###### Continuous Uniform Distribution

The continuous uniform distribution is such that the random variable X takes values... **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 – r_{BD, }HPY, EAY, and r_{MM}.

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.

-r_{MM }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.

- r
_{MM }= HPY * (360/t)

Alternatively, HPY = r_{MM} * (t/360)

- EAY = (1 + HPY)
^{ 365/t}– 1

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:

$$ 2 * 8.16 = 16.32\% $$

QuestionA project has an EAY of 16%. Calculate its BEY;

A. 107.7%

B. 7.7%

C. 15.4%

SolutionThe 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.*