Limited Time Offer: Save 10% on all 2021 and 2022 Premium Study Packages with promo code: BLOG10    Select your Premium Package »

Yield Conversions

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

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.

Featured Study with Us
CFA® Exam and FRM® Exam Prep Platform offered by AnalystPrep

Study Platform

Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Online Tutoring
    Our videos feature professional educators presenting in-depth explanations of all topics introduced in the curriculum.

    Video Lessons



    Sergio Torrico
    Sergio Torrico
    2021-07-23
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    diana
    diana
    2021-07-17
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    2021-07-16
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    2021-06-28
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Marwan
    Marwan
    2021-06-22
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    2021-05-10
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.