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# Equity tranche spread wrt correlation

#### afterworkguinness

##### Active Member
Hi,
I'm having trouble reconciling the effect of an increase in default correlation between the Meissner and Malz readings. To me they sound like they are saying the opposite of each other, so I must be missing something.

Meissner figure 1.7 shows for the equity tranche as default correlation in the underlying increases, the spread decreases.

Malz shows that the equity tranche likes correlation and ceteris paribus an increase in default correlation increases the value of the tranche.

EDIT:

Further reading is hinting to me that I am missing something about the meaning of spread here. Meissner says hedge funds shorted the equity tranche to collect the large spread. So then spread must not be the same as the value of the tranche, but the cost to invest in the equity tranche?

Last edited:

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @afterworkguinness

Meissner graphs spread, while Malz is likely graphing value. For the equity tranche, as default correlation increases the value of the tranche value increases which corresponds to a decrease in the spread. (To help with this, think about a simple bond: an increase in the spread implies an increase in yield which implies a decrease in price; or a decrease in price implies a higher yield and higher spread above risk-free rate). I hope that helps!

#### afterworkguinness

##### Active Member
Hi @David Harper CFA FRM CIPM ,
Thank you very much for replying so quickly and on a Saturday none the less; greatly appreciated!

I am left with another question though after reading your reply and the linked post... A naïve question, but I'm not understanding the role of a spread in a secularization. I thought it was related to the equity tranche's internal rate of return over a risk free rate, but reading your post it seems like I'm quite wrong on that.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @afterworkguinness no worries! There are many details and definitions involved here but your thought is conceptually true! There are different definitions of spread (Malz 7.1 gives a few). But as an anlogy to But we can use a single bond analogy. If a 5-year zero-coupon $100 face bond has a yield of 4.0%, it's price is about 100*exp(-4%*5) =$81.87; if the riskfree rate is 2.0%, we can say the spread is 2% because 2% risk free + 2% spread equals 4% yield. (And YTM is the IRR, so 4.0% is the IRR). Now, assume the bond becomes riskier. It's coupon's (or lack therefore) do not change, it's price lowers. Maybe it's price decreases to $77.88 to reflect a higher spread of 3%, as in$77.88 = 100*exp[-(2%+3%)*5]. Keep in mind I could use a coupon-bearing bond. So the dynamic is:
• Bond's promised cash flows don't change
• At some point, perception changes and bond is deemed riskier (default probability increases)
• Price decreases
• Given same promised cash flows, yield increases which given the same benchmark (riskfree, LIBOR) is necessarily an increase in the "spread"
Securitizations vary and spread definitions vary. But structured products generally issue liabilities (debt) and sell an equity tranche to investors. Senior debt might expect floating coupons of libor + 1% (notice that's just a bond) and junior debt might expect libor + 3%; equity might receive the excess cash flow (aka, excess spread, Malz chapter 9 details on whole structure). But investors can also be, for example, sellers of credit protection such that they are receiving a fixed spread in exchange for a promise to pay in the event of default. If the risk of a tranche goes up, the value (price) goes down, and the spread (which has several definitions) goes up (and the IRR goes up). If the investor are receiving fixed spreads, the market spread goes up (i.e., new investors would require higher payments) which is a loss in the value of the position. I hopes that helps with the high-level relationship.

#### afterworkguinness

##### Active Member
Hi David,

A

I can see when you are selling credit protection in exchange for receiving a fixed spread, how an increase in the risk (default correlation in this case) will result in the spread for new investors needing to be higher and thus the price (value) of your position dropping. This sounds like a bond or position in a CDS index. Long CDS index = sell protection = long credit risk

I can't reconcile though what the spread is in the context of a long CDO equity tranche. The equity tranche doesn't receive a fixed spread over LIBOR or another reference rate. They receive the spread between the income on the collateral and the principal + interest payments to the debt holders (sr and mezz tranches) (forgetting about the O/C account for simplicity).

If the default correlation goes up, causing the price of the tranche to go up, what spread is decreasing? Is it the spread between the income on the collateral and the principal + interest payments to the debt holders ? I can't see that making sense so it must not be that. Put in a naive way... spread over what? I've gone through Malz 7.1, but I can't fit what's there to my understanding of the equity tranche of a CDO because they don't have a fixed coupon.

B

One last thing, Meissner says "Shorting the equity tranche means being short credit protection or selling credit protection, which means receiving the (high) equity tranche contract spread". I thought if you are long one of the tranches of a CDO you are selling credit protection because you are buying the credit risk off of the originator?

#### hmntgpt14

##### New Member
Hi sir, can you please explain me.
IMT Bank have contacted a group of CCFA students to help in securitizing the loan portfolio. IMT Bank have mandated that they need an AAA senior tranche. As per Credit Rating organizations criteria, an Equity Tranche of $15 Mn is required. An excess spread of 85 bps is also required. IMT Bank suggests that they are happy to have BBB rating for the Junior Tranche. As per market data, an AAA rated bond could be issued with a 9% coupon and a BBB rated with 12% coupon. Calculate the amount to be issued for Senior and Junior Tranche Credit Enhancement Coupon Amount Issued Excess Spread N/A 85 Bps Equity Tranche N/A$150,00,000
Senior Debt - AAA 9.0% ?
Junior Debt - BBB 12% ?

How to calculate amount issued in senior debt and junior debt ?

Thanks

#### hmntgpt14

##### New Member
Hi sir,
One more question i want to ask.

The central bank which regulates IMT Bank, have passed a resolution that organizations should start following the Basel III regulations for capital requirements for loan portfolios. IMT Bank’s risk management team comprises of CCFA students who are required to calculate the regulatory capital. Calculate the total Risk Weighted Assets for credit exposures of IMT Bank. Assume that there was no true sale of loans in the securitization deal. Use Internal Risk Based method.
how to calculate the regulatory capital ?

Thanks

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @hmntgpt14 (cc: @Nicole Manley ) I don't recognize these questions. Can you share the source, please? I hesitate to spend time on questions that may not be trustworthy; for example, you haven't shared enough information in your second question (surely it is incomplete). Thank you!

#### Vishal Singh

##### New Member
Hello Sir,

Question 1
Part a)
Consider the following assets present in loan portfolio of IMT Bank Ltd, all the assets below are
mortgage loans.
Exposure 1 Exposure 2 Exposure 3 Portfolio
Commitment $100,000,000$120,000,000 $150,000,000 Outstanding$50,000,000 $25,000,000$10,000,000
Internal risk rating BBB+ A AA
Maturity 1 year 3 years 10 years
Type Non-secured Secured Senior Secured
Usage Given Default 57.83% 45% 40%
Expected Default on Portfolio 5.48% 3.26% 1.35%
Standard deviation of EDF 23% 18% 12%
Loss given default 50% 35% 10%
Standard deviation of LGD 25% 20% 13%
Adjusted exposure on default $78,915,000$67,750,000 $66,000,000 Expected loss$2,162,271 $773,027.50$89,100 $3,024,398.5 Unexpected loss$10,098,110.92 $4,870,142.15$1,254,568.69 $11,276,496.67 Risk Contribution (RC)$9,092,406.34 $2,267,215.99 -$83,125.66 $11,267,496.67 Coupon 15% 10% 5% How to calculate total coupon of the portfolio Correlation Exposure 1 Exposure 2 Exposure 3 Exposure 1 1 5% -15.00% Exposure 2 5% 1 -10.00% Exposure 3 -15.00% -10.00% 1 IMT Bank have contacted a group of CCFA students to help in securitizing the loan portfolio. IMT Bank have mandated that they need an AAA senior tranche. As per Credit Rating organizations criteria, an Equity Tranche of$15 Mn is required. An excess spread of 85 bps is also required. IMT Bank suggests that they are happy to have BBB rating for the Junior Tranche.
As per market data, an AAA rated bond could be issued with a 9% coupon and a BBB rated with 12% coupon. Calculate the amount to be issued for Senior and Junior Tranche

Credit Enhancement Coupon Amount Issued
Equity Tranche N/A \$15,000,000
Senior Debt - AAA 9.0%
Junior Debt - BBB 12%

Part b)
The subprime mortgage crisis have hard hit IMT Bank, all the three exposures have defaulted and bank could recover only 40% of the portfolio. Calculate,
Actual Loss of the portfolio:
Loss Absorbed by all Credit Enhancements available:

Equity Tranche:
Junior Tranche:

Part c)
Assuming that one such method which the new director agreed to is, buying CDS on the portfolio, calculate the risk neutral/fair price credit spread that IMT Bank would be ready to pay for the portfolio.