Money market yield understanding the math behind the equation

CFA Level I Quant
#1

Hello!

Please, help me to understand the mathematical logic behind the money market yield.

Here is the equation:

money market yield = [360 x r BD] / [360 - (t x rBD)]

where rBD is the band discount rate; t - days till maturity.

For example:

rMM = (360)(0.05)/[360 − (120)(0.05)] = 0.0508

Here is how I started interpreting the math (but stumbled):

  1. in the numerator we have 360 x bank discount rate = 360 x 0.05 = 18; this seems to give the number of periods within a year, during which 0.05 could be earned; is that so?

  2. (120)(0.05) = 16 this also gives the number of periods, but what these periods mean?

  3. [360 − (120)(0.05)] = 360 - 16 = 354 what happens here?

  4. finally 18 / 354 = 0.0508 I guess I will be able to understand what happens here if I understand three previous ones.

Thank you very much!

#2

I went through the derivation here a few years ago. You can search for it if you like.

My suggestion at the time, and my suggestion now, is to ignore that formula.

Learn the basic formulae for the yields, and how to get from each yield to the current market price. That’s all you need.

I wrote an article on all of the yield measures in Quantitative Methods (http://www.financialexamhelp123.com/yield-measures-quant/) and another on how they compare to each other (http://financialexamhelp123.com/comparing-yield-measures-quant/).

(Full disclosure: as of 4/25/16, there is a charge to read the articles on my website. You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)