Treasury Bill Discount Yield vs Coupon-Equivalent Yield

The quoted discount yield on a Treasury bill is lower than its actual annualized return because it uses a 360-day year, ignores compounding, and calculates return as a fraction of face value rather than investment outlay. Converting to a coupon-equivalent yield reveals the true apples-to-apples comparison with other short-term fixed-income instruments.

The origin of discount yield

Treasury bills are sold at a discount to par value. If you buy a $10,000 face value T-bill maturing in 90 days and pay $9,750, you earn $250 at maturity. Dealers quote this return using a formula:

Discount Yield = (Discount / Face Value) × (360 / Days to Maturity)

In the example: Discount Yield = ($250 / $10,000) × (360 / 90) = 10%.

This method, called the bank discount basis, has been the market standard since the 1920s. It is efficient for quick mental math, but it has three quirks that understate true economic return.

Three reasons discount yield understates actual return

1. Use of 360-day year instead of 365

The formula divides by 360, not 365. This convention traces back to manual calculation when 360 was convenient (12 months × 30 days). It inflates the quoted yield by about 1.4 % (365 ÷ 360 = 1.014).

2. Return is calculated on face value, not actual cash invested

You invest $9,750 today and receive $10,000 tomorrow. Your true return is $250 ÷ $9,750, not $250 ÷ $10,000. Dividing by face value alone understates your yield, especially for longer-dated bills.

3. No mention of compounding

The discount yield is a simple, non-compounded rate. If you roll a 90-day bill over four times per year, your compound interest is not captured in the quoted number.

The coupon-equivalent yield conversion

To convert discount yield to a true apples-to-apples return, use the coupon-equivalent yield (also called bond-equivalent yield or effective annual yield):

Coupon-Equivalent Yield = (Discount / Purchase Price) × (365 / Days to Maturity)

Returning to the example:

• Purchase price = $9,750
• Discount = $250
• Days to maturity = 90

Coupon-Equivalent Yield = ($250 / $9,750) × (365 / 90) = 10.59%

Compare this to the quoted discount yield of 10%. The coupon-equivalent yield is 59 basis points higher, a material difference for a cash manager deciding between a T-bill and a money-market fund or a short-term corporate bond.

Worked example: 180-day bill

Suppose a 180-day T-bill is quoted at a discount yield of 5.2%.

Step 1: Calculate the dollar discount.

• Discount = Face Value × Discount Yield × (Days / 360)
• Discount = $10,000 × 0.052 × (180 / 360) = $260

Step 2: Calculate purchase price.

• Purchase Price = $10,000 − $260 = $9,740

Step 3: Calculate coupon-equivalent yield.

• Coupon-Equivalent = ($260 / $9,740) × (365 / 180)
• Coupon-Equivalent = 0.0267 × 2.028 = 5.41%

The investor earns 5.41%, not 5.2%.

When the gap matters most

For very short-dated bills (e.g., overnight or one-week), the gap is small—often under 10 basis points—because the proportion of the year is tiny. For a full-year bill (52 weeks), the gap can exceed 100 basis points.

Practical use: comparing investment options

A treasurer evaluating where to park $10 million for 180 days might compare:

• A T-bill quoted at 5.2% discount yield → 5.41% coupon-equivalent
• A Treasury bond quoted as 5.35% coupon rate
• A high-yield bond quoted at 6.8% coupon rate

Using coupon-equivalent, the T-bill appears more competitive versus nominal coupon rates on other securities, and risk-adjusted comparison becomes clearer.

Modern context: dealer conventions persist

Electronic platforms (Bloomberg, MarketAxess) still quote T-bills using discount yield because it is the convention accepted by the Federal Reserve and FINRA. Understanding the conversion is essential for anyone trading bills, doing cash-flow forecasts, or comparing short-term financing costs across instruments.

Some money managers and central banks have advocated for quoting bills on a coupon-equivalent basis to reduce confusion, but the market has not shifted. The discount yield remains the lingua franca.

See also