A one-year zero-coupon corporate bond promises €1,000 at maturity and trades at €850. Investors expect to receive only €900 after allowing for possible default.
- A.Calculate the yield to maturity.
- B.Calculate the expected holding-period return.
A one-year zero-coupon corporate bond promises €1,000 at maturity and trades at €850. Investors expect to receive only €900 after allowing for possible default.
17.65%
5.88%
YTM uses promised cash flows. Expected return uses expected cash flows. The gap here reflects expected credit losses; YTM is not the expected return of this risky bond.
Answer the following fixed-income questions.
YTM is the discount rate equating price to promised cash flows. Default or delayed payments can reduce expected cash flows, so expected return can be below promised YTM. With no default, holding to maturity and reinvesting coupons at YTM yields that realised annual compound return; a default-free zero-coupon bond held to maturity does not require a reinvestment assumption. Interim returns also depend on interest-rate changes.
Investment-grade bonds occupy the higher credit-rating categories and generally have lower estimated default risk. Speculative-grade (high-yield or junk) bonds have weaker credit quality and ordinarily require larger credit spreads. A higher promised yield is not a guarantee of a higher realised return.
Yes, with a negative yield. With a positive yield it trades below par; at zero yield it trades at par.
The price of an outstanding fixed-rate bond falls, holding credit risk and promised cash flows fixed. A bond repaid tomorrow is almost insensitive. A floating-rate bond close to its reset date tends to remain near par if its contractual spread still matches its credit risk. A same-maturity zero-coupon bond generally has greater duration than a positive-coupon bond.
Holding expected cash flows, growth and risk premia fixed, the required return rises and the discounted value falls. In practice those other inputs can change too.
Yes. It may trade above par if its contractual spread is more generous than the currently required spread; between reset dates there can also be accrued-interest and rate effects. Near-par pricing is a useful approximation, not an identity.