Understanding the ratio formula

[Vital]

Homework Statement

Hello!

Please, help me to understand the mathematical logic behind one of the financial instruments called the "money market yield".

Here is the equation:

money market yield = [ 360 x r _BD ] / [360 - (t x r_BD)]

where r_BD is the band discount rate, and for simplicity we can just treat it as any rate of return;
t - days till maturity of the bond;
360 - the convention for the number of days in a year (instead of 365)

Homework Equations

For example:

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

The Attempt at a Solution

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!

 

[BvU]

Google is your friend - but the advertisers make it messy.
I liked the expose here

 

[Vital]

Google is your friend - but the advertisers make it messy.
I liked the expose here

Thank you very much. But this link doesn't address any of my questions, as all of them refer to the mathematical logic of ratios computed. The same description of the yield I have in my textbook, which doesn't explain the math behind the formula, and I am truly interested in understanding how to interpret those ratios, which I show in my 4 questions. )

 

[BvU]

Did you at least understand $$MMY = \quad HPR * \displaystyle{360\over t} \quad = \quad \displaystyle{F-P\over P}* \displaystyle{360\over t} \ \ \ ?$$

And do you understand the formula better when it is wwritten as
$$ MMY = {BDY\over 1 - \displaystyle{t\over 360} * BDY} \quad ? $$

 

[Vital]

Did you at least understand $$MMY = \quad HPR * \displaystyle{360\over t} \quad = \quad \displaystyle{F-P\over P}* \displaystyle{360\over t} \ \ \ ?$$

Yes, I think I understand this one. We annualize the difference between the face value and the purchase price by taking the ratio of this difference to the price and then multiplying it by the number of t periods we have during the year, thus getting the annual MMY as if we could have hold the bond for all 360/t periods.

And do you understand the formula better when it is wwritten as
$$ MMY = {BDY\over 1 - \displaystyle{t\over 360} * BDY} \quad ? $$

I have to think about this one.

 

[BvU]

$$MMY = \quad HPR * \displaystyle{360\over t} \quad = \quad \displaystyle{F-P\over P}* \displaystyle{360\over t} $$yes. Take $t=360$ as an example: F-P is what you 'earn' and P is what you invest. 360/t is the number of times you can do that in a year; so you'll notice it isn't converted into a compound interest.