# How to derive the Money Market Yield Formula?

Hi All,

This has been asked before but I can’t replicate the answer. In the text we are told that the Money Market Yield is:

Money market yield = (Bank Discount Yield x 360) / [360 - (t)(bank discount yield)]

I can’t work out how to derive this formula based on the other formulas. In a previous post, a user [Credit to S2000Magician] has provided the following proof but I can’t work out how he went from “MMY = 360D / [(F – D)t]” to “MMY= [360D / (F × t)] / [(F – D)t / (F × t)]”.

Can anyone assist? Thanks

HPY = profit / price

HPY = D / (F – D)

MMY = HPY × (360/t) = D / (F – D) × (360/t)

MMY = 360D / [(F – D)t]

MMY= [360D / (F × t)] / [(F – D)t / (F × t)]

MMY = [(D/F) × (360/t)] / [(F – D)/F]

MMY = BDY / [1 – (D/F)]

MMY = (BDY × 360) / {360[1 – (D/F)]}

MMY = (BDY × 360) / [360 – 360 (D/F)]

MMY = (BDY × 360) / [360 – (D/F) × (360/t) × t]

MMY = (BDY × 360) / [360 – (t × BDY)]

I divided both the numerator and the denominator by (F × t).

Thanks, you’re an absolute legend on these forums.

My algebra is a little bit rustyI think I’ve bitten off more than I can chew with the derivation. I can’t make sense of the next step thereafter etc.

In what scenario would you need to know the step by step derivation?

From what I gather, you wouldn’t; I just have an obsessive need to know everything from first principles and I found it curious that you could derive the adjusted MMY by only using the Bank Discount Yield.

Unfortunately, I’m still obsessing over it because I can’t follow S2000’s deconstruction (a reflection of my algebraic skills, not his awesome proofs).

Haha I feel that! My advice would just be ‘let it go’ and when you’ve passed in June before starting level II you can spend as much time as you want learning the derivations for ‘fun’.

I would advise you not to be too bothered about derivations of formulas. There’s far too many things in Level I to remember, and derivations of formulas is not one of them.

I find this video quite helpful in explaining all the different yields, and the relationships between them. By understanding the relationships between the various yields, it becomes quite easy to tweak one formula to another to get what we want.

[video:https://youtu.be/vqoUi10K4uU width:480 height:270]