## DEFINITION of 'Yield Basis'

The yield basis is a method of quoting the price of a fixed-income security as a yield percentage, rather than as a dollar value. This allows bonds with varying characteristics to be easily compared.

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## BREAKING DOWN 'Yield Basis'

Unlike stocks, which are quoted in dollars, most bonds are quoted with a yield basis. For example, assume a company is listed with a 6.75% coupon rate and is set to mature 10 years from the date of issuance. The \$1,000 par bond is trading at a dollar value of 940.00.

The yield basis can be calculated using the current yield formula presented as: Coupon / Purchase Price

Following our example above, the coupon to be paid annually is 6.75% x \$1,000 = \$67.50. Therefore, the yield basis is \$67.50 / \$940 = 0.0718, or 7.18%. The bond will be quoted to investors as having a yield basis of 7.18%. The yield quote tells a bond trader that the bond is currently trading at a discount because its yield basis is greater than its coupon rate (6.75%). If the yield basis is less than the coupon rate, this would indicates that the bond is trading at a premium since a higher coupon rate increases the value of the bond in the markets. A bond trader could then compare the bond to others within a certain industry.

The yield basis of a pure discount instrument can be calculated using the bank discount yield formula, which is:

r = (Discount / Par Value) x (360/t)

where r = annualized yield

discount = Par value minus Purchase price

t = time left to maturity

360 = bank convention for the number of days in a year

Unlike the current yield, the bank discount yield takes the discount value from par and expresses it as a fraction of the par value, not the current price, of the bond. This method of calculating the yield basis assumes simple interest, that is, no compounding effect is factored in. Treasury bills are quoted only on bank discount basis.

For example, assume a Treasury bill with a \$1,000 face value is selling for \$970. If its time to maturity is 180 days, the yield basis will be:

r = [(\$1,000 - \$970)/\$1,000] x (360/180)

r = (\$30/\$1,000) x 2

r = 0.06, or 6%

As Treasury bills pay no coupon, the bondholder will earn a dollar return equal to the discount if the bond is held until it matures.

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