Understanding Bond Pricing and Yield

Bonds can be sold at their face value, at more than their face value or at less than their face value. Because the market cannot change the fixed coupon rate—which is set in stone when the bond is issued—the market affects the price at which the bond is sold.

As the interest rate changes in the market, so does the price. The following are some useful definitions in understanding yield and pricing in bond-speak. While most new issue corporate bonds are generally issued at par, new issue municipal bonds may be sold at par, at a discount or at a premium. The coupon rate of the bond sets the interest payments.

The amount of interest that you receive is the coupon rate multiplied by the face value of the bonds that you hold. The actual price that you pay for the bonds and the yield that you receive are based on market conditions. The connection between yield and price is important to grasp. In this case, the bond sells at a premium an increase over face value. Occasionally, a bond will sell at its face value, and at such times it is said to sell at par. It is often thought that newly issued bonds are priced at par, but this need not be the case.

These changes affect you only if you choose to sell a bond you already own prior to its due date or seek to purchase a bond on the open market. Corporate bonds, Treasury bonds and U. Simply move the decimal point one place to the right to find the dollar equivalent. To find out what your total cost would be, multiply the dollar amount by the number of bonds.

As suggested, imagine a bond coupon as a fulcrum that creates the equilibrium between bonds sold at different prices, just like a seesaw. The coupon is the interest rate of a bond stated as a percentage of its face value. The value of bonds declines when interest rates rise, and the value of bonds increases when interest rates decline.

In short, we say that yield moves inversely to price. This concept is so important that we highlight it here: Bonds are bought and sold based on yield, not on price. This represents a key distinction between bonds and stocks.

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Stocks are always bought and sold in terms of price. Yield is the general term for the percentage return on a bond investment, taking into account the price of the bond. It is often called the rate of return.

In bond language, the yield is very different from the stated coupon rate. It is critical to understand these concepts in order to understand how bonds are valued, bought and sold. Sellers of individual bonds use a variety of yield terms. Bond professionals in particular have come up with a bewildering array of meanings.

Each term, in its own way, seeks to create comparability among bonds with different financial characteristics.

Coupon vs Yield | Top 8 Useful Differences (with Infographics)

Understanding the different measures of yield will enable you to buy bonds and invest wisely. We explain the different measures of yield that you should ask about in order to understand and compare the returns available on different bonds. The most important measures are current yield, yield-to-maturity and yield-to-call. Most of the yields require a financial calculator for you to compute them accurately. However, your broker or adviser will provide you with all of the relevant measures of yield if you so request before you buy a bond.

Current yield CY is the only simple calculation among the lot and it is used as a measure of cash flows. It is the cash on cash return. Be sure to omit the percentage sign from the coupon rate the numerator , otherwise the equation will not work. If you are looking solely at cash flow, then current yield is a useful tool to compare cash flows from taxable and tax-exempt municipal bonds.

However, to look at bonds this way may lead you to misinterpret the value of an investment. Unlike current yield, all other bond yield calculations take compound interest into account. Compound interest is complex because it adds the interest to your principal and then compounds the new total; in effect, interest is being earned on interest. Municipal bonds compute yield on a day calendar.

Other investment products may compute yield on the day calendar. Minor differences in yield calculations of different investment products may result in their compound interest yields not being directly comparable. Compounded interest is based on the premise that money is constantly reinvested to generate further income. Yield-to-maturity and yield-to-call are based on the concept of compound interest. Yield-to-maturity YTM is a common measure of return on which individual bonds are traded and quoted.

In the bond world, calculations assume that money never lies fallow or is hidden away in a mattress. Rather, it is constantly reinvested to generate further income. Although YTM is not a perfect measure of return, it is widely used because it is a unifying standard for all bond pricing. For example, it enables you to compare a premium bond to a discount bond or to compare a bond coming due in five years to a bond coming due in 20 years. YTM makes the following assumptions: 1 You retain ownership until the bond comes due and 2 all interest payments are reinvested at the quoted YTM rate.

However, since interest rates change over time, your actual YTM on a bond will change as well. Keep in mind that the cash flow will not vary. If rates rise, for example, and you are able to reinvest the semiannual interest payments at a higher rate, your actual return will be higher than the quoted YTM.

If interest rates decline over the life of the bond and you reinvest the interest payments at a lower rate, your actual YTM will be lower. Note that the key concept underpinning all this is compound interest.

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The YTM calculation assumes reinvestment of every interest payment at the YTM rate, because the calculation could not otherwise be made. One exception to the variation just mentioned is a zero-coupon bond. In this case, since there is no cash coupon, the stated YTM is precisely correct.

Bond Yield Vs the Coupon Rate

If a bond is callable, you should be quoted two rates, the yield-to-maturity and the yield-to-call YTC. YTC is particularly important when interest rates have been falling because there is a good possibility that the issuer may decide to exercise its right to call the bond before its due date. In this case the issuer buys your bond back from you, generally at its face value.

This is especially likely if the coupon rate of the bond is higher than the prevailing rate of interest. Yield-to-worst YTW is the lowest possible yield you could receive for the bond. Consider the following complex but logical concept:. If a bond is sold at a premium and there are multiple calls, the YTW is the yield to the first call date.

Bond Yield and Return

When a bond becomes callable, it may be called at the first call date or any date thereafter. The later a bond is called after the first call date, the higher the yield-to-worst will actually be if there is only a par call. If a bond is sold at a discount and the bond is callable, the yield-to-worst is the yield-to-maturity. The yield-to-worst is defined as the lower of the yield-to-call or yield-to-maturity.

When a bond is sold at a discount and is called prior to maturity, the discount is earned quicker so that the yield-to-maturity is lower than the yield-to-call. If a bond is sold at par, the current yield, the yield-to-maturity and the yield-to-call will all be the same. That way you are not surprised by the possibility that you will get a lower yield. Calculating Bond Yields in Microsoft Excel. As Stan and Hildy Richelson explain, most bond yields require a financial calculator to be calculated correctly.

Individual investors who are familiar with Microsoft Excel can use a spreadsheet to calculate yields as well. Current Yield CY. The formula is annual coupon payment dividend by price. Yield-to-Call and Yield-to-Worst. The calculation is essentially the same for yield-to-worst, but if there are multiple calls, you must ensure the inputs reflect the yield to the first call date. For this bond:. Though this example has the highest coupon and the highest price, this still may be the best investment depending upon how you see the future.

A: The coupon rate tells you the annual amount of interest paid by a fixed income security. The coupon rate, however, tells you very little about the yield. For most securities, the yield is a good proxy for the return of the fixed income security that is, how much you can expect your wealth to increase if you purchase the security and is far more meaningful than the coupon rate. To illustrate, consider these two Treasury bonds:. Both bonds mature around the same time, but they have enormous differences in coupon.