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# Yield Basis

## What Is 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. The yield basis is calculated by dividing the coupon amount paid annually by the bond purchase price.

### Key Takeaways

• The yield basis method quotes the price of a fixed-income security (such as a bond) as a yield percentage instead of a dollar value.
• The yield basis method helps bond buyers easily compare the characteristics of various bonds before making a purchase.
• The yield quote tells the bond trader whether the bond is currently trading at a discount or premium compared to other bonds.
• Purchasing a bond on a net yield basis means the yield also includes the broker's profit or markup for executing the trade.

## Understanding 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.

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 indicate 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.

## Bank Discount Yield

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 a 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.

## Special Considerations

When purchasing bonds, it's important for the investor to understand the difference between the yield basis and the net yield basis. On the secondary market, you can purchase bonds through a broker/dealer, who could charge you a flat commission for this service. However, in lieu of a commission, your broker may opt to sell bonds on a net yield basis.

Net yield means the yield also includes the broker's profit for the transaction. This is the broker's markup, which is the difference between what the broker paid for the bonds and what the broker sells them for. If a broker offers bonds on a net yield basis, they've already included their markup. For example, if an online broker sells you a bond with a 3.75% yield to maturity (YTM), their profit is embedded directly in the price you pay and there is no separate commission.

When comparing various bonds for a possible purchase, bond buyers should ask their broker if the bonds are on a net yield basis or if they charge a separate commission to execute the trade. Brokers might charge other fees, such as a broker-assisted fee for transactions not conducted online. Your overall cost for the trade may also include accrued interest, which is the interest accrued on the bond between the last payment and the settlement date.

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