L2 Malz ch. 8 AIM 25.7 realized market value

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Hello,

When looking at Malz chapter 8 (which, btw, currently holds top honors in highly-contested "FRM curriculum most poorly source material") and the calculation of realized market value used to compute the probability of reaching a default thereshold at a specified confidence level, what is it that I'm actually calculating? What's the unit, and what's the meaning?

It's in your materials on page 43, but, with all due respect, explained as poorly as in Malz, it's essentially copy and paste.

Regards,


Wojtek

 

[David Harper CFA FRM]

Hi Wojtek,

The market index or factor (m) is a latent variable (http://en.wikipedia.org/wiki/Latent_variable ) which has no fundamental interpretation. In Malz's usage, it is a standard normal, ~N(0,1) (see 6.8) and represents the return(%) on the (latent) market index. It's a very symbolic model: the product term [beta*m] exist to give a easy mechanism, at the expense of any realism, perform a conditional "scenario" where the asset goes from an unconditional default probability to a conditional default probability based on some assumption about the market index/factor return (m) and the asset's correlation to the the market index. The model gives the simplest of means from which to:

• shift from an unconditional PD; i.e., assume beta = 0 such that --> firm's asset return = just the idiosyncratic e ~ n(0,1)
• to a conditional PD; assume correlation (beta) to some latent adverse market situation (m); e.g., if m ~ N(0,1) then Malz example 8.4 assumption of m = -1.0 is "modest downturn" and m = -2.33 (a 1% quantile in the standard normal) is a "severe economic downturn"

I tried to give some practice to these in T6.310 and .311 (these are the relevant PDF)

• http://forum.bionicturtle.com/threads/p2-t6-310-single-factor-credit-model-malz-section-8-3.6968/
• http://forum.bionicturtle.com/threa...ng-single-factor-model-malz-section-8-4.6979/

Re: "it's essentially copy and paste." I agree. I view the new Malz and Gregory as somewhat recklessly assigned, we are on our heels with it frankly. If it survives the the draft 2014 AIMs, then our revision will need to be much improved, thanks,

 

[wanderer87]

Hi David,
I am a little confused on page no. 43 of Malz reading, I can't figure out why both k as well as p(m) are assigned the value -2.33.
As per my understanding p(m) has been assigned this value as we are considering a portfolio loss (dependent on the market conditions to be 0.01) so we are finding the probability of market sliding below 0.01, but why is the same being used for k?
In case of k ,-2.33 is the threshold under unconditional probability (independent of m).

 

[David Harper CFA FRM]

Hi @wanderer87

Good question, but first, please let's note that k = -2.33 happens to be Malz's example of a "middling credit;" for example, a higher-quality credit would have a lower (more negative) k value to signify a lower unconditional default probability (greater distance to default). In Malz's single-factor credit model, there are two parameters: (k) which represents the unconditional default probability (credit quality) of the firm; and beta with represents correlation to the single market factor (or "cyclicality").

• In the example, k = -2.33 signifies a "middling" credit quality firm where its unconditional default probability = N(-2.33) = 1.0%. Because the firm defaults if a(i) < k, where a(i) is firms' return on assets, (k) is directly a function of the firm's default threshold.
  
• p(m) represents the (cumulative) conditional default probability: it is the conditional probability that that asset return, a(i), will fall below the -2.33. So, given the assumption that the firm (e.g.) defaults unconditionally if a(i) < -2.33, then the susbequent question is what is the conditional probability that cumulative p(m) < -2.33. I hope that helps,

 

[afterworkguinness]

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