CDO Tranche Spreads with respect to Correlation between Assets in CDO

[HHo0951]

Hi, re the discussions on CDO tranche spreads with respect to correlation between the assets in the CDO, I am referring to page 125 of Chapter 7 of Market Risk Measurement & Management 2022 edition, it states:

"Importantly, the correlation of the bonds in CDOs (which originally were only investment-grade bonds) decreased, since bonds of different credit qualities are typically lower-correlated. This led to huge losses of hedge funds, which had put on a strategy where they were long the equity tranche of the CDO and short the mezzanine tranche of the CDO. Figure 7.7 shows the dilemma. Hedge funds had invested in the equity tranche10 (0% to 3% in Figure 7.7) to collect the high-equity tranche spread. They had then presumably hedged11 the risk by going short the mezzanine tranche12 (3% to 7% in Figure 7.7). However, as we can see from Figure 7.7, this “hedge” is flawed."

...where they were bolded in the text above, they are the exact opposite to what the BT Forum discussion threads ( https://forum.bionicturtle.com/thre...n-in-risk-management-meissner-chapter-1.8207/ ) have described, ie Short equity tranche and Long mezzanine tranche.

Am I missing something fundamental here, pls?

Appreciate any help / inputs to clarify this, pls.

 

[David Harper CFA FRM]

Hi @HHo0951 Yea, I think it's already explained in the thread, to my satisfaction anyway. As I wrote, it's my opinion that(new emphasis mine)....

• With respect to the equity position, per Arrow #1 below, lower default correlation implies higher spread (lower value) for the CDO tranche. But (here's where I was originally confused ) the hedge fund did not own/short the CDO equity tranche, it has sold credit protection on the tranche (aka, short CDS that referenced the tranche) so its "short" position is a short CDS which is synthetically long the underlying bonds. They lost on this written protection when the underlying bonds downgrade, in the same way they would experience a M2M loss on a short CDS that referenced the bonds directly (without the intermediation of a CDO, so to speak)

My additional evidence (aside from the coherent profit/loss narrative, is that here is Meissner is the first version of his book (with footnote 10):

"Importantly, the correlation of the bonds in CDOs that referenced investment grade bonds decreased, since bonds of different credit qualities are typically lower correlated. This led to huge losses of hedge funds, which had put on a strategy where they were short the equity tranche of the CDO and long the mezzanine tranche of the CDO. Figure 1.7 shows the dilemma. Hedge funds had shorted the equity tranche [footnote 10: Shorting the equity tranche means being short credit protection or selling credit protection, which means receiving the (high) equity tranche contract spread.]" -- 1st edition, Meissner, Gunter. Correlation Risk Modeling and Management. (p. 40). Wiley. Kindle Edition.

... then here is the same section in his second edition:

"Importantly, the correlation of the bonds in CDOs (which originally were only investment-grade bonds) decreased, since bonds of different credit qualities are typically lower-correlated. This led to huge losses of hedge funds, which had put on a strategy where they were long the equity tranche of the CDO and short the mezzanine tranche of the CDO. Figure 1.7 shows the dilemma. Hedge funds had invested in the equity tranche [footnote 10: Investing in the equity tranche means “assuming credit risk” since a credit deterioration hurts the investor. This is similar to a bond, where the investor assumes the credit risk. Investors in the equity tranche receive the high equity tranche contract spread.] "-- Meissner, Gunter. Correlation Risk Modelling and Management (pp. 61-62). Risk Books. Kindle Edition.

Notice the directional (long/short) substance of his footnote did not change, but he decided to change the meaning of "long" versus "short" the CDO tranche. As I carefully discussed in my dissection of the case, it's very clear to me that the hedge funds with respect to the equity tranche were collecting premiums or "collect[ing] the high-equity spread" (even here he probably means, collecting the equity's high-spread, more imprecisions!). As these are synthetic CDOs, that means selling credit protection or short CDS.

Original thread here at https://forum.bionicturtle.com/thre...management-meissner-chapter-1.8207/post-47639

Hi @RobKing I imagine you mean to refer to Meissner's Chapter 1. Please note there some debate-disagreement last year about certain of his assertions, or at least his semantics (eg, https://forum.bionicturtle.com/threads/error-in-meissner-text.9137/#post-40675)

In my previous post (full text is copied below; link here @ https://forum.bionicturtle.com/thre...anagement-meissner-chapter-1.8207/#post-43073) I tried to explain Meissner's GM/Ford correlation-related crisis. For me, the key is to focus on his two arrows (#1 and #2 in this graph).

But I think it firstly helps to keep in mind some fundamentals:

• The CDO itself issues tranches of liabilities to investors. Here we expect the following classic dynamic with respect to a decrease in default correlation (please note that is a movement from right to leftin Meissner's Fig 1.7 above)
  • Equity tranche spread increases (lower ρ --> lower value/higher spread as confirmed by Arrow #1 above)
  • Senior tranche spread decreases (lower ρ --> higher value/lower spread as confirmed by non-arrowed tranche 15%-30% above, say)
  • I agree with Brian's point elsewhere that Mezzanine dynamic depends, so we can't say anything general and necessary about the mezz
• Separately, the hedge fund investors took positions that referenced the CDO tranches. The look similar to positions in credit indices (eg, Markit's iTraxx or CDX); e.g., 0 to 3%, 3 to 7%. Meissner writes (emphasis mine) "This led to huge losses of hedge funds [sic], which had put on a strategy where they were short the equity tranche of the CDO and long the mezzanine tranche of the CDO. Figure 1.7 shows the dilemma. Hedge funds had shorted the equity tranche [endnote 10] (0% to 3% in Figure 1.7) to collect the high equity tranche spread. They had then presumably hedged [endnote 11] the risk by going long the mezzanine tranche [endnote 12] (3% to 7% in Figure 1.7)."

I think endnotes 10 and 12 tell the story:

• Endnote 10: "Shorting the equity tranche means being short credit protection or selling credit protection, which means receiving the (high) equity tranche contract spread."
• Endnote 12: "Going long the mezzanine tranche means being long credit protection or buying credit protection, which means paying the (fairly low) mezzanine tranche contract spread."
• So it looks like the hedge funds under consideration wrote CDS (sold credit protection) on the CDO equity tranche and, in an attempt to hedge, bought CDS (bought credit protection) on the CDO mezz tranche expecting them to react similarly to correlation shifts. If the mezzanine position was a hedge, they must have expected the mezzanine trance to react to lower correlation in a way similar to the equity: they expected lower default correlation to associate with higher spreads (lower value). But it acted more like a senior tranche.
• With respect to the equity position, per Arrow #1 below, lower default correlation implies higher spread (lower value) for the CDO tranche. But (here's where I was originally confused ) the hedge fund did not own/short the CDO equity tranche, it has sold credit protection on the tranche (aka, short CDS that referenced the tranche) so its "short" position is a short CDS which is synthetically long the underlying bonds. They lost on this written protection when the underlying bonds downgrade, in the same way they would experience a M2M loss on a short CDS that referenced the bonds directly (without the intermediation of a CDO, so to speak)
• With respect to the mezz, the hedge wasn't long (owning) the CDO tranche but rather it was long CDS that referenced the tranche (aka, buying protection on the tranche) such that lower default correlation did unexpectedly increase the value of the tranche (ie, lower spread per Arrow #2 below) but gives a loss to the long CDS that it references. I hope that is clarifying!

From https://forum.bionicturtle.com/thre...anagement-meissner-chapter-1.8207/#post-43073

I think @brian.field and @QuantMan2318 have explained this difficult idea brilliantly. I definitely agree that, as an exam matter, superficially the correct answer with respect to the Mezzanine (when we have no other information) is exactly what Brian says: "The effect in the Mezzanine Tranche is unclear."

@arkabose In regard to your specific observation, I think you are referring to Meissner's statement which references his Figure 1.7 (below): "In addition, the hedge funds lost on their long mezzanine tranche positions, since a lower correlation lowers the mezzanine tranche spread; see arrow 2. Hence the spread that the hedge funds paid in the original transactions was now higher than the market spread, resulting in another paper loss. "

• Re equity tranche: You can see most visibly here the typical dynamic of the equity tranche (Arrow #1; 0-3%): as correlation increases (ie, left to right on the x-axis), the spread is decreasing, so the value of the tranche is increasing (same point as question 502.3 above). Same as Brian's point about equity and, I assume, the QuantMan's positive convexity
• Re senior tranche: You can generally see this in the 15-30% tranche: as correlation increases, spread increases and value decreases.
• Re: Mezzanine: This is illustrated by Meissner's Arrow #2 (3 to 7% tranche) and you will notice that, typically, its plot is initially (at lower correlations) concave down (the slope is continually decreasing; as QuanMan says, negative convexity) but then shifts to approximately positively convex. So, even when referring to this tranche itself under these assumptions, we cannot say the Mezzanine tranche value is only increasing or decreasing. Rather, starting from zero correlation, as correlation increases, the Mezzanine value initially is acting more like a senior bond with increasing spread (decreasing value) but then shifts over the acting more like the equity tranche with decreasing spread (increasing value). I hope that helps! From https://forum.bionicturtle.com/thre...anagement-meissner-chapter-1.8207/#post-43073

 

[HHo0951]

Hi @HHo0951 Yea, I think it's already explained in the thread, to my satisfaction anyway. As I wrote, it's my opinion that(new emphasis mine)....

My additional evidence (aside from the coherent profit/loss narrative, is that here is Meissner is the first version of his book (with footnote 10):

... then here is the same section in his second edition:

Notice the directional (long/short) substance of his footnote did not change, but he decided to change the meaning of "long" versus "short" the CDO tranche. As I carefully discussed in my dissection of the case, it's very clear to me that the hedge funds with respect to the equity tranche were collecting premiums or "collect[ing] the high-equity spread" (even here he probably means, collecting the equity's high-spread, more imprecisions!). As these are synthetic CDOs, that means selling credit protection or short CDS.

Original thread here at https://forum.bionicturtle.com/thre...management-meissner-chapter-1.8207/post-47639

Hi David, thank you much for the clarification. It is reassuring to see the explanation from you and now I’m happy with the essence of the case study.

Thanks again!!