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Stulz chapter 18

Hend Abuenein

Active Member
Hi David,

In your T6 notes page 97, there's a 3D chart that plots relationship between credit spread, time to maturity, and interest rates.

I can see that the widening in CS only took place at the region of much deeper increase in T happened. But chart shows that CS is not affected by interest rate increase.

1- If T is held constant, what is interest rate's effect on CS?

2- Schweser's note's explanation on this is a bit confusing:
If interest rates increase, the expected value of the firm will increase, which decreases risk of default, and this narrows CS.

Why assume that a firm's risk of default is solely dependent on the firm's expected value?
I understand that under Merton's model firm value predicts its repayment, but what they're saying is that if interest rate goes up, a firm will be more likely to repay its debts regardless of all else going on in the firm or the economy that could be reducing firm value.

Do you agree with this?
I feel like this points at Merton model's disadvantages of non realistic assumptions.
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi Hend,

No, I don't agree with it, I agree with you. I don't think i could agree more with "I feel like this points at Merton model's disadvantages of non realistic assumptions."

This is all based on Stulz Chapter 18, which has proved to be very confusing over the years. Please note a difference between:
  • Higher interest rate --> higher firm value. I don't agree with this even within the model; the only legitimate basis for this (to my thinking) can be in the initial simultaneous solution of firm value and volatility. This needs to be explained before I would believe this; it may be correct, but i think it must be in an esoteric way.
  • Merton's "distance to default" says something far more credible: that a higher expected future firm value implies a lower probability of default. It replaces the Rf rate with the firm's drift (expected return). It says, given a a known FACE value of debt, the greater the firm's value today and/or the greater the expected growth in the firm's value, the less likely is default. Notice that riskfree interest rate enters none of this directly!
Then there are Merton-based statements about the debt spread that invoke option pricing:
  • What's not Merton is the dangerously simplistic: S = -1/T*LN(D/F) - Rf. This is instructive for simply solving for the spread (S) in a zero-coupon bond: D = F*EXP[-(Rf+S)T]. In this, the simplest of all possible "models," the spread is a directly decreasing function of the riskfree rate; i.e., + 1% RF --> -1% spread. This isn't Merton, it's as unrealistic as it is simple to follow.
  • The Merton is a less simple model, in the case of senior debt: risk debt = riskless debt - put option on the firm, such that an increase in the risk free rate will decrease[value of riskless debt] and decrease[value of the put], but the former will tend to overpower the latter such that the with an increase in the rate, the value of risky debt goes down (as we'd expect) and the spread consequently increases.
  • Similarly, we can infer for the other Merton equality: value of risky debt = firm value - equity[call option], where an increase in rates increases the value call option and, for a given firm value, similarly lowers the value of the risky debt. Note: both of the last two assume a firm value, so they are not evidence to support the idea that higher Rf rate --> higher firm value. All we get from these last two is a fancy variation on: higher yield --> lower bond price.
About any of these, we have two problems (IMO):
  1. To your point, they are very simple models in the sense that, regardless of the math, a limited number of factors are included; e.g., inflation is excluded;
  2. Even if the models are roughly okay, Stulz' applications are generally ceteris paribus: we change one variable and assume the other inputs are unchanged. For example, if the interest rate increases, Stulz use cases generally assume firm value is constant (as opposed to Schweser's statement; or even as as opposed to a drop in firm value). Unfortunately, the risk-free rate has a complicated effect on the other inputs; the risk free rate is not just exogenous.

    ...
    even with S = -1/T*LN(D/F) - Rf; if we lower the Rf, we should also lower the (D). Arguably, we are immediately circular :eek:
My agreement with you, then, is sort of doubly so: i think they are naive use cases of naive models.

Even if we could "fix" Stulz' assertions so that the multiple/feedback dynamics are captured, we would still fall a long way from reality (maybe too far, that's a model question). There are layers of reality here. First, traditionally increasing the rate implies discounting firm cash flows at higher discount rates and therefore LOWERING firm value, not increasing it. Second, interest rate interface with inflation expectations, which are realistic inputs into firm value.

Now, the really challenging part of Stulz 18 is that he commingles these model-based assertions with citations from empirical studies, in some cases, where the empirical studies contradict. So, my view is the first thing to do is keep straight the difference between:
  • A simple model and what happens in the model when we change a riskfree rate. Instructive? Yes. Realistic enough? who knows
  • The empirical studies that, often, don't put forth any model, they just cite an observed correlation (which in turn depend on the sample)
Sorry for the length! You can see why I try every year to boot the Stulz readings from the FRM (we got rid of Chapter 2, just two more to go, for the sake of clarity and sanity, and to cure a bad case of Merton myopia :eek:)
 

Hend Abuenein

Active Member
...
  • What's not Merton is the dangerously simplistic: S = -1/T*LN(D/F) - Rf. This is instructive for simply solving for the spread (S) in a zero-coupon bond: D = F*EXP[-(Rf+S)T]. In this, the simplest of all possible "models," the spread is a directly decreasing function of the riskfree rate; i.e., + 1% RF --> -1% spread. This isn't Merton, it's as unrealistic as it is simple to follow.
  • The Merton is a less simple model, in the case of senior debt: risk debt = riskless debt - put option on the firm, such that an increase in the risk free rate will decrease[value of riskless debt] and decrease[value of the put], but the former will tend to overpower the latter such that the with an increase in the rate, the value of risky debt goes down (as we'd expect) and the spread consequently increases.

...For example, if the interest rate increases, Stulz use cases generally assume firm value is constant (as opposed to Schweser's statement; or even as as opposed to a drop in firm value). Unfortunately, the risk-free rate has a complicated effect on the other inputs; the risk free rate is not just exogenous.

Dear David,
Thank you so much...that wasn't long...it was VERY GOOD!

If you wrote like this in your notes, I promise you not I nor any other FRM candidate would need any of the other competitors' solutions, because the depth and extent you take a concept to is really the essence of the learning experience. Not to pass the exams, but to master what we're learning.

I really wish you write notes the way you answer questions in the forum, with this same eagerness to teach and expalin...and am sorry to tell you that I ordered Shweser's notes only because I saw how skimmed your notes were :(. And I'm not talking page counting here, I don't care for that, I'm talking about not stating ideas before and after what you're trying to explain the way you do here on the forum.
In your notes, you seem to assume reader/candidate has already been through the detailed assigned reading and only needs to be reminded of the core concepts, you only use short bullet points, no explanatory elaborations. But here in the forum, you not only assume candidate needs to be presented to idea A, but also go a step farther and build on it idea B (which sometimes I wouldn't know existed, and definitely was too ignorant to ask about :confused:) that really helps in reenforcing perception and retention of both ideas.

Sorry for long answer, but I just couldn't help it. I've had it on my mind for a while now how it seems like the person who writes notes and the one who answers in the forum are seemingly two different people :) because THIS HERE eagerness to explain and share knowledge is not evident at all in the notes.

Thank you for all your efforts.
 

Hend Abuenein

Active Member
Under the same subject please,

(according to Shweser) Stulz says that for very low rated debts, longer T means a narrowing in CS

Even if we restrict effect of long T on D AND assume T won't change RF, this sounds contra intuitive to me.

Is there an underlying assumption that if firm remains of value despite very low rating, and is expected (for reason I don't understand here) to survive until T, then the only way its value is going is up, resulting in a lowered PD?

I see this as lacking for grounds because a low rated firm could go on for years being low rated with PD constantly high through T. So why do you think was the generalization made by Stulz about low rated firms?

Thank you
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi Hend,

The first "problem" with such assertions is, they don't clarify the basis for the relationship:
  • Is it an empirical observation? Is so, we can ask (eg), what sample/horizon
  • Is it a model? If so, which model
Since this is Stulz, and we know his unhealthy obsession is Merton, it's a safe bet he's relying on Merton:
risky debt = riskless debt - put option on the firm (T)

In most cases, an increase in (T) will increase the value of the put, and therefore decrease the value of the risky debt (and therefore increase the CS)
However, the exception is a deeply in the money put (a deeply in the money Euro put is unique for its possibility of a positive theta! ... we can connect this to Hull's Greeks: options have negative Thetas with the possible exception of a deep ITM put and, if the debt is extremely risky, that is what we've got!), a deep ITM put can here have positive theta such that put value decreases with longer maturity and value of risky debt increases (narrowing the CS)

I guess the intuition, which I am not defending, is something like: if you held a bond where the company is insolvent (i.e., face value of bond > firm's asset value; i.e., K >> S, deep ITM ), and it's due soon, you think it's virtually worthless. But, if you give them more time, it actually becomes more valuable due to the optionality.

Finally, I did read your point above, about the Study Notes. I appreciate the feedback. I have a complicated reaction and, as I am under deadlines (as usual, while giving forum support), I can't reply with all of my thoughts but just briefly:
  • To some degree, I think you are correct and we should endeavor to get the best stuff into the notes
  • On the other hand, the notes are for ruthless summary, some of the nuance is not necessary to the notes purpose
  • Much of the nuance and insight in the forum does, in fact, manifest in the videos and the practice questions; and, eventually we try to get into the notes
  • It's true, the questions and videos get more attention than the notes. I am not going to stake our business on study notes, it would be stupid.
  • Some customers will just never be satisfied: if we put more effort into one aspect, they will ask for something else. We can't please everybody all of the time. These tend to be the same customers who don't realize everything takes time and resources. The same ones who constantly ask for status updates. Maybe we don't want these customers.
  • I have been criticized for spending too much time in the forum (e.g., I answered your question last night instead of my plan to watch Adele and the Grammy's ... it's okay, i recorded her!) ... but I like to chat about the material, it is how i learn. I did not start a forum because I am an expert in finance, rather i become more expert by engaging with my forum. Oops, I have revealed that my self-interest is also a factor :eek:
  • It all requires time and effort and resources, every year I try to look at the feedback and adjust accordingly; e.g., admittedly i have increased my time allocation to deep quality and quantity of practice questions (and mock exams, which will arrive when they arrive, so this is not an invitation to receive a request on their status).
That's just the quick version of my instant reaction, unfiltered because i am under extreme deadlines (as you know). I copied it to Suzanne because we take the feedback very seriously. Thanks!
 

6Mil

New Member
I don't see any practice problems for Stulz 18. Am I missing something? Thanks in advance...
 

Hardlearner

New Member
Hi Suzanne,

unfortunately I can't find P2.T6. Credit Risk Measurement & Management (Reading 40) on your site. Did you remove this document? How can I find the study notes concerning Stulz, Chapter 18?

Thanks a lot!
 

Hardlearner

New Member
Hi Suzanne,

up to now I can't find neither study notes nor practice questions concerning Stulz, Chapter 18.
What are your plannings concerning the release?
Thanks a lot!
 
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