Expected Bond Yields and Default Risk in Discounting
Summary
The document asks whether two bond valuation approaches treat default risk inconsistently. One approach defines expected yield to maturity for a zero-coupon corporate bond by discounting its probability-weighted expected payoff. The other values expected coupon payments using risk-adjusted discount rates that include default and market risk. The central issue is how default risk appears in expected cash flows versus the discount rate.
The text sets out the pricing equations and points to finance lecture materials, but it does not answer the question or resolve the apparent contradiction. It therefore serves as a prompt for distinguishing expected-payoff valuation from cash-flow discounting, rather than as a complete explanation. Its discussion is limited to the stated bond examples; it does not develop assumptions, derive a relationship between the approaches, or provide empirical evidence.
Key ideas
- The question compares expected-yield discounting of an expected bond payoff with risk-adjusted discounting of expected payments.
- The expected yield approach is presented as combining the risk-free rate with a premium that excludes default risk.
- The document asks whether including default risk in the discount rate for expected payments creates an inconsistency.
- No resolution or derivation is provided in the text.
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# Expected Yield to Maturity & Default Risk Premium
# Expected Yield to Maturity & Default Risk Premium
For a corporate bond, which natuarally has a default risk, the expected yield to maturity (EYTM) is defined as the probability-weighted average of all possible yields. Hence, for a 10-year zero-coupon bond which has expected payoff $E(N)$ and has a price (at time 0) $P$, we have $$P=\frac{E(N)}{(1+EYTM)^n},$$ where $n$ is maturity. This formula tells us that if in numerator we have expected payoff, then we should discount it using EYTM, which is rougly speaking the sum of risk free rate and risk premium (excluding default risk) (for more details see slide 47&48 from the link:https://ocw.mit.edu/courses/sloan-school-of-management/15-401-finance-theory-i-fall-2008/video-lectures-and-slides/MIT15_401F08_lec04.pdf). Ok, this part is intuitive for me. But when I read about Divident Discount Model (DDM) for bond price valuation I observe the following formula: $$P_t=\frac{E_t[D_{t+1}]}{1+r_{t+1}}+...,$$ where $E_t[D_{t+1}]$ is expected divident, and $r_{t+1}$ is risk-adjusted discount rate for cashfow at time $t$. Please note, that $r_{t+1}$ takes into account time value of money, default risk of company as well as market risk (for more details see slide 7 from the link: https://ocw.mit.edu/courses/sloan-school-of-management/15-401-finance-theory-i-fall-2008/video-lectures-and-slides/MIT15_401F08_lec07.pdf).
For both models described above, we have uncertain cash flow in the future, but the first one is discounted using EYTM, which doesn't take into account default risk, but for the DDM the expected divident is discounted using interest rate which takes into account default risk. Is this a contradiction. If no, why? Many thanks in advance!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.