What is the difference between discount yield and money market yield on T-bill futures, and how do you convert between them?
I keep mixing up the discount yield and the money market (or bond equivalent) yield when working T-bill futures problems. The textbook says T-bills are quoted on a discount basis but you need money market yield for comparison. Can someone clarify the formulas and show a conversion?
T-bill futures are quoted using a discount yield convention, but for comparing returns across instruments you often need the money market yield (also called bond equivalent yield for short maturities). Here is how both work.
Discount Yield (d)
The discount yield relates the dollar discount to the face value:
d = [(Face - Price) / Face] x (360 / Days)
Money Market Yield (MMY)
The money market yield relates the dollar discount to the purchase price:
MMY = [(Face - Price) / Price] x (360 / Days)
Conversion Formula
MMY = (360 x d) / (360 - d x Days)
Worked Example
Whitfield Capital purchases a 91-day T-bill at a price of $99.10 per $100 face value.
| Metric | Calculation | Result |
|---|---|---|
| Discount yield | (100 - 99.10) / 100 x (360/91) | 3.56% |
| Money market yield | (100 - 99.10) / 99.10 x (360/91) | 3.59% |
| Cross-check via formula | (360 x 0.0356) / (360 - 0.0356 x 91) | 3.59% |
The difference is small for low rates and short maturities, but it becomes material for longer-dated bills or higher rate environments.
Why This Matters for T-Bill Futures
CME T-bill futures settle against the discount yield of the delivered bill. If you are comparing the implied repo rate or hedging against a SOFR position, you must convert to the money market yield basis first.
Common Exam Trap: Students apply the discount yield formula but use the purchase price in the denominator instead of face value — this accidentally produces the money market yield. Always check which denominator the question requires.
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