Terminology - Bond equivalent basis

[Dr. Jayanthi Sankaran]

Hi David,

Q. 315.3. Assume the reference term structure, which happens to be the theoretical Treasury spot rate curve, is flat at a semiannually compounded rate of 1.30% per annum. A $100 par bond with a 20-year maturity pays a 4 3/8 coupon (4.375% coupon rate) and has a current price of $95.82. Which is nearest to the bond's spread with semi-annual compounding; a.k.a., bond-equivalent basis?
a) 1.74%
b) 3.40%
c) 4.00%
d) 4.70%

A. 315.3 Although computing the bond spread = 3.4% is easy, what exactly does the term "bond-equivalent basis" mean in this context?

Thanks
Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran I will quote Fabozzi, this is from the CFA text and is the most helpful that I've read; ie, "In general, when one doubles a semiannual yield (or a semiannual return) to obtain an annual measure, one is said to be computing the measure on a bond-equivalent basis":

Fabozzi in full:

"1. THE BOND-EQUIVALENT YIELD CONVENTION: The convention developed in the bond market to move from a semiannual yield to an annual yield is to simply double the semiannual yield. As just noted, this is called the bond-equivalent yield. In general, when one doubles a semiannual yield (or a semiannual return) to obtain an annual measure, one is said to be computing the measure on a bond-equivalent basis.
Students of the bond market are troubled by this convention. The two questions most commonly asked are: First, why is the practice of simply doubling a semiannual yield followed? Second, wouldn’t it be more appropriate to compute the effective annual yield by compounding the semiannual yield?
The answer to the first question is that it is simply a convention. There is no danger with a convention unless you use it improperly. The fact is that market participants recognize that a yield (or return) is computed on a semiannual basis by convention and adjust accordingly when using the number. So, if the bond-equivalent yield on a security purchased by an investor is 6%, the investor knows the semiannual yield is 3%. Given that, the investor can use that semiannual yield to compute an effective annual yield or any other annualized measure desired. For a manager comparing the yield on a security as an asset purchased to a yield required on a liability to satisfy, the yield figure will be measured in a manner consistent with that of the yield required on the liability.
The answer to the second question is that it is true that computing an effective annual yield would be better. But so what? Once we discover the limitations of yield measures in general, we will question whether or not an investor should use a bond-equivalent yield measure or an effective annual yield measure in making investment decisions. That is, when we identify the major problems with yield measures, the doubling of a semiannual yield is the least of our problems." -- FIXED INCOME ANALYSIS, Second Edition, Frank J. Fabozzi, PhD, CFA, CPA. Chapter 6, Page 122

 

[Dr. Jayanthi Sankaran]

Thanks David - this is crystal clear - got it Yes, the difference between bond-equivalent basis and effective annual yield definitely ran through my mind...

Jayanthi