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maturity adjustment -IRB credit risk weight function

David Harper CFA FRM

David Harper CFA FRM
Staff member
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#2
Nanchary,

They partly justify this by saying the function is not only about the probability of default, but deterioration (downgrades): "maturity adjustments can be interpreted as anticipations of additional capital requirements due to downgrades."

So, from the IRB note (p 10)

"Economically, maturity adjustments may also be explained as a consequence of mark-to-market (MtM) valuation of credits. Loans with high PDs have a lower market value today than loans with low PDs with the same face value, as investors take into account the Expected Loss, as well as different risk-adjusted discount factors. The maturity effect would relate to potential down-grades and loss of market value of loans. Maturity effects are stronger with low PDs than high PDs: intuition tells that low PD borrowers have, so to speak, more “potential” and more room for down-gradings than high PD borrowers (mine). Consistent with these considerations, the Basel maturity adjustments are a function of both maturity and PD, and they are higher (in relative terms) for low PD than for high PD borrowers.

In others words, they imply the "average" cumulative transition matrix would bear this out: the row of AAA cumulative downgrade transition probabilities would increase, in relative terms, faster than the BB row, over longer horizons (I can't reference that, it's just their implication)

The other inference you could possibly draw here is: this is another built-in conservatism. By "penalizing" longer maturities, they offset the low capital requirement for highly rateds.

David
 
#3
I kind of think this way: Low PDs = better credit ratings = paying lower interest rates, so the issuers tend to keep the outstanding issues; high PDs = lower credit ratings = paying higher interest rates, so the issuers will redeem the outstanding when upgraded or interest rate regime changed to favor borrowers. Hence high PDs is more sensitive and have a shorter maturity adjustment than low PDs.
 
#4
Nanchary,

They partly justify this by saying the function is not only about the probability of default, but deterioration (downgrades): "maturity adjustments can be interpreted as anticipations of additional capital requirements due to downgrades."

So, from the IRB note (p 10)

"Economically, maturity adjustments may also be explained as a consequence of mark-to-market (MtM) valuation of credits. Loans with high PDs have a lower market value today than loans with low PDs with the same face value, as investors take into account the Expected Loss, as well as different risk-adjusted discount factors. The maturity effect would relate to potential down-grades and loss of market value of loans. Maturity effects are stronger with low PDs than high PDs: intuition tells that low PD borrowers have, so to speak, more “potential” and more room for down-gradings than high PD borrowers (mine). Consistent with these considerations, the Basel maturity adjustments are a function of both maturity and PD, and they are higher (in relative terms) for low PD than for high PD borrowers.

In others words, they imply the "average" cumulative transition matrix would bear this out: the row of AAA cumulative downgrade transition probabilities would increase, in relative terms, faster than the BB row, over longer horizons (I can't reference that, it's just their implication)

The other inference you could possibly draw here is: this is another built-in conservatism. By "penalizing" longer maturities, they offset the low capital requirement for highly rateds.

David
Hi David,

could you please explain, why the parameter M in the IRB maturity adjustment cannot be larger than 5?

Thanks
Andi
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
#5
Hi @andi2384 I am not aware of an upper bound (much less at 5) for the (M) param in the IRB function; it would seem to defeat the purpose. I don't see the source of this claim, sorry? Thanks,
 
#6
Hi David,

im am refering to paragraph 320 of International Convergence of Capital Measurement and Capital Standards (page 89):

Except as noted in paragraph 321, M is defined as the greater of one year and the remaining effective maturity in years as defined below. In all cases, M will be no greater than 5 years. [...]

Thanks
Andi
 
#9
OK. Thank you. The only good information I could find was in "The Internal Ratings-Based Approach from 2001" (bcbs). Unfortunately at that time a ceiling of 7 years was discussed and I couldn't find a more recent document adressing this issue...

135. The proposal places a ceiling of 7 years on effective maturity as measured for IRB purposes. As described below, the proposed methods of adjusting IRB risk weights for the effects of maturity approximate these adjustments as linear functions of M. Research suggests that as M extends much beyond around 7 years this approximation begins to significantly overstate the impact of maturity on economic capital for credit risk
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
#10
@andi2384 Thanks, that is better than what I could find. I have several deep Basel resources and I still can find no specific explanation. I wondered (hypothesized) if, maybe, the adjustment function "tapers " such that longer maturities have diminishing impact. So I ran the scenarios below; y-axis is the adjustment (multiplier) on UL that results for a given combination of maturity (M) and PD (each line is a different PD), but the function is not asymptomatic and I had hypothesized. I suppose this observation inadvertently, I could argue, supports your quotation above: as the actual impact of maturity ought to be asymptotic (or concave or decelerating), but the function is nearer to linear, the arbitrary cutoff is required. For what it's worth .. but thank you for your follow-up (+ star for great question/insight)

 
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