Interest rate change, debt value, and stock value

[ajsa]

Hi David,

“Interest rate changes impact the price of debt in two ways:
1） An increase (decrease) in rates reduces (increases) the present value of debt.
2） Less directly, interest rates tend to be inversely correlated with a firm’s value and its stock
price.” (I wonder if this should be debt price instead? Or you mean rising IR will decrease firm value, debt value, and stock value?)

also how does IR volatility affect the risk of default? increase?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

It is meant as written because it merely parrots Stulz from chapter 18; like the Stulz spread, it is part of the section I asked GARP to remove due to confusion it causes every year. The problem is he vacilates (commingles, confuses) from fundamental explains to empirical statements, and this is another example. So the (1) above is a fundamental dynamic - it's intuitive from our models.

But the (2) from 18.1.4 is "merely" an empirical assertion: "empirical evidence suggest that stock prices are negatively correlated with interest rates." (p582) So he means that we observe inverse correlation btwn rates and stock price and then he goes on to use that *empircal* observation to assert that lower stock price implies lower firm asset value (debt + equity) which (since debt value under Merton is riskfree debt - value of put on firm assets; and lower asset value increases value of the put, decreases the value of the risky debt) decreases debt...but it's fraught with challenges...IMO largely b/c he is switching back and forth w/o warning between "here is simple model" and "here are observed empirical relationships." .... for one thing, in regard to a financial institution, the impact of rates on value probably should first make us thing about duration of liabilities versus assets:

we are better off to ignore this is be mindful of (a la Saunders on balance sheet hedging)
e.g., if bank's liability (dollar) duration exceeds asset (dollar) duration, then firm value goes up if rates increase

so honestly i would not fret this stulz section too much *except* for the credit spread formula we were refering to yesterday (D = F*EXP[-(r+s)T) ... that's likely the only key takeaway aside from the Merton model mechanics...David