# bank discount yield

Can a bank discount yield be converted into HPY?? if yes, could anyone please give the formula and explain the logic as well . Thanks in advance

Last chance to walk away.

No? OK, here goes:

HPY = profit / price

HPY = D / (F – D)

BDY = (D / F) × (360 / t)

D = (BDY × t × F) / 360

price = F – D = F – (BDY × t × F) / 360 = (360F – BDY × t × F) / 360 = (360 – BDY × t)F / 360

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

= 360D / (360 – BDY × t)F = 360 / (360 – BDY × t) × (D / F)

D / F = BDY × (t / 360)

HPY = 360 / (360 – BDY × t) × BDY × (t / 360)

HPY = (BDY × t) / (360 – BDY × t)

Remember, you wanted this.

Amazing sir. Thank you loads. Appreciate the effort taken by you. Thanks a lot again .

My pleasure.

Hi S2000magician,

Are you sure, that : HPY = (BDY × t) / (360 – BDY × t)

isn’t it Rmm (money market) = (BDY × t) / (360 – BDY × t), at least this is in Schwesser p.149.

Thanks for clarifing,

Czemp

Howdy.

Pretty sure. Did you follow the derivation step by step?

Let’s give it a try: suppose that a 90-day T-Note sells at \$990. Then the BDY is:

\$10 / \$1,000 × (360/90) = 4%.

The HPY is:

\$10 / \$990 = 1.01%.

Using the formula I gave, we get:

(90 × 4%) / (360 – 90 × 4%)

= 3.6 / 356.4

= 1.01%.

Looks right.

The MMY would be:

1.01% × (360/90) = 4.04%.

If I were you I’d write Schweser and tell them that they have the wrong formula.

My pleasure.

Wow.

Rmm = (360 x BDY) / (360 – BDY x t) This is _ correct _: note the _ 360 _ instead of _ t _.

Then something wrong with the formula in official materials

My mistake: I didn’t read the formula you’d quoted carefully.

Your formula has _ 360 _ in the numerator, not _ t _. It’s correct: it’s been annualized.

I reread p. 149 in the SchweserNotes: it has BDY × _ 360 _ in the numerator, not BDY × _ t _.

It’s correct.

We both need to be careful when we read.

For the sake of clarity and completeness:

HPY = (BDY × t ) / (360 – BDY × t)

MMY = (BDY × 360 ) / (360 – BDY × t)

Now . . . do not bother to memorize either of these formulae!

If you’re given BDY and you want HPY or MMY, do what I did in the example above: calculate the discount and the price, then calculate the HPY, then, if you want MMY, multiply it by 360/t.

Ok, it’s cool than we’ve solved problem with these formulae ty