How do you convert between bank discount yield, holding period yield, money market yield, and bond equivalent yield?

Money market yield conversions are one of those CFA Level I topics where a systematic framework saves enormous time. The key is understanding that each yield measure differs along two dimensions: (1) the denominator (face value vs. purchase price) and (2) the day count (360 vs. 365).

The Four Yields at a Glance

Where D = dollar discount (F - P), F = face value, P = purchase price, t = days to maturity.

Worked Example: Hawthorne Capital 90-day T-bill (fictional)

Step 1: Dollar discount

D = $10,000 - $9,870 = $130

Step 2: Bank Discount Yield

BDY = ($130 / $10,000) x (360/90) = 0.013 x 4 = 5.20%

Step 3: Holding Period Yield

HPY = $130 / $9,870 = 1.3171% (not annualized)

Step 4: Money Market Yield

MMY = 1.3171% x (360/90) = 5.269%

Step 5: Bond Equivalent Yield

BEY = 1.3171% x (365/90) = 5.342%

Quick Conversion Shortcuts

MMY from BDY: MMY = (360 x BDY) / (360 - t x BDY)

BEY from MMY: BEY = MMY x (365/360)

Why BDY Is Always the Lowest

BDY uses face value in the denominator, which is always larger than the purchase price. A larger denominator produces a smaller yield. Additionally, BDY uses 360 days instead of 365, giving fewer 'periods' of annualization. Both effects push BDY below the other measures.

Ordering Rule (for the exam): BDY < MMY < BEY (always true for discount instruments)

Exam Tip: If a question gives you one yield and asks for another, identify the two differences (denominator and day count) and adjust accordingly. Most students find it easiest to compute HPY first, then derive the others from there.

Practice yield conversions in our CFA Level I question bank.