Bond Equivalent Yield Calculator

A bond equivalent yield (BEY) calculator converts the yield on a discount security or non-annual bond into an annualised, semi-annual basis yield to allow comparison with standard US Treasury bonds and other semi-annual coupon instruments. It is used by fixed-income investors and analysts comparing bonds with different coupon frequencies and discount instruments such as Treasury bills.

How to Use the Bond Equivalent Yield Calculator

1. Enter the purchase price of the discount security (or the periodic yield if converting a non-semi-annual bond).
2. Enter the face value (for discount securities) or the stated periodic yield.
3. Enter the number of days to maturity (for T-bills) or the number of coupon periods per year.
4. Click calculate to see the bond equivalent yield.

The Formula

For a discount security (such as a Treasury bill):

BEY = ((Face Value - Purchase Price) / Purchase Price) x (365 / Days to Maturity)

For a bond paying coupons more frequently than semi-annually (for example, monthly or quarterly):

BEY = ((1 + Periodic Rate)^2 - 1)

Where Periodic Rate is the rate per coupon period. This adjusts the more-frequent compounding to a semi-annual equivalent.

For a bond with fewer than 6 months to maturity:

BEY = (Face Value - Price) / Price x (365 / Days to Maturity)

Real-World Example

A 90-day Treasury bill is purchased for $9,850 with a face value of $10,000.

BEY = ((10,000 - 9,850) / 9,850) x (365 / 90) = (150 / 9,850) x 4.0556 = 0.01523 x 4.0556 = 0.0617 or 6.17%

This means the T-bill's return, expressed on an annualised semi-annual basis, is approximately 6.17%, allowing it to be compared directly with a Treasury note yielding 6.0% semi-annually. In this case, the T-bill offers a slightly higher BEY.

Why Bond Equivalent Yield Is Used

Fixed-income markets quote yields on different bases depending on instrument type. US Treasury notes and corporate bonds typically pay semi-annual coupons, and their yields are quoted on a semi-annual bond basis. Treasury bills are discount instruments with no coupon; their yield is often quoted as a discount rate or on a 360-day basis. Without conversion, comparing a T-bill yield of 5.8% with a T-note yield of 6.0% is not meaningful because they are calculated differently. BEY converts all yields to the same basis so comparisons are valid. The 365-day convention (versus 360 days used in some discount rate calculations) is another source of difference that BEY corrects for. For UK investors, gilt yields are quoted on an actual/actual basis with semi-annual coupons, and similar yield conversion is needed when comparing gilts with other instruments.

Frequently Asked Questions

What is the difference between bond equivalent yield and effective annual yield? BEY annualises a yield on a semi-annual compounding basis, which understates the effective annual yield slightly because it does not account for compounding within the year. Effective annual yield (EAY) is: EAY = (1 + BEY/2)^2 - 1. For a BEY of 6%, EAY = (1.03)^2 - 1 = 6.09%. The difference is small but matters when comparing with annually-compounding instruments.

What is the discount rate on a T-bill, and how does it differ from BEY? The bank discount rate is calculated on face value and a 360-day year: Discount Rate = ((Face Value - Price) / Face Value) x (360 / Days). BEY uses purchase price in the denominator (not face value) and a 365-day year. Because BEY uses the purchase price (which is lower than face value) and a longer year, it consistently produces a higher percentage than the bank discount rate for the same instrument.

Can BEY be used for corporate bonds? Yes. BEY is the standard way to quote bond yields in the US market, regardless of issuer. Investment-grade corporate bonds paying semi-annual coupons are typically quoted with a yield to maturity that is already on a bond equivalent basis. BEY conversion is mainly needed when comparing discount securities or bonds with non-standard coupon frequencies to these standard instruments.

Does BEY account for reinvestment risk? No. BEY assumes that coupon payments are reinvested at the same rate, as does yield to maturity. In practice, reinvestment rates change over time. Total return analysis, which explicitly models the reinvestment rate assumption, is a more accurate tool for comparing bonds when the reinvestment environment is expected to change materially.

The same bill on three different bases

One Treasury bill produces three different percentages depending on which convention you use. All three describe the same instrument bought at $9,850 and repaid at $10,000 after 90 days.

The bank discount rate divides the $150 gain by the $10,000 face value and annualises over 360 days. The bond equivalent yield divides the same gain by the $9,850 actually paid and annualises over 365. Both changes raise the figure. Using the price rather than the face value raises the numerator's denominator, and moving from 360 to 365 days raises the multiplier.

The gap between the discount rate and the bond equivalent yield is 0.176 percentage points on this bill. On a 180-day bill sold at a deeper discount the gap widens, which is why the two rates are never compared directly without conversion.

Two more bills worked through

The ordering holds whenever the price sits below face: discount rate lowest, bond equivalent yield next, effective annual yield highest. The reason is compounding. The effective annual yield assumes the gain is reinvested at the same rate for the remainder of the year, and the simple 365-day bond equivalent yield does not.

Converting a coupon frequency to a bond equivalent basis

A bond paying more often than each half year needs a conversion before it can be compared with a semi-annual instrument. The general form works out the rate per half-year that compounds to the same result as the more frequent payments, then doubles it.

The formula listed above, taking the periodic rate plus one and squaring it, gives the rate per half year. It covers the quarterly case in the page's own example. For a monthly payer the exponent is six rather than two, because six months divide into six monthly periods, and squaring the monthly rate would understate the half-year rate badly.

Reading a bill quote from a screen

A Treasury bill quote usually shows the discount rate, because that is the convention on the dealer screen. A 90-day bill quoted at 6.00% on a discount basis is the bill priced at $9,850 in the example above: multiply 6.00% by 90 over 360 and the resulting 1.5% is the discount off face value. To reach the figure that compares with a note, convert in two steps. Divide the gain by the price paid rather than the face value, then annualise over 365 days rather than 360. Both steps raise the number, so a bill that appears to yield less than a note on the screen can yield more than it once converted. A reader who compares the two quoted rates without converting will rank the instruments wrongly.

What the conversion assumes about the bill

The bond equivalent yield here treats a discount security as one cash flow at maturity, with nothing paid in between. It assumes the instrument is held to maturity and that no fees, taxes or bid-offer spread sit between the purchase price and the redemption value. It uses a 365-day year, so a leap year shifts the divisor by one day on bills that straddle 29 February.

The conversion holds for instruments shorter than a year, where the number of days is settled at purchase. Beyond a year the day count convention changes and compounding cannot be ignored, so the effective annual yield becomes the measure to quote rather than a simple annualised rate.

A note on the 360-day convention

The 360-day year behind the bank discount rate is a convention rather than a description of the calendar, and it survives because it makes hand division easy. US Treasury bills are quoted on it. The add-on yield that the CFA Institute curriculum sets out, which is the bond equivalent figure on these pages, uses a 365-day basis instead, and the two conventions are the reason a quoted bill yield and a quoted note yield are not comparable until one has been converted. The same curriculum's worked example, a 180-day bill quoted at a 4.5% discount rate, converts to a bond equivalent yield of about 4.67%.

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