Topic: Assessing the quality of risk measures

[Unusualskill]

Statement 1: A common trade during 2004 and 2005 was to sell protection on the equity tranche
and buy protection of the mezzanine tranche of the CDX.NA.IG index.

Statement 2: The trade was long credit spread risk on the equity tranche and short credit
spread risk on the mezzanine tranche.

Hi @David Harper CFA FRM , May I ask why is statement 1 and 2 equivalent? particularly what is the meaning of long credit spread risk and short credit spread risk referring to the above scenario? Thank you!

 

[Rinkesh86]

Credit spread is difference between Yeild of Corp bond and risk free bond. When you long credit spread you will be paying if the spread increases( yeild on Corp bond goes up, as it's price declines because of some reason like credit rating downgrade etc). Which also means you are protection seller.

 

[Jaskarn]

Hi @David Harper CFA FRM ,

Under this thread i.e. Malz, Chapter 11 (Section 11.1): Assessing the Quality of Risk Measures

I wanted to ask 2 things
1. Isn't this true that under stress situation correlation increases? In notes, it mentioned that correlation fell during the crisis.
2. Under this chapters subtopic " The implied correlation fell for two reasons" ( Page 7 in your notes) 2nd reasons I didn't understand especially line "Although spreads were widening and the credit environment was deteriorating, some buyers of protection on the IG4 index found willing sellers among trader’s long protection in the equity tranche who were covering the short leg via the index as well as via the mezzanine tranche itself."

Thanks a lot for your time.

 

[David Harper CFA FRM]

Hi @Jaskarn

1. Yes, a thematic idea is that return correlations increase (e.g, spike toward 1.0) during stress. Basically, during stress this implies that positions (or components) are experiencing (strongly) negative returns simultaneously
2. The case study in Malz Chapter 11 (11.1.4 Case Study: The 2005 Credit Correlation Episode) refers to default correlations within junior/mezzanine/senior tranches. Here is an example of a question about that https://forum.bionicturtle.com/thre...-default-rate-and-correlatio.7030/#post-74208 There are many forum threads on this topic, but the high-level idea is: At a given default rate, an increase (decrease) in default correlation implies an increase (decrease) in the equity tranche value. A binomial is a good way to illustrate: say the equity tranche is associated with just the first default (i.e., it is wiped out when the first default happens) among 10 credits who each have PD = 1.0%. If the default correlation is zero, then this equity tranche is wiped out with probability of 1 - 98%^20 = 18.3%. Now increase the correlation to 1.0, and it is only wiped out with probability of 2.0%. In this way, a decrease in default correlation decreases the value of the equity trance but increases the value of the senior tranche.

About the case, Stulz says

"The implied correlation of the equity tranche dropped sharply. Stated equivalently, its mark-to-market value dropped more and its points upfront rose more sharply than the widening of the IG 4 spread alone would have dictated." ... The implied correlation fell for two reasons. The automotive parts supplier bankruptcies had a direct effect. All were in the IG4, which meant that about 10 percent of that portfolio was now near a default state. But the correlation fell also because the widening of the IG 4 itself was constrained by hedging. The short-credit position via the equity tranche could be hedged by selling protection on a modest multiple of the mezzanine tranche, or a large multiple of the IG4 index. Although spreads were widening and the credit environment was deteriorating, at least some buyers of protection on the IG4 index found willing sellers among traders long protection in the equity tranche who were covering the short leg via the index as well as via the mezzanine tranche itself."

The equity tranche is a tranche of the CDX.NA.IG index (aka, the IG3 or IG4). The overall backdrop is spread widening due to credit deterioration. The value of the equity tranche (of the IG4 index) is firstly a function of the spread movements in the IG4 but also a function of default correlations within the tranche (or default correlation may be inferred by index spread and the tranche spread). The value of the equity tranche dropped more than it should drop if the drop were only associated with the IG4 spread widening; the "excess" value drop is inferred to be decrease in correlation. Abstractly something like: Δequity_spread = ΔIG4_index_spread + Δ↓default_correlation + other_omitted_factors. In this way, change in default correlation is inferred from difference in change of value between tranche and index. That is, Δ↓default_correlation = Δequity_spread - ΔIG4_index_spread. All other things being equity, whatever compresses (tightens) the index spread can be inferred as contributing to a drop in the implied correlation of the equity tranche. His second point is that hedge trades where doing that: not everybody was selling, some were buying if only to hedge. Phew. I hope that's helpful,

 

[Jaskarn]

Hi @Jaskarn

1. Yes, a thematic idea is that return correlations increase (e.g, spike toward 1.0) during stress. Basically, during stress this implies that positions (or components) are experiencing (strongly) negative returns simultaneously
2. The case study in Malz Chapter 11 (11.1.4 Case Study: The 2005 Credit Correlation Episode) refers to default correlations within junior/mezzanine/senior tranches. Here is an example of a question about that https://forum.bionicturtle.com/thre...-default-rate-and-correlatio.7030/#post-74208 There are many forum threads on this topic, but the high-level idea is: At a given default rate, an increase (decrease) in default correlation implies an increase (decrease) in the equity tranche value. A binomial is a good way to illustrate: say the equity tranche is associated with just the first default (i.e., it is wiped out when the first default happens) among 10 credits who each have PD = 1.0%. If the default correlation is zero, then this equity tranche is wiped out with probability of 1 - 98%^20 = 18.3%. Now increase the correlation to 1.0, and it is only wiped out with probability of 2.0%. In this way, a decrease in default correlation decreases the value of the equity trance but increases the value of the senior tranche.

About the case, Stulz says


The equity tranche is a tranche of the CDX.NA.IG index (aka, the IG3 or IG4). The overall backdrop is spread widening due to credit deterioration. The value of the equity tranche (of the IG4 index) is firstly a function of the spread movements in the IG4 but also a function of default correlations within the tranche (or default correlation may be inferred by index spread and the tranche spread). The value of the equity tranche dropped more than it should drop if the drop were only associated with the IG4 spread widening; the "excess" value drop is inferred to be decrease in correlation. Abstractly something like: Δequity_spread = ΔIG4_index_spread + Δ↓default_correlation + other_omitted_factors. In this way, change in default correlation is inferred from difference in change of value between tranche and index. That is, Δ↓default_correlation = Δequity_spread - ΔIG4_index_spread. All other things being equity, whatever compresses (tightens) the index spread can be inferred as contributing to a drop in the implied correlation of the equity tranche. His second point is that hedge trades where doing that: not everybody was selling, some were buying if only to hedge. Phew. I hope that's helpful,

So earlier people thought that equity spread is explained by index spread but actually they ignored default correlation. In reality Δequity_spread = ΔIG4_index_spread + Δ↓default_correlation + other_omitted_factors. According to this equation at any particular point in time equity spread>= Index spread { Greater only during crisis time, due to correlation, otherwise in normal times it was observed to be equal}

keeping in mind below equation
Δ↓default_correlation = Δequity_spread - ΔIG4_index_spread
and trying to understand with numbers, let's say equity spread = 30 and index spread =10 difference is 20 which is contributed by correlation drop i.e. during crisis time, correlation drop which increases PD of equity tranche which in turn reduces its value and contributed to increases in equity tranche spread.

So hedge trades were trying to tighten( Pushing down) index spread let's say from 10 to 8 by buying index spread. But my understanding fail here that why were they buying index spread? I mean how were they hedging there position by buying index spread?
Also, when you say "not everybody was selling, some were buying if only to hedge." what do you exactly mean? I mean Buying and selling what? Protection in tranches?

In short, I am trying to understand this line from your notes ( green text indicates lines that I could understand)
"Although spreads were widening and the credit environment was deteriorating, some buyers of protection on the IG4 index found willing sellers among trader’s long protection in the equity tranche who were covering the short leg via the index as well as via the mezzanine tranche itself."

Green text understanding:
What I understood about the above line is that when the spread of equity tranche increases people rush to buy protection on equity tranche and they found willing sellers who were ready to sell protection on equity tranche and those sellers were traders. Please help in understanding red text

Sorry, I feel like a poor kid trying to make my way to understand this. Can't really go ahead without understanding what is happening

 

[David Harper CFA FRM]

Hi @Jaskarn I trust you are aware we are talking about Malz Chapter 11.1 and that you are asking me about Malz statements that are repeated in our notes? We can jointly be referring to the assigned Malz. The reason I say that is that this paragraph by Malz is written in an extremely confusing way. At a certain point, we could give feedback to GARP about the confusing language in Malz page 403. GARP assigns these readings, often without understanding some of the details themselves, then leaves it to EPPs like us to deal with confusions that ensue, which is especially challenging when the writing is poor (or worse, if there is a mistake ...)

It's been a very long weekend, and I don't want to get too bogged down in the language of Malz right now. Rather than go through your compound questions (which may take me longer to interpret than answer), let me just step back and tell you what I understand as simply as possible. However, this particular case study does depend on prior concepts, so part of the problem, or solution rather, may just be that you need to get clear on definitions of the items involved; e.g., equity tranche of the index.

Okay, so here is what I can explain as simply as possible, I am bone-bone tired so I will check this tomorrow for typos, but don't expect this to be perfect (i.e., assume it is has not been proofed). I'm started from the top because often confusions are due to a lack of clarity on the definitions employed:

1. The CDX.NA.IG index has an Equity tranche, a junior Mezzanine tranche, a Senior tranche etc. Per https://www.theice.com/products/28555645/Markit-CDXNAIG it looks like the index includes 125 names. So, maybe the equity trance is 0 to 3% and the Junior Mezz is 3 to 7%. The equity tranche is exposed to the first loss, and wiped out when the loss reaches 3% of the notional. The IG3 and IG4 are versions (series) of this CDX.NA.IG index.

2. Traders can trade these tranches of the index. Malz paragraph to which you refer is poorly written, in my opinion, because he switches between three synonymous definitions of a position with respect to the trade. If we consider the equity tranche, let's say you are confident in the underlying names, in fact you think none of the 125 will default. You would buy the equity tranche of the index because you are long the credit risk such that you are willing to sell protection.

3. Sidebar: the value of the equity tranche is a function of both the credit quality of the portfolio (i.e., default probability) and the default correlation among credits in the portfolio. If credit quality of the portfolio weakens, the spreads widen for the index and also for the equity tranche. If the overall index default probability is unchanged (average credit quality among all 125 names is roughly unchanged), but the value of the equity tranche drops (ie, tranche spread widens), then default correlation (among all names in the index) has decreased. Because lower default correlation increases the probability of greater losses in the first 3%.

4. About the basic trade, Malz (not me) writes "A widespread trade among hedge funds, as well as proprietary trading desks of banks and brokerages, was to sell protection on the equity tranche and buy protection on the junior mezzanine tranche of the CDX.NA.IG. The trade was thus long credit and credit-spread risk through the equity tranche and short credit and credit-spread risk through the mezzanine." Here is my shorthand summary of that trade:

• Re the 0-3% equity tranche: buy the index = sell protection = long the credit (and credit-spread) risk
• Re the 4-7% Jr Mezz tranche: sell the index = buy protection = short the credit (and credit-spread) risk

5. The broad backdrop was overall credit deterioration. The equity tranche of the IG4 experienced a dramatic price drop. Largely, Malz infers the decrease in default correlation because the equity tranche price dropped more than can be explained by value drop (spread widening) in the IG4 index. A key idea here is the implied default correlation change is a function of excess tranche spread widening (or price decline).

6. You are currently focused on this paragraph written by Malz:

"The implied correlation fell for two reasons. The automotive parts supplier bankruptcies had a direct effect. All were in the IG4, which meant that about 10 percent of that portfolio was now near a default state. But the correlation fell also because the widening of the IG 4 itself was constrained by hedging. The short-credit position via the equity tranche could be hedged by selling protection on a modest multiple of the mezzanine tranche, or a large multiple of the IG4 index. Although spreads were widening and the credit environment was deteriorating, at least some buyers of protection on the IG4 index found willing sellers among traders long protection in the equity tranche who were covering the short leg via the index as well as via the mezzanine tranche itself."

I think his first reason is simply that: a spike in default probability directly impacted the value of the equity tranche and that can be inferred (as above) as a fall in implied correlation; I tend to think this part is somewhat circular.

With respect to the almost hilariously badly-written second reason, I can somewhat confidently back into what he is trying to say, only because I understand how he got here. The second reason here is virtually impossible to grok without understanding the pieces of the puzzle. As above, anything that tends to constrains spreads on the (all 125 names) IG4 index while spreads on the equity tranche are widening, by definition, contributes to a decline in implied default correlation. If everybody is selling the index (aka, buying protection, short credit risk) then the index spread is widening, but anybody who is buying the index (aka, selling protection, long credit risk) "constrains" the widening of the IG4 [itself] index. So what we can safely infer from this second point is that the "constraining" hedging activity was activity that was selling protection or buying the index/tranche (aka, long credit risk). Therefore my interpretation is that "The short-credit position via the equity tranche [note: this is not the trade above: this is the opposite trade by different hedgers] could be hedged by selling protection on a modest multiple of the mezzanine tranche, or a large multiple of the IG4 index [aka, buy the IG4 index; long the credit risk of the index]. Although spreads were widening and the credit environment was deteriorating, at least some buyers of protection on the IG4 index [aka, sellers of the IG4 index who are short the credit risk of the index] found willing sellers among traders long protection in the equity tranche [aka, selling the tranche because they are short the credit risk of the equity tranche] who were covering the short leg via the index [i.e., by buying the IG4 index] as well as via the mezzanine tranche itself." I hope that's helpful, I'll review it tomorrow to confirm that I believe what I write. Okay, tired.

 

[Jaskarn]

Hi @Jaskarn I trust you are aware we are talking about Malz Chapter 11.1 and that you are asking me about Malz statements that are repeated in our notes? We can jointly be referring to the assigned Malz. The reason I say that is that this paragraph by Malz is written in an extremely confusing way. At a certain point, we could give feedback to GARP about the confusing language in Malz page 403. GARP assigns these readings, often without understanding some of the details themselves, then leaves it to EPPs like us to deal with confusions that ensue, which is especially challenging when the writing is poor (or worse, if there is a mistake ...)

It's been a very long weekend, and I don't want to get too bogged down in the language of Malz right now. Rather than go through your compound questions (which may take me longer to interpret than answer), let me just step back and tell you what I understand as simply as possible. However, this particular case study does depend on prior concepts, so part of the problem, or solution rather, may just be that you need to get clear on definitions of the items involved; e.g., equity tranche of the index.

Okay, so here is what I can explain as simply as possible, I am bone-bone tired so I will check this tomorrow for typos, but don't expect this to be perfect (i.e., assume it is has not been proofed). I'm started from the top because often confusions are due to a lack of clarity on the definitions employed:

1. The CDX.NA.IG index has an Equity tranche, a junior Mezzanine tranche, a Senior tranche etc. Per https://www.theice.com/products/28555645/Markit-CDXNAIG it looks like the index includes 125 names. So, maybe the equity trance is 0 to 3% and the Junior Mezz is 3 to 7%. The equity tranche is exposed to the first loss, and wiped out when the loss reaches 3% of the notional. The IG3 and IG4 are versions (series) of this CDX.NA.IG index.

2. Traders can trade these tranches of the index. Malz paragraph to which you refer is poorly written, in my opinion, because he switches between three synonymous definitions of a position with respect to the trade. If we consider the equity tranche, let's say you are confident in the underlying names, in fact you think none of the 125 will default. You would buy the equity tranche of the index because you are long the credit risk such that you are willing to sell protection.

3. Sidebar: the value of the equity tranche is a function of both the credit quality of the portfolio (i.e., default probability) and the default correlation among credits in the portfolio. If credit quality of the portfolio weakens, the spreads widen for the index and also for the equity tranche. If the overall index default probability is unchanged (average credit quality among all 125 names is roughly unchanged), but the value of the equity tranche drops (ie, tranche spread widens), then default correlation (among all names in the index) has decreased. Because lower default correlation increases the probability of greater losses in the first 3%.

4. About the basic trade, Malz (not me) writes "A widespread trade among hedge funds, as well as proprietary trading desks of banks and brokerages, was to sell protection on the equity tranche and buy protection on the junior mezzanine tranche of the CDX.NA.IG. The trade was thus long credit and credit-spread risk through the equity tranche and short credit and credit-spread risk through the mezzanine." Here is my shorthand summary of that trade:

• Re the 0-3% equity tranche: buy the index = sell protection = long the credit (and credit-spread) risk
• Re the 4-7% Jr Mezz tranche: sell the index = buy protection = short the credit (and credit-spread) risk

5. The broad backdrop was overall credit deterioration. The equity tranche of the IG4 experienced a dramatic price drop. Largely, Malz infers the decrease in default correlation because the equity tranche price dropped more than can be explained by value drop (spread widening) in the IG4 index. A key idea here is the implied default correlation change is a function of excess tranche spread widening (or price decline).

6. You are currently focused on this paragraph written by Malz:

I think his first reason is simply that: a spike in default probability directly impacted the value of the equity tranche and that can be inferred (as above) as a fall in implied correlation; I tend to think this part is somewhat circular.

With respect to the almost hilariously badly-written second reason, I can somewhat confidently back into what he is trying to say, only because I understand how he got here. The second reason here is virtually impossible to grok without understanding the pieces of the puzzle. As above, anything that tends to constrains spreads on the (all 125 names) IG4 index while spreads on the equity tranche are widening, by definition, contributes to a decline in implied default correlation. If everybody is selling the index (aka, buying protection, short credit risk) then the index spread is widening, but anybody who is buying the index (aka, selling protection, long credit risk) "constrains" the widening of the IG4 [itself] index. So what we can safely infer from this second point is that the "constraining" hedging activity was activity that was selling protection or buying the index/tranche (aka, long credit risk). Therefore my interpretation is that "The short-credit position via the equity tranche [note: this is not the trade above: this is the opposite trade by different hedgers] could be hedged by selling protection on a modest multiple of the mezzanine tranche, or a large multiple of the IG4 index [aka, buy the IG4 index; long the credit risk of the index]. Although spreads were widening and the credit environment was deteriorating, at least some buyers of protection on the IG4 index [aka, sellers of the IG4 index who are short the credit risk of the index] found willing sellers among traders long protection in the equity tranche [aka, selling the tranche because they are short the credit risk of the equity tranche] who were covering the short leg via the index [i.e., by buying the IG4 index] as well as via the mezzanine tranche itself." I hope that's helpful, I'll review it tomorrow to confirm that I believe what I write. Okay, tired.

You are a pure blessing to us David. I have no words to thank you.