Is the call value equal to value of equity?

[Steve Jobs]

Hi,
In FRM1, it was S+c = Ke + p

In FRM2, I found 2 practice questions:
-In first question, the question gives the V for Value of firm, F for Face value debt, S for value of equity and then asking for p.
In the provided answer, the c is substituted with value of equity and p is calculated.


-In the second question, the value of c is given and then the question is asking for value of equity.
To calculate the value of equity, this formula used E=A-Dt which is understandable but not consistent with the answer provided for the first question; I though according to the first question c = value of equity.

Do you see the inconsistency?

 

[David Harper CFA FRM]

Hi Steve,

You have p.c. parity misstated, it should be : c+K*exp(-rT) = p+S;
I like to recall by noting the right-hand side is a protective put, so my memory device-phrase is "call + cash = protective put"

In Merton model, call price is equity (what can be confusing is that firm/asset value substitutes for stock price) such that:
c = value of equity, in Merton = V - D = p + V - F*exp(-rT) per p.c. parity, where V = c + D and D = PV(risky debt) < F*exp(-rT)
... more detail here http://forum.bionicturtle.com/threads/merton-model-a-summary-of-the-issues.5646/

I don't understand your paraphrase of the second question, thanks,

 

[Steve Jobs]

Apologies for the misstated formula.

Let me write it again:

In question 1:
-This is given: V for value of firm, F for face value of debt, S for value of equity (S is not Spot price anymore as it was in FRM1); and also r for risk free rate
-Asking for value of p
-Answer provided: p = S + Fe^(-r(T-t) - V, hence the c(value of call) in the call-put parity formula is substituted with S(value of equity), so the assumption is that c=S

In question 2:
-This is given: V for value of assets, F for value of debt, c for value of call, p for value of put; and also r for risk free rate,
-Asking for value of equity
-Answer provided: E(equity) = A - D(value of debt) and D(value of debt) = Fe^(-r(T-t) - p , hence it is not assumed that c=E(Value of equity) or S(Value of equity).

 

[David Harper CFA FRM]

Hi Steve,

Interesting comparison, but they appear compatible (maybe I am missing something):

• In first: S=c, such that per p.c. parity, p = c + F*exp^(-rT) - V; i.e., put-call parity where c is equity and V is firm's asset value
• In second: c = V - D = V - [F*exp^(-rT) - p] = V - F*exp^(-rT) + p; which is the same p.c. parity.

 

[Steve Jobs]

I might be missing something because I'm mentally little tired and haven't taken a break since long time, but this is how I see it:

In question, it's assuming that c=equity
In question 2, c is already given, if c=equity, then no need to calculate, the answer which is c is already given.

 

[David Harper CFA FRM]

As the answer mechanics to question 2 don't require c, it's hard to identify the issue unless you want to copy the entire question, i'll be glad to look at the entire question, thanks,

 

[Steve Jobs]

hmm...

 

[acebhavik]

Hi Steve,
Can you copy down the first question as well?

 

[acebhavik]

hmm...

 

[David Harper CFA FRM]

Okay, thanks ... this question was asked before at http://forum.bionicturtle.com/threads/merton-model-a-summary-of-the-issues.5646/page-3#post-25831

Steve Jobs you make an EXCELLENT observation: the question is indeed inconsistent. Under Merton Model, the value of the call option must equal (because it is, by definition) the equity value, and it cannot here be $1.00. What I wrote before was:

Hi Jonathan, you don't have asset volatility which you want to price the call. Without asset vol, you need to infer call from the put. However, at quick glance, the problem is that the value of the equity (under Merton) should equal the price of the Euro call option on firm assets with strike = FV of debt; i.e., equity would be the $1.00. But the $1.00 is internally inconsistent, the price of the call must be at least 180 - 107*exp(-5%); i.e., minimum value.

Notice you can also use put call parity: if the put is priced at 1.50, then the price of the call option should be the value of the equity = 180-107*exp(-5%)+1.5 ~= $79.72; i.e., c+K*exp(-rT) = S + c. Same result as what the question is looking for: risky debt = riskfree debt - put = 107*exp(-5%) - 1.50 with equity = asset - risky debt = 180 - [107*exp(-5%) - 1.50] = 79.72. But the question's assumption that the call = $1.00 cannot be true,

 

[Steve Jobs]

Hi David, acebhavik,

So I understand that in the exam, I should consider call value = equity value. Please advise.

 

[David Harper CFA FRM]

Steve Jobs - In the context of Merton, yes (i.e., your instinct at the top of the thread were good). In the case of Merton, and where the firm has only debt + equity (two classes: simple capital structure), the value (PV) of equity is equal to the value of a call option (denoted 'c') where the option has strike equal to face value of debt and the underlying is the firm's (asset = debt + equity) value; i.e., equity is a call option to exercise (pay the strike = debt face value) and if done, by paying off the debt, results in owning the entire firm. As noted above, it's clear to me that your question #1 has an error (internal inconsistency); the call is equity so it cannot have a price of only $1.

(on a minor caveat note, this is within the context of Merton, where firm value, V, replaces S in BSM, and firm equity value is given by c. An ordinary non-Merton BSM prices c as a function of underlying, S, of course, so we wouldn't otherwise say "call value = equity value"). Thanks,

 

[Steve Jobs]

David, I'll be optimistic and assume cal value = equity value in the exam for all questions whether merton or non-merton!

 

[David Harper CFA FRM]

Okay but the FRM is clearly able to distinguish between Merton model (i.e., where equity is the "derivative call" on the underlying firm's asset value) and ordinary run-of-the-mill BSM (i.e., where the derivative call is on an underlying asset price which is often the equity [stock] price). I just want to clarify, because I would never suggest candidates assume call value = equity value as a general rule. One lemon question does not warrant that simplification. (sorry, I am not trying to be a prude, I just don't want future readers to attach to "call value = equity value" without thinking about it) Thanks,

 

[Steve Jobs]

I just came back from a public lecture organized by a business school which I enjoyed very much and excited to share few points. The lecturer said that the last 2 paragraphs of Merton's paper(or all the 3) are the most important text he ever read and it's that the equity owners with limited liability are like the owners of call option on assets in which the downside is limited and the more risk taken, the higher the up-side would be, pointing at the level of debt, banks 10% CAR and their attempt to minimize it, zero value of equity of Northern Rock just before its financial crisis, etc.

 

[cdbsmith]

Okay but the FRM is clearly able to distinguish between Merton model (i.e., where equity is the "derivative call" on the underlying firm's asset value) and ordinary run-of-the-mill BSM (i.e., where the derivative call is on an underlying asset price which is often the equity [stock] price). I just want to clarify, because I would never suggest candidates assume call value = equity value as a general rule. One lemon question does not warrant that simplification. (sorry, I am not trying to be a prude, I just don't want future readers to attach to "call value = equity value" without thinking about it) Thanks,

David,

I'm struggling with my focus today, so I've been reading the forum hoping to regain some energy and focus. I mean, these are the dog days of the exam prep process, and it is very difficult to stay focused after working 10+ hours today.

That said, I stumbled upon this thread, and am just amazed at the direction it took. I mean, I wasn't sure if I should LOL or frown with bewilderment. The notion that "call value = equity value" (even in relation to the Merton Model) makes no intuitive sense whatsoever. As far back as I can remember in the earliest years of my life (in my college finance courses), I learned that calls (and puts) result in asymmetric payoffs. That is, the worst outcome is losing the cost of the call, and the best outcome is the difference between the current stock price and the exercise (strike) price, minus (net of) the cost of the call. That fact alone precludes any chance of a call's value equaling it's underlying asset.

I will say this, many finance authors (or thought leaders) have relied too conveniently on the put-call option concept to explain some the more esoteric financial concepts, in my opinion. The Merton Model is a good example. Equating a stock to a call purchased from the debt holders can easily add more confusion to an already complex concept, and is a mistake in my opinion. That said, I understand why the put-call option comparison is so often used. In the Merton Model, it clearly demonstrates that the holders of equity (call option) have limited downside (i,e., the cost of the equity) and unlimited upside (i.e., Max, equity value - debt value, 0). In other words, if the firm liquidates, the equity holders will let their "call option" expire un-exercised as the firm's value has fallen below the value of its debt. This will leave debt holders fighting for recovery during the bankruptcy process while the equity holders walk away from the investment losing no more than the amount tendered for the stock (call).

Most folks understand a call to be option to buy stock (or underlying asset), which is correct. The problem with the Merton Model is that the stock (equity) becomes the call and the debt becomes the underlying, which is difficult to process. I believe that is the reason many folks may struggle with the Merton Model when first introduced to it, unless a better comparison is used (or more effort is put forth) to explain it.

Anyway, that's my two cents on the matter. I think I may have some energy now.

Back to the books, oops, study notes....

 

[David Harper CFA FRM]

Hi @cdbsmith Thanks for sharing, great point of view! I think you mean "The problem with the Merton Model is that the stock (equity) becomes the call and the debt becomes the strike, which is difficult to process.?" (One of us is illustrating how confusing it is, it could be me! ).

I happen to totally agree with you that many authors, in my opinion academics especially, over-depend on BSM/Merton (it is elegant, there is no denying that!). Here is one of our images:

My favorite part of your post is "I think I may have some energy now."

 

[cdbsmith]

Thanks David!

My mind was saying that the debt (e.g., bond) is the underlying and its face value is the strike, but I didn't clarify that in my reply. Thanks for helping out!

I definitely like the comparative illustration you provided as it clearly demonstrates how the Merton Model is similar to a call. Unfortunately, we don't see illustrations like yours in the text books. That's why I made the comment that financial authors should put more effort in explaining complex financial concepts.

To digress, I have a quick question: I've been reading through the Op. Risk material and that stuff is totally dry. I mean, it's just pure text. What can I expect to see on the FRM 2 exam in this area? I'm asking because I need to gauge how much effort I need to put forth in memorizing it.

Thanks!