Tranching Numerical

[monsieuruzairo3]

Hi @David Harper CFA FRM CIPM

Following questions are a part of 4 questions from Structured finance BT

130.1 For these first four questions, assume a firm issues only three capital claims: zerocoupon
senior debt with face value of $300 million; zero-coupon junior debt with face value
of $500 million; and $200 million in equity. What is the credit enhancement provided to the
senior debt?
a) $200 million
b) $300 million
c) $500 million
d) $700 million

Fairly simple

But problem in next

130.2 The position of the investor in the senior debt is most similar to:
a) Long a call option on the firm’s assets with strike of $800 million
b) Long a riskless loan of $300 million plus (+) short a put on the firm’s assets with
strike price of $300 million
c) Long a riskless loan of $500 million plus (+) short a put on the firm’s assets with
strike of $800 plus (+) long a put on the firm’s assets with strike of $300 million
d) Long a call option on the firm’s assets with strike of $200 million

The answer given is B
Payoff= 300(1+Rf) -300+Value of firm

Not sure how does it equate to a position in Senior debt which has zero payoff till 700 mn

Also I was not able to fiugre out the rest two questions but probably if you can help me understand this one I might be able to crack the rest two

KR
Uzi

 

[Roshan Ramdas]

Hi @David Harper CFA FRM CIPM

Following questions are a part of 4 questions from Structured finance BT

130.1 For these first four questions, assume a firm issues only three capital claims: zerocoupon
senior debt with face value of $300 million; zero-coupon junior debt with face value
of $500 million; and $200 million in equity. What is the credit enhancement provided to the
senior debt?
a) $200 million
b) $300 million
c) $500 million
d) $700 million

Fairly simple

But problem in next

130.2 The position of the investor in the senior debt is most similar to:
a) Long a call option on the firm’s assets with strike of $800 million
b) Long a riskless loan of $300 million plus (+) short a put on the firm’s assets with
strike price of $300 million
c) Long a riskless loan of $500 million plus (+) short a put on the firm’s assets with
strike of $800 plus (+) long a put on the firm’s assets with strike of $300 million
d) Long a call option on the firm’s assets with strike of $200 million

The answer given is B
Payoff= 300(1+Rf) -300+Value of firm

Not sure how does it equate to a position in Senior debt which has zero payoff till 700 mn

Also I was not able to fiugre out the rest two questions but probably if you can help me understand this one I might be able to crack the rest two

KR
Uzi

Hi,
F - Senior Debt face value
V - Value of firm at time of debt maturity
The payoff to the senior debt holders at the time of debt maturity = V - max (K-V, 0)
The highlighted part matches the payoff from a put option.
The present value of a senior debt holders position can be seen as a combination of risk free investment (V) and short position in a put option - max (K-V, 0)
Thank you

 

[southeuro]

conceptually, my 2 cents: senior tranche gets the value of the firm unless losses eat up the junior tranches. If that happens it'll eat into the gains accruing from the risk free investment (V). How much will it eat into it? as much negative distance there will be between K and V, provided that it (K) is beyond V -- hence the max (K-V, 0). Hope this helps.

This set of questions also gave me a hard time to crack. I think they are one of David's finest set of questions

 

[Roshan Ramdas]

conceptually, my 2 cents: senior tranche gets the value of the firm unless losses eat up the junior tranches. If that happens it'll eat into the gains accruing from the risk free investment (V). How much will it eat into it? as much negative distance there will be between K and V, provided that it (K) is beyond V -- hence the max (K-V, 0). Hope this helps.

This set of questions also gave me a hard time to crack. I think they are one of David's finest set of questions

Apologies,...I made a mistake with the payoff to senior debtholders.
Should be -> F- max (F-V, 0)
The equation as such simply talks about the payoff received by senior debt holders and the fact that :
They max payoff they receive is par (when firm value (V) is greater than par value (F))
The min payoff they receive is firm value (when firm value (V) is less than par value (F))
Thank you

 

[hamu4ok]

I thought this question is really about Merton model (or the version in Stulz with subord debt). Under Merton Model, the Debt is equal to PV of zero-coupon bond with par value being equal to value of Debt (=Long a riskless loan of $300 million) + short position in put for company assets (= short a put on the firm’s assets with strike price of $300 million)
Dt = D * exp[-rt] - put [X=D]

 

[Roshan Ramdas]

I thought this question is really about Merton model (or the version in Stulz with subord debt). Under Merton Model, the Debt is equal to PV of zero-coupon bond with par value being equal to value of Debt (=Long a riskless loan of $300 million) + short position in put for company assets (= short a put on the firm’s assets with strike price of $300 million)
Dt = D * exp[-rt] - put [X=D]

Its all one and the same. F- max (F-V, 0) is payoff at time of debt maturity.
Present value = F*exp(-rt) - value of put option

 

[David Harper CFA FRM]

Here is the source question and where I elaborated on 130.2 at https://forum.bionicturtle.com/threads/l2-t6-130-tranching-and-subordination.4253/#post-26405

i.e.,

in regard to 130.2: this illustrates the (Rene Stulz-ish) concept that, in a simple two-class capital structure, the payoff (and value) of risky debt = riskless debt - put option on firm's assets (with strike equal to face value of debt). High testability. Here the senior debt has face value of $300 MM, such that if, at the end of the period, the firm's asset value is greater than, or equal to, this $300, the senior lender gets repaid. But, say, the firm asset value drops below the "default threshold" of $300, to something like $200. Then the senior lender can only get repaid $200. This is the same payoff as as if the senior lender received the full $300 as "riskless" repayment but, at the same time, makes a payout of $100 due to WRITING a put with strike of $300. As the payoff of the risky loan is given by [Firm's Asset Value(t), $300] and the payoff of a riskless loan plus a written put is given by $300 - MAX[0, $300 - Firm's Asset Value(t)], we have:

• MIN[Firm's Asset Value(t), $300] = $300 - MAX[0, $300 - Firm's Asset Value(t)]; i.e., risky 300 = riskless 300 - put[K=300]

In regard to 130.3, the concept is extended. In this case, the junior debt holder is long a riskless $500 loan plus long short a bear spread (i.e., capped upside due no gain above repayment and capped downside due to the equity tranche that absorbs the last $200).
... see note below. The sale of a put option with strike = 800 plus the purchase of a put option with strike = 300 can be characterized either as long a (put) bull spread or short a (put) bear spread.

• Recall the capital structure is: 300 senior > 500 junior > 200 equity, and imagine these outcomes:
• If firm asset value declines from 1,000 to 800, equity absorbs the entire loss. At firm value = 800, junior debt is repaid in full; equivalent to riskfree 500 plus two unexercised options.
• If firm asset value declines to 700, senior debt is repaid in full (300) but only 400 remains for junior; equivalent to riskfree 500 - $100 paid on written call with strike of 800 (i.e., -MAX[0, 800-700]) with long put unexercised as MAX[0, 300-700] = 0
• If firm asset value declines to 100, senior debt is paid 100 and nothing remains for junior debt; equivalent to 500 - MAX[0,800-100] + MAX[0,300-100] = 500 - 700 + 200 = 0
• Similarly, if asset value declines to zero, junior debt also wiped out; equivalent to 500 - MAX[0,800-0] + MAX[0,300-0] = 500 - 800 + 300 = 0. I hope that explains!

 

[monsieuruzairo3]

Hi @David Harper CFA FRM CIPM

Thanks for the explanation

On my final review now

Here's a short doubt on a schweser question

Which of the following is the typical way an asset manager employs interest rate swaps in subprime securitized
pools?
A) Long-term, receive fixed swap.
B) Short-term, pay fixed swap.
C) Long-term, pay fixed swap.
D) Short-term, receive fixed swap.

Answer is A)

I am of the opinion that it could be B). Since 2-3 Years initially securitized pool is going to generate fixed rate coupons as the mortgage is 2/28 or 3/27. So asset manager may want to swap this fixed rate and receive floating in exchange

What do you think?

KR
Uzi