Why is the yield to maturity of a zerominus coupon, riskminus free bond that mat
ID: 2792155 • Letter: W
Question
Why is the yield to maturity of a
zerominus
coupon,
riskminus
free
bond that matures at the end of a given period the
riskminus
free
interest rate for that period?
A.
Since a bond's price will converge on its face value as the bond approaches the maturity date, the Law of One Price dictates that the
riskminus
free
interest rate will reflect this convergence.
B.
Since interest rates will rise and fall in response to the movement in bond prices.
C.
Since such a bond provides a
riskminus
free
return over that period, the Law of One Price guarantees that the
riskminus
free
interest rate equals the yield to maturity.
D.
Since there is, by definition, no risk in investing in such bonds, the return from such bonds is the best that can be expected from any investment over the period.
Explanation / Answer
option C: Since such a bond provides a risk free return over that period, the Law of One Price guarantees that the risk free interest rate equals the yield to maturity. Law of one price is the law of one expected return. This governs the idea that securities with similar asset prices and similar risks would be expected to generate similar returns. A default-free zero-coupon bond that matures on date n provides a risk-free return over that time period equal to the yield to maturity. Thus, the Law of One Price guarantees that the risk-free interest rate equals the yield to maturity on such a bond.
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