# Bond Equivalent Yield

An annual yield used for security comparisons.

This is used to convert securities that have coupons either quarterly, semi-annually or monthly and convert them into an annual yield.

This is a non-annual bond yield expressed in annual terms.

Semi-annual bonds always have there yield quoted as BEY.

The BEY is the yield quoted in the newspapers.

This is the quick formula used to compare securities that have different compounding frequencies.

This yield is calculated either as fractional or simple interest.

This convention is carried over to yield calculations for other type of fixed income securities.

### Semi-Annual

Multiplying a semi-annual interest rate by 2 to calculate an annual interest rate will result in an underestimate of the effective annual yield.

The correct way to annualise a semi-annual interest rate is to take compounding into account.

SS - equation

For more details on converting a nominal interest rate to an effective interest rate, please refer to __Interest Rates > Nominal Interest__ page.

### Example - Semi Annual

Consider a semi-annual interest rate of 4.35%

The BEY would be (4.35 * 2) = 8.7% (ignoring the compounding)

The correct effective annual rate (taking compounding into account) would be

Effective = (1 + 0.0435)^2 -1

Effective = (1.0435)^2 - 1

Effective = 8.889%

### Example - Annual

In the US interest is paid semi-annually although in other markets it is paid annually.

BEY = 2 * SQRT( (annual rate + 1) -1 )

For example consider an annual interest rate of 8.60%

The BEY would be

SS - equation

Notice that the BEY will always be less than the annual interest rate.

### Formula 1

BEY for semi-annual, quarterly or annual with 6 (or less) months to maturity

SS - equation

### Formula 2

BEY for annual with more than 6 months to maturity

SS x 4 ??

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