relationship of credit spreads, time to maturity, and interest rate
- Thread starter ajsa
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Right, I asked GARP last year to remove this section b/c for years it has given confusion to alert candidates (that would be you!): Stulz appears to contradict his formula (longer term = lower spread) later with an emprical observation that spreads (on highly rated) debt widen with longer maturity..
In regard to the formula, it is nothing more than re-arranged bond pricing:
price of bond = Face * EXP[-yT]; i.e., our simple formula for discounting a zero-coupon bond- yes?
if you let yield (y) = riskless (r) + spread (s) , then solve for spread (s), you get the formula:
s = -1/T * LN(price/face) - r
viewed this way, we can say: for a given bond price and a given face value, (r) must decline as T increases.
e.g., par 100 zero 1 yr maturity @ 5% yield = 100*e^(-5%) = 95.x
now if you increase the maturity, and keep price at 95.x, yield must drop
David
In regard to the formula, it is nothing more than re-arranged bond pricing:
price of bond = Face * EXP[-yT]; i.e., our simple formula for discounting a zero-coupon bond- yes?
if you let yield (y) = riskless (r) + spread (s) , then solve for spread (s), you get the formula:
s = -1/T * LN(price/face) - r
viewed this way, we can say: for a given bond price and a given face value, (r) must decline as T increases.
e.g., par 100 zero 1 yr maturity @ 5% yield = 100*e^(-5%) = 95.x
now if you increase the maturity, and keep price at 95.x, yield must drop
David
...thinking about this formula, i think the *fallacy* may be to mistake the mathematical fact that, ceteris peribus (holding price constant), longer term implies lower yield with the reality that longer maturity will lower the price...so it's like maturity is really independent of price...David
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