Calculating and comparing bond yields isn't easy. Bonds can have varying frequencies of coupon payments; the number of days in the year may also differ. Because fixedincome investments use a variety of yield conventions, it is important to convert the yield to a common basis when comparing different bonds. Taken separately, these conversions are straightforward; however, when a problem contains both compounding period and day count conversions, the correct solution technique is not so obvious. In this article, we'll take a look at a couple of the common problems investors run into when calculating these yields and show you how to work them out. (To learn all about bonds, see our Bond Basics and Advanced Bond Concepts tutorials.)
Current Conventions
U.S. Treasury bills (Tbills) and corporate commercial paper are quoted and traded in the market on a discount basis. This means that there is no explicit coupon interest payment  the difference between the face value at maturity and the current price is the implicit interest payment. The amount of the discount is stated as a percentage of the face value, which is then annualized over a 360day year. (Keep reading about commercial paper in Money Market: Commercial Paper and AssetBacked Commercial Paper Carries High Risk.)
The problems with rates quoted on a discount basis are wellknown: first, a discount rate is a downwardly biased representation of the investor's rate of return (or the borrower's cost of funds) over the term to maturity; and, second, the rate is based on a hypothetical year that has only 360 days. The downward bias comes from stating the discount as a percentage of the face value. In investment analysis, one naturally thinks of a rate of return as the interest earned divided by the current price, not the face value. Since the price of a Tbill is less than its face value, the denominator is too high, so the discount rate understates the true yield.
Bank CDs have historically been quoted on a 360day year also, and institutionally, many still are. However, because the rate is a little higher using a 365day year, most retail CDs are now quoted using a 365day year. Returns are marketed using annual percentage yield or APY. This rate is not to be confused with APR or annual percentage rate, the rate at which most banks quote mortgages. In an APR calculation, the interest rate received during the period is simply multiplied by the number of periods in a year. The effect of compounding is not included. APY, however, takes effects of compounding into account. (To learn more, read APR Vs. APY: How The Distinction Affects You.)
A sixmonth CD that pays 3% interest has an APR of 6%. However, the APY is 6.09%, calculated as follows:
APY = (1 + 0.03)^2 – 1 = 6.09% 
Yields on Treasury notes and bonds, corporate bonds and municipal bonds are quoted on a semiannual bond basis (SABB) because their coupon payments are made semiannually. Compounding is twice a year, and a 365day year is used.
Conversions
365 Days Vs. 360 Days
In order to properly compare the yields on different fixedincome investments, it is important to use the same yield calculation. The first and easiest conversion is changing a 360day yield to a 365day yield. To change the rate, simply "gross up" the 360 day yield by the factor 365/360. A 360day yield of 8% would equate to a 8.11% yield based on a 365day year.
8% x (365/360) = 8.11% 
Discount Rates  182 Days
Discount rates, commonly used on Tbills, are generally converted to a bondequivalent yield (BEY), sometimes called a couponequivalent or an investment yield. The conversion formula for "shortdated" bills with a maturity of 182 or fewer days is the following:
Where:
BEY = the bondequivalent yield
DR = the discount rate (expressed as a decimal)
N = the number of days between settlement and maturity
Long Dates
For "longdated" Tbills that have a maturity of more than 182 days, the usual conversion formula is a little more complicated because of compounding. The formula is:
Short Dates
For shortdated Tbills, the implicit compounding period for the BEY is the number of days between settlement and maturity. However, the BEY for a longdated Tbill does not have any welldefined compounding assumption which makes its interpretation rather difficult.
BEYs are systematically less than the annualized yields for semiannual compounding. In general, for the same current and future cash flows, more frequent compounding at a lower rate corresponds to less frequent compounding at a higher rate. A yield for more frequent than semiannual compounding  such as is implicitly assumed with both shortdated and longdated BEY conversions  must be lower than the corresponding yield for actual semiannual compounding.
BEYs and the Treasury
BEYs reported by the Federal Reserve and other financial market institutions should not be used as a comparison to the yields on longer maturity bonds. The problem is not that the widely used BEYs are inaccurate, they just serve a different purpose. That purpose is to facilitate comparison of yields on Tbills, Tnotes and Tbonds maturing on the same date. To make an accurate comparison, discount rates should be converted to a semiannual bond basis (SABB), because that is the basis commonly used for longer maturity bonds.
To calculate SABB, the same formula to calculate APY is used. The only difference is that compounding happens twice a year. Therefore, APYs using a 365day year can be directly compared to yields based on SABB.
A discount rate (DR) on an Nday Tbill can be converted directly to a SABB with the following formula:
A convenient feature in this equation is that it is stated as a function only of N and DR, which are directly observable for any traded Tbill. It is not necessary to calculate the price of the bill, making the equation a little easier to program into a spreadsheet and avoiding unnecessary rounding errors. Another key feature is that this conversion formula applies to both shortdated and longdated Tbills. Unlike BEYs, the SABB presents the yields in a form fully comparable to the yields on Treasury notes and bonds. The formula converts the Tbill discount rate, quoted for a 360day year and 360/N compounding periods per year, to a more reasonable investment yield, quoted for a 365day year and two compounding periods.
Conclusion
In summary, comparison of alternative fixedincome investments always requires conversion of yields to a common basis. The general rule is that the effects of compounding should be included and conversions should always be done on a 365day bond basis. Comparing bond yields may not be easy, but it shouldn't be too difficult for the average investor either.

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