# Yield Basis

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### A fixed-income security's price can be expressed using the "yield basis" as a percentage of its annual income rather than as a fixed dollar amount. As a result, comparing securities with various features, such as coupon rates, maturity dates, and par values, is made simpler.

You can get the yield basis by dividing the security's purchase price by the yearly coupon amount, which represents the interest payment. For instance, if you purchase a \$1,000 bond with a 6% coupon rate, you will earn \$60 in income per year. Your yield basis is \$60 divided by \$950, or 0.0632, or 6.32%, if you paid \$950 for the bond.

The yield basis informs you of the amount of income you can expect from your investment in relation to its purchase price. Additionally, it lets you know whether the security is selling for more or less than its face value. When the purchase price is below par value, it is said to be at a discount, and when it is over par value, it is said to be at a premium.

A bond that is trading at a discount will have a higher yield basis than its coupon rate, because you are paying less for the same amount of income. When a bond is selling at a premium, the yield basis will be lower than the coupon rate because you are paying more for the same amount of income.

A bond with a \$1,000 par value and a 6% coupon rate, for instance, could cost \$1,050, so your yield basis would be \$60 / \$1,050, or 0.0571 percent, or 5.71%. If you had purchased the bond at par, you would have received a higher return compared to your initial cost.

The bank discount yield is yet another method for estimating the cost of a fixed-income instrument. This technique is only applied to pure discount instruments, like Treasury bills, which don't pay coupons and are offered at a discount to their face value.

The difference between the face value and the purchase price is divided by the face value, and the annualized result is determined using a 360-day year. For example, if you buy a Treasury bill with a face value of \$1,000 and a maturity of 180 days for \$970, your bank discount yield will be:

(\$1,000 - \$970) / \$1,000 x (360 / 180) = 0.06, or 6%.

The bank discount yield tells you how much return you will earn from holding the security until maturity relative to its face value. However, it uses an arbitrary number of days in a year and ignores the effect of interest compounding. As a result, it is not a reliable indicator of the security's actual yield.

The effective annual yield (EAY), which accounts for compounding and actual calendar days in a year, is a more precise indicator of a fixed-income security's true yield. The EAY can be calculated by using the following formula:

EAY = (1 + HPY) ^ (365 / t) - 1

where HPY is the holding period yield and t is the number of days until maturity.

The holding period yield is calculated by dividing the total return from holding the security by its purchase price. The total return includes both interest income and capital gain or loss.

For example, if you buy a bond with a par value of \$1,000 and a coupon rate of 6% for \$950 and sell it after one year for \$980, your holding period yield will be:

(\$60 + \$30) / \$950 = 0.0947, or 9.47%.

Your effective annual yield will be:

(1 + 0.0947) ^ (365 / 365) - 1 = 0.0947, or 9.47%.

Note that in this case, the EAY is equal to the HPY because the holding period is one year. If the holding period is less than one year, the EAY will be higher than the HPY because of compounding.
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