# What Is a Zero Coupon Yield Curve?

The zero coupon rate is the return, or yield, on a bond corresponding to a single cash payment at a particular time in the future. This would represent the return on an investment in a zero coupon bond with a particular time to maturity. The zero coupon yield curve shows in graphical form the rates of return on zero coupon bonds with different periods to maturity. The reason for constructing a zero coupon yield curve is for use as a basic tool in determining the price of many fixed income securities.

A zero coupon bond does not pay interest but instead carries a discount to its face value. The investor therefore receives one payment of the face value of the bond on its maturity. This face value is the equivalent of the principal invested plus interest over the life of the bond. The yield on the bond might be calculated on the basis of the amount of discount and the length of time to maturity, and it is equivalent to the internal rate of return on the investment. It is possible to use a Treasury bill that is close to maturity as an equivalent of a zero coupon bond and to use the yield on this bond to compute the yield curve.

At any particular time, the interest rate that may be paid on a financial instrument depends on the term of the investment. A yield curve sets out on a graph the return on financial instruments such as bonds that have a similar credit risk and currency but a different period of time until maturity. The horizontal axis of the graph represents the time to maturity, and the vertical axis shows the yield. A typical yield curve would rise from left to right because yield rises with longer periods to maturity.

Bonds with a shorter time period until maturity carry less risk for the investor and would therefore have a lower yield, and the risk and yield normally tend to increase as the period to maturity becomes longer. A flat yield curve is possible, if the outlook is uncertain. A negative or downward-sloping yield curve could occur if investors are expecting reduced inflation in the longer term.

The price of a bond at any particular time depends on the market conditions, including the expectations of the market in respect of the future movements in interest rates. The zero coupon yield curve might change with each fluctuation in market sentiment or in economic conditions. The changes in the zero coupon yield curve are useful as a guide to the changes affecting the whole market. The use of this basic tool can therefore help investors and analysts to understand the effects of these changes on a range of investments.

## Discussion Comments

@Nefertini - That's good advice. Keep in mind also that many zero coupon bonds have a long time before they mature. You may have to wait ten, twenty, or thirty years to see a return on your money.

In addition to determining the zero coupon bond yield prior to purchasing one, look at the taxes you may have to pay. On some bonds you may have to pay state or federal taxes before the bond matures.

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