Question for a 2007 exam problem

[[email protected]]

Hi David, could you please help me with this problem?
Synthetic collateralized debt obligation (CDO) tranches are structured securities whose performance depends on the number of defaults in a portfolio of credit default swaps (CDS) .A typical synthetic CDO with an equity, mezzanine, senior tranche, and super senior tranche is shown below. Each of the tranches receives a contractual spread in exchange for absorbing losses in the portfolio. For instance, the equity tranche receives a 1,250 bps running spread in exchange for absorbing losses form 0% to 3%.

CDO tranche size and structure
Tranche Size Notional (in millions USD) Spread over LIBOR
Equity 0%-3% 3% 30 12.50%
Mezzanine 3%-6% 3% 30 2.50%
Senior 6%-9% 3% 30 0.90%
Super Senior 9%-100% 91% 910 0.20%

Which of the following statements is correct?
a. The equity tranche holder is short a call option with a strike price of USD 30 million written on the value of the portfolio of CDS.
b. The super senior tranche holder is short a put option with a strike price of USD 90 million written on the value of the portfolio of CDS.
c. The mezzanine tranche holder is short a put option with a strike price of USD 60 million written on the value of the portfolio of CDS.
d. The senior tranche holder is long a put option with a strike price of USD 60 million written on the value of the portfolio of CDS.

The answer is d. I understand that the senior tranche holder is long a put option. But why is its strike price 60 million? I think it should be (1000 - 60 = 940 million)?

Thanks a lot!

 

[David Harper CFA FRM]

Hi ldcn, you can almost visualize the tranches if you reverse their sort order. Equity is "on the bottom" and detaches at $30, which is that attachment of the Mezz which detaches at $60 ... the 910 super senior is "at the top." The senior tranche is subordinated by 30 + 30; it's "safe" until loss exceed $60 and breach its own attachment at $60.

(I think i say your point, you can re-express the option analogy such that the strike is a function not of losses but rather of principal intact ... in a way, i think your answer is quite natural! So this may be an issue more of semantic convention frankly ... the option is after all an analogy and yours has an advantage: losses exceeded 60 correspond to a DROP in 1000 - loss. The more i think about it, the more we could argue your analogy is better, i think, but you get the point)

Thanks, David

 

[[email protected]]

Thank you, David. I think about this again. 940 is not a correct strike either if it's long a put. I understand the answer better now. You are always helpful!

 

[AG]

David,

one thing here... should not the positions of senior, mezzanine tranche holders have two options, one long-one short, so that the maximum gain is capped at 30.

AG

 

[David Harper CFA FRM]

AG,

Great point, the senior tranche is really a bear/bull spread ... now that you mention it, isn't the answer actually wrong?

What i mean is, let's keep with the strike of $60 million, in which case, IMO (let me know if you disagree?), the senior position is:
short call option with strike @ 60, plus
long call option with strike @ 90
... (d) is incorrect because it's a short not a long: the payoff is the "capped" on the upside with the riskfree + margin yield, with downside. This is writing an option not long an option.
To stress test this:
If defaults = 30, both options unexercised and net premium collected (passes test: yield received)
if defaults = 70, short call exercised
if defaults = 100, both exercised, but to to AG's point, loss capped at (90-60)

Or, if we want to reference the underlying portfolio, I could also see (equivalently):
short put option at $940 (i.e., portfolio value)
long put option at $910
e.g., "collect premium" if defaults don't reach attachment and portfolio value is 970

In this way, the senior tranche is like a bear spread (former) or a bull spread (latter) ...

Thanks for your follow-up AG! ... until somebody corrects me, I am thinking this answer is incorrect for saying "long @ 60"

Thanks, David

 

[[email protected]]

Hi David,
I am confused. For the senior tranche holders, I think they believe the senior tranche would not be affected by loss, that is, the loss would be below 60 and the portfolio value would be above 940?

 

[David Harper CFA FRM]

Hi ldcn,

Agreed, say the losses are only 40 (i.e., equity tranche wiped out, 10 of mezzanine) such that senior incurs no losses, then portfolio value is 960. I'm saying that is either (depending on how you characterize the reference)

• short call with strike at 60: option doesn't get exercised, senior noteholder "collect their premium" --- losses need to rise above strike for senior notes to suffer (i.e, have the option exercised)
• Or, short put with strike at 940: as value (960) is above strike, put also not exercised ... value needs to drop below strike for put to be exercised

the long position (in the answer), on reflection, doesn't make sense to me for the senior note-holders: I buy the equity tranche as long an option, but the senior notes are assuming downside risk for capped yield (a short option position, I don't think the put/call is terribly important myself, but i do think the short position is important).

Thanks, David

 

[[email protected]]

I see. Thanks. I agree. It should be a short call at 60 instead of a long put.But why does the senior tranche holder have two options, short call and long call, instead of one short call only? Where is the long call from?

 

[David Harper CFA FRM]

That's AG's observation. The senior tranche has a width of 30 (attach 60, detach 90). From losses of 60 up to 90, senior tranche is losing principal (i.e., the written call option gains intrinsic value). But at losses of 90, the senior tranche is wiped out. Losses capped at 30 (width of tranche). Say losses are 100. Senior tranche is not exposed for the additional 10, this is then like a bear spread:

• the written call at 60 is exercised for loss of 40 (100 - 60)
• the long call has gain of 10 (100 - 90). Net to senior noteholder = +10 - 40 = -30 loss.

Any loss of principal above 90 will always produce a loss, on the bear spread, of 30. If X is losses to principal above 90, then, to senior noteholder:

• loss of (X - 60) +
• gain of X - 90.
  
  For X > 90, senior noteholder total = (X-90) - (X-60) = -90 +60 = -30; i.e., tranche wiped out

 

[[email protected]]

Got it. Thanks a lot!

 

[AG]

Glad to help.

AG