Hi David,

i am unable to comprehend intuitevely these things:

1.why the credit spread falls as value to debt rises(mathematically its ok.)

2.why spread falls when interest rates rise?

3.for low value firm subordinaed debt increases as interest rate increases?

Please help

Anil

Hi Anil,

Stulz (Ch 18) on credit spread is (to use Gujarati’s term) strictly mathematical and not necessarily realistic (i.e., not necessarily statistical to use Gujarati’s term). So an intuition will be limited to his structural/mathematical framework. I say that because, these Stulz assertions are “holding the other variables constant” or “all other things being equal” (ceteris paribus).

In each case, it helps to keep in mind that:
yield (y) = riskless rate (r) + credit spread (s)
so instead of bond price = Face*EXP[-(y)(T)], we are using
bond price = Face*EXP[-(r+s)(T)]

1. Within the limits of his math, it is the same intuition as: when yield falls, price of bond increases.
So, we know: Price of debt = Face*EXP(-yT)
if yield falls, price/value of debt rises due to higher PV as function of lower discount.
Now just substitute in (r+s) for the yield.
And if hold constant (r), but lower spread (s), we are just discounting the face as a lower rate, to give a higher PV
or, if you like: if i buy a bond with lower default risk (i.e., lower spread), I shall expect to pay a higher price (PV) for it, such that return is lower.

2. mathematically, this is given:
y = r + s, and holding (y) constant, then
higher (r) implies lower (s)

statistically (realistically), I don’t think Stulz really goes here, but you get into factors not in the simple model. For example, a common argument is:
higher riskless rates (r; Treasury yield) is the yield curve predicting inflation and strong economic growth. Economic growth implies companies less like to default (lower PD). Which implies, in turn, lower spread (s).
But, statistically, as we are invoking factors not in the model, we can make other arguments

3. This continues the “structural” argument, where
Firm value = value [sr debt] + value [sub debt] + value [equity]; i.e., right hand Balance sheet = left-hand
So, the Stulz argument is: if interest rate increases, then value[sr debt] must fall.
And if we assume firm value and value[equity] are unchanged, then:
value [sub debt] must increase.

The other way to view, which is the same thing really, is again
Price [sub bond] = Face*EXP[-(r+s)(T)]

And Stulz is saying: normally higher (r) will lower the price of a bond (typical).
But under the special circumstance of a low value firm; i.e., a firm with high PD
in this special case, an increase in (r) is first acting to lower the value/price of the senior debt,
which in turn is making the subord debt LESS LIKELY TO DEFAULT.
and so, an increase in (r) is offset by a decrease in (s)!

This is tricky, this all comes from Stulz’ point that subordinated debt literally has characteristics of both debt and equity, with a tilt toward debt (when the firm is strong) and equity (when the firm is weak). And, statements like “spread falls with rate rise” IMO should be treated very narrowly in the Stulz framework which leaves out more than it includes. As more general statements, they would rightly invite debate.

hope that helps, David

Thanks David,

Your explanations are awesome.

Anil