# A 10-year spot rate is least likely the:

A) appropriate discount rate on the year 10 cash flow for a 20-year bond.
B) yield-to-maturity on a 10-year coupon bond.
C) yield-to-maturity on a 10-year zero-coupon bond.

The correct answer is B. The explanation given is A 10-year spot rate is the yield-to-maturity on a 10-year zero-coupon security, and is the appropriate discount rate for the year 10 cash flow for a 20-year (or any maturity greater than or equal to 10 years) bond. Spot rates are used to value bonds and to ensure that bond prices eliminate any possibility for arbitrage resulting from buying a coupon security, stripping it of its coupons and principal payment, and reselling the strips as separate zero-coupon securities. The yield to maturity on a 10-year bond is the (complex) average of the spot rates for all its cash flows.

Can somebody explain why the answer is not C. Zero coupon bonds pay not interests hence 10-year spot rate is not likely to anything to a zero coupon bond, isn’t so?

How do you compute a bond’s YTM?

Yes, I think ZCB do not payment any interest hence the relevant spot rate is of the year in which the bond matures.

How do you compute a bond’s YTM?

YTM is the discount rate used to discount the cashflows (coupons and principal repayment) from a bond to equal to present value of the bond.

And what are all of the cash flows on a 10-year, zero coupon bond?

No coupon payments but only the principal payment in the year of maturity.

So . . . a single payment 10 years from now.

And what rate do you use to discount a single payment 10 years from today to get the present value of that bond?

The spot rate of year 10.

Voilà!

Thank you very much.

My pleasure.