Bond Equivalent Yield Explained

A bond equivalent yield takes the return on a short-term discount instrument—such as a Treasury bill or commercial paper—and converts it to an annualised rate on a semi-annual compounding basis. This conversion lets an investor compare apples-to-apples a 91-day T-bill (sold at a discount, no coupon) with a coupon-bearing bond that pays interest twice a year.

The problem: incomparable yield conventions

In the fixed-income markets, two types of instruments have different quoting conventions:

Discount instruments (T-bills, commercial paper): Sold at a discount to face value. The buyer pays less today and receives face value at maturity. Return is the difference between purchase price and face value. These are quoted using a simple annual yield—often on a 360-day year basis (the “bank discount yield”).

Coupon bonds: Sold at or near par, with periodic interest payments. Yields are quoted on a semi-annual compounding basis—standard in the US Treasury and corporate bond markets.

Comparing a 90-day Treasury bill yielding 4.5% (bank discount basis) with a 10-year bond yielding 4.2% (semi-annual compounding) looks like the T-bill is better. But the two yield numbers are calculated differently, so the comparison is misleading. The T-bill yield is a simple 360-day yield; the bond yield accounts for compounding and uses a 365-day year. A true apples-to-apples comparison requires converting one to the other’s basis.

How bond equivalent yield works

The bond equivalent yield (BEY) standardises discount-instrument yields to the bond market’s semi-annual compounding convention.

Given:

• Purchase price: P
• Face value: F
• Days to maturity: d
• Year basis: 365 days

The money market (bank discount) yield is: Bank Discount Yield = (F − P) / F × (360 / d)

To convert to bond equivalent yield:

BEY = (F − P) / P × (365 / d) × 2

The factor of 2 converts from a simple annualized rate to a semi-annual compounding basis. This matches how coupon bond yields are reported.

Worked example

A Treasury bill is purchased for $99,000 and matures in 91 days at face value of $100,000.

Bank discount yield: (100,000 − 99,000) / 100,000 × (360 / 91) = 0.01 × 3.956 = 3.956% (or ~3.96%)

Bond equivalent yield: (100,000 − 99,000) / 99,000 × (365 / 91) × 2 = 0.01010 × 4.011 × 2 = 0.0809 or 8.09%

The BEY is roughly double the bank discount yield because:

1. The denominator is the purchase price (99,000), not face value (100,000), slightly raising the rate.
2. The 365-day year vs. 360-day year adds ~1.4%.
3. The factor of 2 accounts for semi-annual compounding.

Now the T-bill’s 8.09% BEY can be compared directly with a coupon bond’s semi-annual yield. If a bond is quoted at 7.80%, the T-bill is slightly more attractive on a yield basis.

Why semi-annual compounding?

US Treasury and corporate bonds pay coupon payments twice per year. The yield-to-maturity quoted in bond markets reflects this semi-annual frequency. A bond quoted at 4.00% yield means:

• 2.00% paid every six months.
• (1.02)^2 − 1 = 4.04% effective annual return.

Short-term instruments like T-bills don’t have multiple payment periods, so the bond market’s semi-annual convention is imposed artificially—but consistently. This makes all fixed-income securities comparable on a single yield basis.

Bond equivalent yield vs. other yield measures

Several yield measures exist for short-term instruments. Understanding the differences prevents errors:

For a 91-day T-bill bought at $99,000 (face $100,000):

• Bank discount yield: 3.96%
• Money market yield: 4.06%
• Bond equivalent yield: 8.09% (this is the 2× factor)
• Effective annual yield: 8.04%

(The effective annual yield is close to BEY because a 91-day investment doesn’t compound much.)

Investors and traders need to know which basis they are working with. Many T-bill quotes are given in bank discount yield, but regulators require disclosure in BEY.

Semi-annual compounding in detail

The semi-annual adjustment is not arbitrary. In the bond market, a 4.00% yield means:

• Six months: earn 2.00%
• Next six months: earn 2.00% on the compounded base

Total return = (1 + 0.02) × (1 + 0.02) − 1 = 1.0404 − 1 = 4.04% (effective annual)

For a short-term instrument using BEY, we mimic this by multiplying the annualized simple rate by 2:

BEY = Simple Annual Rate × 2

where the simple annual rate is (F − P) / P × (365 / d).

This factor-of-2 adjustment assumes that the investor could reinvest the mid-year return at the same rate. In practice, reinvestment rates vary, so BEY is an approximation. But it standardises comparisons across the market.

Practical application

For investors evaluating short-term holdings: A money market fund or T-bill portfolio yielding 3.50% in bank discount terms is actually 3.59% in money market yield and 7.18% in bond equivalent yield. If comparing to a short-duration bond fund quoted at 3.70% (semi-annual), the bond fund offers marginally more; if the short-term yield is quoted as 7.50% BEY, they are nearly identical.

For bond traders: Converting T-bill yields to BEY is essential when constructing hedges or comparing the relative value of bills vs. short-dated coupon bonds. A futures contract on a Treasury bill may be quoted in one basis; a short-dated Treasury bond in another. The trader must reconcile them.

For SEC disclosure: Money market funds and other short-term investment vehicles are required to disclose yields on a bond equivalent basis so that retail investors can compare them to bond-fund yields transparently.

Limitations and caveats

• Assumes reinvestment: The factor-of-2 adjustment assumes you reinvest the first six months’ earnings at the same rate. In reality, rates may move.
• Applies only to short instruments: BEY is most relevant for items maturing within a year. For longer-dated instruments, there are multiple coupon periods, and the semi-annual compounding is more accurate (not an approximation).
• Ignores credit risk differences: Comparing a Treasury bill’s BEY to a corporate paper’s BEY ignores credit risk. The corporate paper is riskier and should yield more.
• Not the same as effective annual yield: BEY is an annualized rate assuming semi-annual compounding, but it does not account for the exact timing or frequency of all cash flows. For precise comparisons over long periods, use effective annual yield or yield-to-maturity.

See also