bond yield and interest rates

[aditya]

dear david,
i have always find your way of clearing concepts useful and suggested to many of my frens abt you , i was about to buy your notes but
due to my illness (ulcerative colitis) i had to leave the job and then i could not buy your notes.........

here i am messed up between two concepts....



1 ) if interest rate increases then expected value of the firm also increases (value of firm = value of equity + value of debt)this implies that probability of default decreases which further implies that less risk, so bond yields should decrease.
2) if there is a increase in interest rates then to give more profit on bonds, the bond yield should increase.

please tell me what is wrong in either of them

 

[David Harper CFA FRM]

Hi adi,

Thanks for your kind note, I wish you well in your recovery...

I like to distinguish between model-based (within model) statements and empirical statements. What I mean is, in the FRM, mostly we study models that are simplified versions of reality. The advantage of these models is they have right/wrong answers (absolute truth); the disadvantage is, well, they often don't work! There are many examples (e.g., CAPM, cost of carry, bond pricing) where we can draw "within the model" conclusions in absolute, concrete terms. Empirical assertions (e.g., higher interest rates correlate with lower stock prices), on the other hand, tend to be practical but, on the other hand, they are infinitely debatable (specifically, they are subject to sample bias, so a different sample can gives a different conclusion).

I frame it this way b/c your questions (from my perspective) draw from Stulz and he has always given us difficultly here because he commingles a model (the Merton model, a structural model) with empirical findings that occasionally contradict. The contradictions may reconcile in: the model obviously omits things, it does not capture the complex reality.

Here is another thread. In short, my opinion is that Stulz's statement on page 576 ("the expected value of the firm at maturity increases with the risk-free rate") should be either ignored or seen to have a very specific meaning (i.e., the under the Merton model, the value of the firm grows at some rate, and the higher that rate, the higher the future value of the firm).

So your (1) is consistent with this Stulz statement. But only in this way: higher growth rate means the firm's expected future value is higher. In our context (interest rates versus values), I would ignore it because it confuses interest rates with asset growth rates. So I disagree with (1) and agree with the contradictory assertion in Stulz. That is, generally, we say that higher rates imply lower firm value. Either from an entity perspective (i) higher rates imply higher cost of capital (WACC) so that discounted cash flows give a lower PV, or from a debt perspective (ii) higher yields imply lower price (value) of debt. But I cannot find your answer from this equation: firm/entity = equity + debt. Because lower debt either increases the equity (for a given firm value) or lowers the firm value (given a fixed equity value). And, then empirically which is totally a different angle, as Stulz says, higher rates tend to lower stock (and firm) value due to factors not in the models. So, aside from this one citation, I think Stulz supports "higher rates imply lower debt and firm value."

(2) This might need a clarification in terminology, IMO. But basically this is correct. If we are referring to Stulz, the r = riskless rate, s = spread and (r+s) = yield. So, a corporate bond yield is the sum of the riskless rate (r) plus a spread (s) for credit risk; yield (y) = r + s. Under this, increase (r) and the yield (r+s) goes up. Beyond that, I think we require more definition. It is another question to ask, if rates go up, what happens to the spread? Here, we can venture into a complicated empirical question or, within the Stulz model, we can agree with him that higher rates (r) imply lower spread (s).

Hope that helps! David

 

[aditya]

hi david,

can u please help me here

i think from the two perspectives that u have told (ENTITY and DEBT) it is clear to me that higher rates imply lower debt and firm value . so (1) point should be ended here........... am i right????


now i come to the (2) point....... (spread = risky bond yield - riskfree bond yield) .......... if there is an increase in interest rates,higher yields should be generated to buyers of corporate bond............. and if yield is increased then the spread should increase i.e. higher interest rates should make credit spreads widen........

is this same that u wanted to convey rather than agreeing with the stulz model???????????

and it is often said that in recessions credit spread widens....... plz explain????

thanx for the above explanations.....

adi

 

[David Harper CFA FRM]

Hi adi,

Re (1), yes, correct

Re (2), and "higher interest rates should make credit spreads widen." I don't want to say that. Rather: higher riskless rate (r) implies that yield (r+s) i higher.

And, only per Stulz (FRM assigned): spread = -(1/T)*LN(D/F) - r ,

The above is rearranged from this: Debt Price(P) = Face (F) * EXP[-(r+s)(T)]. See how price is discounted at yield (r+s). So, only per this model, if you increase (r) and all else is the same, then spread must narrow. Only per this model, higher rate (r) implies lower spread (s)

"recessions credit spread widens" Yes, while the above is "within the model," this instead is more of an empirical assertion - the typical argument here is that during a recession, companies will have lower revenue/cash flow and so will be less likely to repay (higher PD). At the same, time, riskless rate could go down b/c flight to quality in Treasuries. So recession leads to lower riskless rate (flight to quality), and higher spread (flight away from risk)

David