Time-Weighted Rate of Return
The time-weighted rate of return (TWRR) measures the compound growth rate of an... Read More
Yield conversion is basically the process of changing from one type of yield to the other. We have already established the 4 main types of yields and their formulae – rBD, HPY, EAY, and rMM.
Given any one of these yields, we can easily find the other two by considering the following important points.
– HPY represents the actual return on a money market instrument assuming that it’s held until maturity.
-When we annualize HPY on the basis of a 365-day year and carry out compounding, the result is the EAY.
-rMM is the annualized version of HPY on the basis of a 360-day year and assuming simple interest.
The following are direct results from the yield formula studied here.
Alternatively, HPY = rMM * (t/360)
Similarly,\( \text{HPY} = (1 + EAY)^{\frac {t}{365}} – 1\)
Assume you purchased a $10,000 U.S. T-bill maturing in 150 days for $9,800. The money market yield is quoted at 4.898%. How do you go about computing the HPY and the EAY?
Solution
First, you should note that in this particular case, we can compute the HPY directly from the question:
$$ \text{HPY} = \cfrac {(10,000 – 9,800)}{9,800} = 2.041\% $$
However, we can still use the money market return given above to get our HPY:
$$ \text{HPY} = = r_{MM} * \left( \frac {t}{360} \right)= 0.04898 * \frac {150}{360} = 2.041\% $$
For the Effective annual yield:
$$ \text{EAY} = (1 + HPY)^{\frac {365}{t}} – 1 = (1 + 0.02041)^{ \frac {365}{150}} – 1 = 5.039\% $$
It refers to an annualized periodic yield calculated by multiplying the periodic yield by the number of periods in a year. U.S. bonds usually have two semi-annual coupon payments. As such, yields are quoted as twice the semi-annual rate. Thus;
Bond Equivalent Yield (BEY) = 2 * semi-annual discount rate.
Example
Assume you have a 3-month loan that has a holding period of 4%. Its bond equivalent yield will be calculated as follows;
First, we convert the 3- month HPY to an effective semi-annual yield:
$$ 1.04^2 – 1 = 8.16\% $$
Secondly, we double it and this will give us the BEY:
$$ 2 * 8.16 = 16.32\% $$
Question
A project has an EAY of 16%. Calculate its BEY;
A. 107.7%
B. 7.7%
C. 15.4%
Solution
The correct answer is C.
Step 1: Convert the EAY to an effective semi-annual yield.
$$ 1.16^{0.5} – 1 = 0.077 \text{ or } 7.7\% $$
Step 2: Double it!
$$ 2 * 7.7 = 15.4\% $$
Reading 7 LOS 7f
Convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields.