Quantitative Finance
Treasury Bill Bank Discount Rate (DISC) & Bond Equivalent Yield Formula
Calculate the 360-day money-market Bank Discount Rate (DISC) alongside the 365-day Bond Equivalent Yield (BEY) to compare zero-coupon T-bills fairly against coupon-bearing notes.
Reconcile 360-day par discount quotes with true 365-day investment return!
Short-term Treasury bills and commercial paper quote on a Bank Discount Rate basis (Excel’s DISC Actual/360 convention), which divides the dollar discount (Par - Price) by Face Value M = 100 over a 360-day year: d = ((M - P) / M) * (360 / Days). Because d divides by 100 instead of the smaller cash price P and uses 360 days instead of 365, it systematically understates the investor’s true annualized return!
To compare a T-bill fairly against coupon bonds or money-market deposit yields, compute the 365-day Bond Equivalent Yield (Investment Yield) for maturities <= 182 days: BEY = ((M - P) / P) * (365 / Days).
| 90-Day T-Bill Price (Par = 100) | Dollar Discount | Bank Discount Rate (360d) | Bond Equivalent Yield (365d) |
|---|---|---|---|
| 99.00 | 1.00 | 4.0000% | 4.0965% |
| 98.50 | 1.50 | 6.0000% | 6.1760% |
| 97.75 | 2.25 | 9.0000% | 9.3350% |
Bank Discount Rate % (360-Day Actual/360 DISC Convention)
Computes annualized percentage Bank Discount Rate from clean price B2, par redemption B3, and days to maturity B4.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Bill Inputs", ROUND(((B3 - B2) / B3) * (360 / B4) * 100, 4))365-Day Bond Equivalent Yield % (BEY)
Measures true simple annualized return on invested cash B2 over a 365-day year.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Bill Inputs", ROUND(((B3 - B2) / B2) * (365 / B4) * 100, 4))Try the example
Use the original values or change them to test your understanding.