Jul 28

FRM 2008 Episode #10: Operational Risk A (OpRisk A)

by David Harper, CFA, FRM, CIPM

FRM |

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About Episode #10 (Operational Risk A)

Please find links to earlier episodes (#1 to #9) at the end of this note. We are following the sequence of GARP's 2008 FRM Study Guide.

This latest screencast episode (Operational Risk A) begins the Operational Risk discipline. This screencast episode has a 121+ page PowerPoint you can download in two parts (part 1= hour plus part 2 = 50 minutes). There is a lot of material, so I'll just offer a few tips that may help.

The dilemma: not enough data

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The first reading in the Operational Risk discipline (Linda Allen) introduces a persistent dilemma: we are most interested in the (extreme) loss tail where catastrophically bad things happen, but we rarely have enough data to discern robust patterns in the tail. Rare events (low frequency, high severity) don't create large data sets!

So we are not surprised that the authors of the Deutche Bank case (LDA at work) must use a parametric distribution to model their extreme loss tail (losses above $50 million): they do not have enough internal data to use an empirical distribution based on their own history.

As a consequence of this classic "data dilemma," the extreme value theory (EVT) introduced by Paul Wilmott in the Quant Discipline plays a big role in operational risk. Where there is not enough data to rely on empirical distributions, we lean on EVT-based parametric distributions (e.g., the GPD is a "specialty" distribution, meant to characterize the pattern of losses in excess of some threshold. It's whole job function is to describe the extreme loss tail).

Bottom up versus top down

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There are several OpRisk approaches to memorize. But here is a guiding principle:

  • Top-down approaches tend to be those an external analyst could use with public information. Armed with an income statement and market data, most of them (e.g., multi-factor model) can be performed by a third-party. Consequently, they are limited but easier to conduct.
  • Bottom-up approaches require an "inside job:" internal data, management interviews. Consequently, they are generally superior but more difficult (data intensive): they are diagnostic, predictive, and often revealing of causality. A key difference is that "top down" approaches do not differentiate between HFLS/LFHS losses but bottom-up approaches can indeed distinguish between HFLS/LFHS losses.

Deutsche bank lda (DB LDA)

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Several customers wrote to say they find the DB LDA reading difficult. Here is my " cliff notes" version of the DB LDA approach:

  • They classify their operational losses into a matrix: a cell is a type of operational loss (event type) that occurs within a business line
  • For each cell (i.e., a particular event type of loss occurring within a business line), they generate a loss distribution. The loss distribution is created by compounding the less important frequency distribution (i.e., how often do losses happen?) with the more important severity distribution. The severity distribution is a mixture (piece-wise) distribution where a parametric EVT (tail) distribution is grafted onto an empirical (body) distribution
  • The within-cell losses are aggregated into Gross Losses. Gross losses minus (the benefit of) insurance equals net losses.
  • The "bottom line" is an economic capital for the organization: operational loss VaR minus expected operational losses. As always, economic capital (EC) = VaR (alpha) - EL. Further, as you know by now, the VaR requires two inputs by the user: confidence and time horizon.
  • The economic capital (EC) for the firm is allocated (budgeted) to the business units.

Compounding frequency and severity

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In Op Risk, we build on the foundation laid by Gujarati in the Quantitative Discipline. In my opinion, sometimes we need to "go backwards in order to make progress." If the distributional ideas here are difficult, consider first reviewing the more basic distributional ideas in Gujarati.

The LDA approach compounds a typically discrete frequency distribution with a typically continuous severity distribution. To the member page, I uploaded two illustrative spreadsheet examples of this: one compounds parametric distributions, the other compounds/tabulates empirical distributions.

Piece-wise (mixture) model

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As mentioned, The DB LD "grafts" a parametric distribution (i.e., for the loss tail), onto an empirical distribution for the body.

I uploaded an illustrated spreadsheet example, for this, too. This is a "poor man's" version of the DB piece-wise model. In both cases,

 

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:

  • Deutsche bank's business line/event type (BL/ET) matrix. Real simple replication of the cells used in the "LDA at Work" reading
  • Loss distribution approach (LDA) using parametric distributions (i.e., compounds a Poisson frequency distribution with a lognormal severity distribution)
  • Loss distribution approach (LDA) using empirical distributions. This also compounds a frequency with a severity distribution, but uses tabulation.
  • Economies of scale illustration (Saunders' technology reading)
  • Mixture distribution where extreme value theory (EVT) is used to model the loss tail (i.e., GPD in the tail). This is sort of advanced so don't bother unless you really want to look.

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. None of the five new spreadsheets have a yellow highlight: I don't think you need to review them from an exam-passing strategy. But feel free to use them to explore these ideas further.

  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 (L. Allen's Extending the VaR approach)

Linda Allen's "Extending the VaR approach to operational risk" itemizes several top-down and bottom-up models. Which of the model(s) is described by the following, or best matches the situation:

(i) Which is (are) Deutsche Bank's approach in "LDA at work?"
(ii) Which is (are) similar to Basel's Basic Indicator Approach (BIA)?
(iii) Which is (are) similar to Basel's Advanced Measurement approach?
(iv) Which is (are) good if we hope to diagnose and prevent operational losses?

Question 2 (L. Allen)

One AIM asks us to "List and describe ways a firm can hedge against catastrophic operational losses." In regard to self-insurance, derivatives, and catastrophe bonds (cat bonds):

(i) Which are likely to, respectively, minimize and maximize moral hazard?
(i) Which are likely to, respectively, minimize and maximize basis risk?

Question 3 (LDA at Work)

(i) Where does Deutsche Bank use EXTERNAL data and why?
(ii) The "short story" version the DB LDA process is: for each cell, they compound two different distribution types, one of which is piece-wise. Explain what this means: what is a cell, what is compounding two distributions, and what is piece-wise?
(iv) How is the tail (i.e., losses greater than $50 MM) modeled?
(v) How do dependencies (dependencies = a more encompassing type of correlation but that allows for non-linear and indirect "correlations") enter in the DB approach?
(vi) How does insurance enter into the DB approach

Question 4 (Operational VaR: Closed End)

(i) For a first-order operational VaR approximation, do we need the entire frequency distribution
(ii) For a first-order operational VaR approximation, do we need the entire severity distribution
(iii) Assume operational VaR over a ONE-MONTH period is $1 million. We apply the square root rule, to estimate a FOUR-MONTH operational VaR of $2 million; i.e., $1 million x SQRT(4/1) = $1 million x (2) = $2 million. Are we correct?

Question 5 (Dowd on Model risk)

(i) What sources of model risk (as itemized in Dowd) are implicated in Ashcroft's Credit Risk reading called "Understanding the Securitization of Subprime Mortgage Credit?"
(ii) If you are a disciple of the strong form of efficient market hypothesis (EMH), and you are concerned with MINIMIZING your firm's model risk, where is your likely focus?
(iii) If you NOT a disciple of the strong form of efficient market hypothesis (EMH), and you are concerned with MINIMIZING your firm's model risk, where is your likely focus?

My answers to these questions

Previous newsletters

Here are links to Episodes #1 through #9:

Thanks very much.

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

David-Harper_100w

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