Stulz Ch 18 - Total Return Swap

[bpdulog]

Hi all,

Can someone explain why the bank gets paid whether or not the bank defaults or not? They receive $20 million, which is the difference between the value at maturity and the value of the debt at t=0. If the debt defaults, they get $30 million which is the difference betweeen the value at the time of credit event and the value at t=0.

I understand why the bank gets paid if there is a default, since they are the protection buyer. But why do they get the $20 million if the debt doesn't default?

 

[David Harper CFA FRM]

Hi @bpdulog Really great observation. My opinion is that Stulz is confused (I agree with you), and strictly speaking, I do not think he is accurately representing the TRS. I *think* what he intends to mean can be understood if we change the line "Suppose the principal is $100 million. In this case, the bank gets a payment at maturity of $20 milllion ..." to the following: "Suppose the principal is $100 million, which represents an appreciation in value of $20 million (from $80 million). In this case, the counterparty gets a payment at maturity of $20 million corresponding to the $100 million minus the initial value of $80 million to the bank." Confusion in engendered here firstly because he is almost suggesting the TRS is funded (i.e., with principal), but the TRS (like the CDS) is not funded. The bank here (the credit protection buyer) is just referencing the $100 par debt with the TRS. According to Hull, if the debt defaults, the bank is compensated for the $30 million loss with a $30 payment from the counterparty. Therefore, if $100 is a +$20 appreciation in value, then the bank pays the appreciation to the counterparty (he appears to have the bond pulling to par from 80 to 100, but that is value appreciation). So I agree with you, I think he's inaccurate here!

 

[irwinchung]

So in your notes, page 17 (on Stulz), it should be "B" (instead of "A") gets $20 mln...?

 

[David Harper CFA FRM]

Hi @irwinchung Yes, absolutely, I can't believe I didn't catch this in the recently revised note (embarrassing ). Thank you!

 

[David Harper CFA FRM]

@bpdulog and @irwinchung So we are going to replace the two paragraphs relating to Stulz total return swap with the following (cc @Nicole Seaman):

For example, suppose a protection buyer (A) owns a debt claim worth today $80.0 million that pays interest of $6.0 million every six months in the absence of default for the next five years; ie, the debt's face value is $100.0 million and its coupon rate is 12.0% per annum. If the issuer of the debt claim is not in default, protection buyer (A) pays the coupon interest every six months to the other party in the swap, let's call them swap counterparty (B). If the issuer fails to pay interest on any due date, then (A) pays no interest to (B), but in return receives six-month LIBOR on the notional principal of $100.0 million.

At maturity, the obligor repays the principal of say $100.0 million if not in default. Because this represents appreciation of $20.0 million from the initial value of $80.0 million, (A) pays the $20.0 million to (B). This is because (A) is transferring the total return of the reference to (B), so that just as (A) receives value depreciation, (A) pays value appreciation. Although realistically the appreciation will be paid along the way (at six month intervals) as the debt is marked to market (pulled to par, in this case). Instead, if the obligor is in default and only pays $50 million at maturity, (A) receives from (B) $80.0 million less $50.0 million or $30.0 million. In this way, per the total return transfer, (B) "keeps whole" (A) on the value. Thus, the total return swap guarantees (A) the cash flows equivalent to the cash flows of a risk-free investment of $80.0 million."