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**Subject 5. Bond Equivalent Yield**

Periodic bond yields for both straight and zero-coupon bonds are conventionally computed based on semi-annual periods, as U.S. bonds typically make two coupon payments per year. For example, a zero-coupon bond with a maturity of five years will mature in 10 6-month periods. The periodic yield for that bond, r, is indicated by the equation Price = Maturity value x (1 + r)

^{-10}. This yield is an internal rate of return with semi-annual compounding. How do we annualize it?The convention is to double it and call the result the bond's yield to maturity. This method ignores the effect of compounding semi-annual YTM, and the YTM calculated in this way is called a

**bond-equivalent yield**(**BEY**).However, yields of a semi-annual-pay and an annual-pay bond cannot be compared directly without conversion. This conversion can be done in one of the two ways:

- Convert the bond-equivalent yield of a semi-annual-pay bond to an annual-pay bond.
- Convert the equivalent annual yield of an annual-pay bond to a bond-equivalent yield.

*Example*

- A Eurobond pays coupon annually. It has an annual-pay YTM of 8%.
- A U.S. corporate bond pays coupon semi-annually. It has a bond equivalent YTM of 7.8%.
- Which bond is more attractive, if all other factors are equal?

**Solution 1**

- Convert the U.S. corporate bond's bond equivalent yield to an annual-pay yield:
- Annual-pay yield = [1 + 0.078/2]
^{2}- 1 = 7.95% < 8% - The Eurobond is more attractive since it offers a higher annual-pay yield.

**Solution 2**

- Convert the Eurobond's annual-pay yield to a bond equivalent yield (BEY):
- BEY = 2 x [(1 + 0.08)
^{0.5}- 1] = 7.85% > 7.8% - The Eurobond is more attractive since it offers a higher bond equivalent yield.

#### Practice Question 1

Which of the following is incorrect?A. BEY is the annual yield calculated from semi-annual, quarterly, or monthly discount-bond or note yields.

B. Bond Equivalent Yield for a semi-annual pay bond is calculated as twice the six month yield.

C. Bond Equivalent Yield for a semi-annual pay bond is more than the real annual return from holding the bond till maturity (assuming no default).Correct Answer: C

BEY will be less than the real return as (1 + x)

^{2}is greater than 1 + 2x.

#### Practice Question 2

The bond equivalent yield for a semi-annual pay bond is most likely ______.A. equal to the effective annual yield

B. more than the effective annual yield

C. equal to double the semi-annual yield to maturityCorrect Answer: C

The bond equivalent yield for a semi-annual pay bond is equal to double the semi-annual yield to maturity.

#### Practice Question 3

What is the bond equivalent yield of a 7% annual-pay bond with semi-annual compounding?A. 6.882%

B. 7.000%

C. 7.123%Correct Answer: A

2[(1.07)

^{0.5}-1] = 6.8826%

#### Practice Question 4

Why is the bond-equivalent yield of an annual-pay bond always less than the annual-pay rate?A. The annual-pay bond is divided by two for the semi-annual equivalent.

B. The annual-pay bond will pay twice as much interest in one payment.

C. The bond equivalent yield compounds only half as often for the annual-pay bond.

D. The square root of the annual-pay yield is taken to convert from one to two pay periods in a year and maintain the same yield when the two periods are compounded back to an annual basis.Correct Answer: D

#### Practice Question 5

A bond equivalent yield is a money market rate stated on a ______ rate basis.A. 360-day discount

B. 360-day add-on

C. 365-day add-onCorrect Answer: C

#### Practice Question 6

The bond equivalent yield of a 120-day banker's acceptance quoted at a discount rate of 4.0% for a 360 day-year is closest to ______.A. 3.89%

B. 3.96%

C. 4.10%Correct Answer: C

C is the only possible answer, as both A and B are lower than 4.0%. By design, a money market discount rate understates the rate of return. The bond equivalent yield has to be higher than 4.0%.

### Study notes from a previous year's CFA exam:

f. convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields.