risk are involved (default, downgrade, and spread)
  • How is default correlation incorporated? Also key, along with PD and LGD, the treatment of default correlation is a key input in the credit risk of a portfolio
  • Is credit risk (e.g., default) conditional on economic conditions, or unconditional?

Credit Derivatives

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I often say the credit derivatives section, unless you already have experience, requires two passes:

  • A first pass to focus on the mechanics. For example, in a CDS, who is paying a premium, what is the reference assets, what is the trigger?
  • But a grasp of mechanics is insufficient for the exam. Questions will tend to be about the application of credit derivatives. So, after you've got the mechanics of CDS/basket CDS/CLN/cash CDO/synthetic CDO, then analyze them through a prism of motives, counterparty cost/benefit and risk transfer. For example, why would a bank issue a CLN instead of CDS, what is the difference? What risk is being transferred? In regard to a CDS, which of default risk, credit deterioration and operational risk are transferred?.

Bivariate

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With the basket CDS and CDO, we get to apply terms from Gujarati's readings. In particular, we go from univariate to multivariate distributions. If we are analyzing a single bond, the probability of default is a univariate CDF; e.g., P[default] = P[X <= x]. If our portfolio has two bonds, we are now interested in the bivariate CDF, the probability that both bonds jointly default; e.g., P[both bonds in portfolio default] = P [X <= x, Y <= y].

copula

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The Hull reading concludes with the famous (notorious?) Gaussian copula. I uploaded a spreadsheet for this. The Gaussian copula employed to model time to default (at right) is useful to us because it underlies the internal ratings-based (IRB) approach to credit risk in Basel II.

New Learning Spreadsheets Added

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For this episode (Credit Risk C), I uploaded the following all-new learning spreadsheets to the member page:

  • Stulz (Chapter 18) on the credit spread: I didn't highlight this, but please note this is not really a new formula. You should be able to derive this on your own. Start with the formula for the price of debt under continuous compounding, where the risky rate is equal to the riskless rate (r) plus a credit spread (s): D = Face*EXP[-(r + s)(T)]. Now solve for the spread (s).
  • John Hull's valuation of a credit default swap (CDS). Another example of where perceived complexity is due to the combination of basic building blocks (time value of money, probability-adjusted values). Take this one step at a time. Before diving in, note the endgame is an equality: the virtually certain expected PAYMENTS by the CDS buyer (protection buyer) must equal the highly contingent expected PAYOFF by the CDS seller (protection seller).
  • John Hull's Gaussian Copula: Although I keyed in the actual calculations (which you can ignore), your mission (should you choose to accept it!) is to wrap your mind around what the copula function does. This is great practice in Gujarati's probability terms. There are only three inputs: two marginal (unconditional) CDFs (e.g., the probability that each credit will default is 5%) and a correlation. The copula function returns a CDF: the probability that both credits will default. That's all it does: given two marginal distributions plus a correlation, it "joins" them with a function (e.g., Gaussian copula) and gives back a single bivariate (bivariate = multivariate but only two) CDF function. In this case, the JOINT PROBABILITY that both credits will default: P[x < X, y < Y].
  • John Hull's one-factor Gaussian Copula Model of Time to Default: the payoff to reviewing this is you will see a version of this again in the Basel II IRB

As I've uploaded about fifty (50) learning spreadsheets, I highlighted in yellow the more critical subset from an exam perspective. Yellow signifies an important or archetypal idea; yellow means: "I hope you review this spreadsheet." Non-yellow can be ignored, if your schedule does not allow. These "learning worksheets" can be accessed in three ways.

  1. Simply view in the browser,
  2. To open directly into Excel! Select File > Export As > Excel (.xls),or
  3. Most have a downloadable "native" Excel file (XLS) associated with the entry.

Screencast Tutorial

Paid member access the screencast in the member section. In addition to the viewable screencast:

  • You can downloadable the underlying Power Point slides (in PDF format). For this episode, there is a single 92 page deck.
  • An ipod format (.m4v)
  • A downloadable version of the screencast in a .zip file. (Save to new directory on local and launch the .html file.)

Non-members can sample the start of the screencast tutorial here.

Practice Questions

As always, I wrote some engagement-type questions just to provoke your thinking on the episode.

Question #1 (Stulz chapter 18)

A firm has two classes of debt (senior and subordinated) in addition to equity. The (market) value of the senior debt is $70 million, with a face value of $100 million, due in five years. The riskless rate is 4%.

(i) What is the implied credit spread?
(ii) If interest rates rise, what happens to the value of the equity? the value of the senior debt? the value of the subordinated debt?
(iii) List the salient shortcomings of the credit portfolio risk models, according to Stulz.

Question #2 (Meissner Chapter 3)

(i) You own a bond but want to transfer the credit (default) risk to a counterparty. What are the differences between issuing a credit linked note (CLN) and buying a credit default swap (CDS)?
(ii) What are essential differences, from a risk transfer perspective between a cash and synthetic CDO?
(iii) In a basket CDS, what is the impact of higher correlation on the (a) senior, (b) mezzanine and (c) junior tranches?
(iv) Does a credit default swap (CDS) provide a hedge against (a) default risk, (b) credit deterioration, (c) market risk and/or (d) operational risk?
(v) Does a total rate of return swap (TROR) hedge against (a) default risk, (b) credit deterioration, (c) market risk and/or (d) operational risk?

Question #3 (de servigny Chapter 6)

For these questions especially, it would be good practice to not peek at the answers. Researching the answers should encourage familiarity with the models!

(i) Which of de Servigny's credit models are analytical (as opposed to simulation-based)?
(ii) The models variously capture three CREDIT EVENTS: defaults, transitions, and changes in spread. Which of the models has the LEAST encompassing definition of credit event; i.e., includes the fewest credit events?
(iii) Which of the models has the MOST encompassing definition of credit event; i.e., includes the most credit events?
(iv) Which of the models are simulation-based?
(v) Which use credit rating transition/migration matrices?
(vi) Which incorporate macroeconomic conditions (e.g., recession)?

Question #4 (Hull chapter 21)

Suppose the marginal probability of default (PD) on a reference asset is 1% and assume LGD = 50% (so recovery = 1 - LGD = 50%). The riskless rate is 4%. What is the CDS spread for a four (4) year credit default swap (CDS) sold on the reference?

Question #5 (Hull Chapter 21)

Suppose that in a one-factor Gaussian copula model the 5-year probability of default (PD) for each name in the iTraxx index (i.e., 125 names) is 2% and the pairwise copula correlation is 0.30. Assume a factor value of -1.0.

(i) What is the default probability conditional on the factor value?
(ii) Conditional on the factor value, what is the probability of more than five (5) defaults?

My answers to these questions

Previous newsletters

Here are links to Episodes #1 through #6:

Thanks very much.

David Harper, CFA, FRM, CIPM
Founder
www.bionicturtle.com

David-Harper_100w

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