Key takeaways
– Yield basis quotes a fixed-income security by its yield (percentage) rather than by dollar price, making bonds with different coupons and prices easier to compare.
– Common yield measures: Current yield (for coupon bonds) and Bank Discount Yield (for pure discount instruments such as Treasury bills).
– Always confirm whether a quoted yield is net (includes broker markup) or gross, and be aware of accrued interest, day-count conventions, taxes, and reinvestment/call risk when comparing yields.
– For apples-to-apples comparisons, convert bank-discount yields to a bond-equivalent or investment yield, or use yield to maturity (YTM) where appropriate.
Understanding yield basis
– Definition: Yield basis = annual coupon amount ÷ current market price. It expresses a bond’s return as a percentage of the price you pay, not as a dollar price.
– Why use it: Two bonds with different coupons and prices may look different in dollar terms but can be compared directly by their yields.
– Basic interpretation:
• If yield basis > coupon rate → the bond is trading at a discount (price < par).
• If yield basis par).
Important formulas and examples
1) Current yield (for coupon bonds)
– Formula: Current yield = Annual coupon payment ÷ Current market price
– Example: Company bond with 6.75% coupon, $1,000 par, trading at $940.
• Annual coupon = 6.75% × $1,000 = $67.50
• Current yield = $67.50 ÷ $940 = 0.0718 = 7.18%
• Interpretation: Quoted as 7.18% yield basis; because 7.18% > 6.75% coupon, the bond trades at a discount.
2) Bank discount yield (for discount instruments such as T‑bills)
– Method: Uses the discount from par, expressed as a fraction of par, assumes a 360‑day year, and applies simple interest.
– Formula: Bank discount yield (BDY) = [(Face value − Price) ÷ Face value] × (360 ÷ Days to maturity)
– Example: T‑bill with $1,000 face, selling for $970, time to maturity = 180 days.
• Discount = $1,000 − $970 = $30
• BDY = ($30 ÷ $1,000) × (360 ÷ 180) = 0.03 × 2 = 0.06 = 6.00%
• Note: Treasury bills are conventionally quoted on the bank discount basis.
Converting bank discount yield to a more comparable yield
– BDY is not directly comparable to yields expressed relative to price. Often converted to a bond-equivalent yield (BEY) or investment yield:
– Approximate conversion (bond-equivalent yield): BEY = [(Face − Price) ÷ Price] × (365 ÷ Days to maturity)
– Using the T‑bill example:
• BEY = ($30 ÷ $970) × (365 ÷ 180) ≈ 0.030927 × 2.0278 ≈ 0.0627 = 6.27%
– Use these conversions when comparing T‑bills to coupon bonds or longer-term instruments.
Other yield measures to know
– Yield to maturity (YTM): The internal rate of return (IRR) assuming you hold the bond to maturity and reinvest coupons at the same rate. YTM is a more complete measure of total expected return than current yield.
– Yield to call: For callable bonds, the yield assuming the bond is called at the earliest call date.
– Net yield basis: A yield quote that already includes the broker’s markup (no separate commission shown). Always ask whether quoted yields are net or gross.
Practical steps for investors — how to use yield basis when buying bonds
1. Identify the quoted measure
• Ask the broker/dealer or check the quote to know whether the figure is current yield, YTM, BDY, or net yield.
2. Compute or verify the yield you need
• For coupon bonds that you might hold long term, use YTM (best single-number estimate of total return).
• For quick comparisons across similar coupon bonds, current yield may be useful.
• For T‑bills, the market quote is BDY—convert to BEY or compute the investment yield if comparing to coupon bonds.
3. Account for transaction costs and broker quoting practice
• Ask: Is the yield quoted net of markup (net yield basis) or is there a separate commission?
• If quoted net, the broker’s profit is embedded in the price you pay.
• Include any broker-assisted fees or platform fees in your effective yield calculation.
4. Add accrued interest (dirty vs clean price)
• When you buy a coupon bond between coupon dates, you pay the seller accrued interest in addition to the quoted (clean) price. Include accrued interest to compute actual cash outlay and effective yield.
5. Consider day-count conventions and compounding
• BDY uses a 360-day year; other yields use actual/365 or actual/actual conventions. These affect conversions and comparisons.
• If you need precise comparisons, use the same day-count and compounding conventions across instruments or compute effective annual yields.
6. Adjust for special features and risks
• Check call provisions, sinking funds, or convertibility—these impact realized returns.
• Account for credit risk, liquidity, tax treatment (e.g., municipal tax exemption), interest rate risk (duration), and reinvestment assumptions.
7. Use calculators or spreadsheets for complex conversions
• For YTM, convert BDY to BEY or compute IRR using cash flows.
• Spreadsheets (Excel/Sheets) functions: YIELD, XIRR, or manual IRR calculation for cash flows.
Limitations and cautions
– Current yield ignores price changes, reinvestment of coupons, and time value of money; YTM is more complete.
– Bank discount yield understates the return relative to price-based yields because it divides the discount by par, not price, and uses a 360-day year.
– Quoted yields may mask embedded costs (net yield) — always confirm whether commissions or markups are included.
– Market quotes for different instruments use different conventions; do not compare raw numbers without conversion.
Quick reference of commonly used formulas
– Current yield = Annual coupon payment ÷ Current market price
– Bank discount yield (BDY) = [(Face − Price) ÷ Face] × (360 ÷ Days to maturity)
– Bond-equivalent yield (approx) = [(Face − Price) ÷ Price] × (365 ÷ Days to maturity)
– Yield to maturity (YTM) = IRR of all cash flows (coupons and principal) given current price
Where to learn more and verify conventions
– Investopedia — “Yield Basis” overview and examples (source article used here)
– Financial Industry Regulatory Authority (FINRA) — “Bonds: Key Terms” and “Bonds: Buying and Selling” for practical investor guidance on quoting and transaction practices
– TreasuryDirect — “Treasury Bills In Depth” for official T‑bill quotation conventions and calculations
Sources
– Investopedia: “Yield Basis”
– Financial Industry Regulatory Authority (FINRA): “Bonds: Key Terms” and “Bonds: Buying and Selling”
– TreasuryDirect: “Treasury Bills In Depth”
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.