Evaluate the following statement: “The yield-to-maturity measure doubles a semiannual yield rather than computing an effective annual yield. While it is more appropriate to compute the effective annual yield by compounding the semiannual yield, it is simply a convention.”
The correct answer and explanation is:
The statement is incorrect in its explanation of the yield-to-maturity (YTM) calculation and its relationship to semiannual yields.
Yield-to-maturity is a measure used to calculate the total return an investor can expect to earn if a bond is held until maturity. The YTM takes into account both the current market price of the bond and the bond’s coupon payments. In the case of semiannual bonds, where coupon payments are made twice a year, the YTM is typically expressed as a semiannual yield.
However, to accurately compare the YTM of semiannual bonds to other investment opportunities (such as savings accounts or other bonds), it is necessary to express the yield on an annual basis. This is because most financial comparisons are made on an annual basis, and yields need to reflect this for better consistency.
While the statement claims that YTM doubles a semiannual yield, this is not entirely true. In reality, to compute the effective annual yield (EAY) from the semiannual yield, compounding needs to be taken into account. The formula for converting a semiannual yield (let’s call it r) to the effective annual yield is: EAY=(1+r)2−1\text{EAY} = (1 + r)^2 – 1
Simply doubling the semiannual yield would not yield an accurate EAY, as this fails to account for the compounding that occurs within the year. For instance, if a bond has a semiannual yield of 4%, doubling this gives 8%, but the actual EAY would be: (1 + 0.04)^2 – 1 = 0.0816 \text{ or 8.16%}
Thus, the correct approach is to compute the effective annual yield by considering compounding, rather than merely doubling the semiannual rate. The convention of doubling the semiannual yield is an oversimplification and should be avoided when making precise financial calculations.