# Yield Conversions

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.

## Yield Conversion Formula Guide

The following are direct results from the yield formula studied here.

1. rMM = HPY * (360/t)

Alternatively, HPY = rMM * (t/360)

1. EAY = (1 + HPY) 365/t – 1

Similarly,$$\text{HPY} = (1 + EAY)^{\frac {t}{365}} – 1$$

## Example

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:

$$\text{EAY} = (1 + HPY)^{\frac {365}{t}} – 1 = (1 + 0.02041)^{ \frac {365}{150}} – 1 = 5.039\%$$

## Bond Equivalent Yield

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

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!

$$2 * 7.7 = 15.4\%$$

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

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