Advanced Bond Concepts: Term Structure of Interest Rates
  1. Advanced Bond Concepts: Introduction
  2. Advanced Bond Concepts: Bond Type Specifics
  3. Advanced Bond Concepts: Bond Pricing
  4. Advanced Bond Concepts: Yield and Bond Price
  5. Advanced Bond Concepts: Term Structure of Interest Rates
  6. Advanced Bond Concepts: Duration
  7. Advanced Bond Concepts: Convexity
  8. Advanced Bond Concepts: Formula Cheat Sheet
  9. Advanced Bond Concepts: Conclusion

Advanced Bond Concepts: Term Structure of Interest Rates

The term structure of interest rates, also known as the yield curve, is a very common bond valuation method. Constructed by graphing the yield to maturities and the respective maturity dates of benchmark fixed-income securities, the yield curve is a measure of the market's expectations of future interest rates given the current market conditions. Treasuries, issued by the federal government, are considered risk-free, and as such, their yields are often used as the benchmarks for fixed-income securities with the same maturities. The term structure of interest rates is graphed as though each coupon payment of a noncallable fixed-income security were a zero-coupon bond that "matures" on the coupon payment date. The exact shape of the curve can be different at any point in time. So if the normal yield curve changes shape, it tells investors that they may need to change their outlook on the economy.

There are three main patterns created by the term structure of interest rates:


1) Normal Yield Curve: As its name indicates, this is the yield curve shape that forms during normal market conditions, wherein investors generally believe that there will be no significant changes in the economy, such as in inflation rates, and that the economy will continue to grow at a normal rate. During such conditions, investors expect higher yields for fixed income instruments with long-term maturities that occur farther into the future. In other words, the market expects long-term fixed income securities to offer higher yields than short-term fixed income securities. This is a normal expectation of the market because short-term instruments generally hold less risk than long-term instruments; the farther into the future the bond's maturity, the more time and, therefore, uncertainty the bondholder faces before being paid back the principal. To invest in one instrument for a longer period of time, an investor needs to be compensated for undertaking the additional risk.

Remember that as general current interest rates increase, the price of a bond will decrease and its yield will increase.



2) Flat Yield Curve: These curves indicate that the market environment is sending mixed signals to investors, who are interpreting interest rate movements in various ways. During such an environment, it is difficult for the market to determine whether interest rates will move significantly in either direction farther into the future. A flat yield curve usually occurs when the market is making a transition that emits different but simultaneous indications of what interest rates will do. In other words, there may be some signals that short-term interest rates will rise and other signals that long-term interest rates will fall. This condition will create a curve that is flatter than its normal positive slope. When the yield curve is flat, investors can maximize their risk/return tradeoff by choosing fixed-income securities with the least risk, or highest credit quality. In the rare instances wherein long-term interest rates decline, a flat curve can sometimes lead to an inverted curve.




3) Inverted Yield Curve: These yield curves are rare, and they form during extraordinary market conditions wherein the expectations of investors are completely the inverse of those demonstrated by the normal yield curve. In such abnormal market environments, bonds with maturity dates further into the future are expected to offer lower yields than bonds with shorter maturities. The inverted yield curve indicates that the market currently expects interest rates to decline as time moves farther into the future, which in turn means the market expects yields of long-term bonds to decline. Remember, also, that as interest rates decrease, bond prices increase and yields decline.

You may be wondering why investors would choose to purchase long-term fixed-income investments when there is an inverted yield curve, which indicates that investors expect to receive less compensation for taking on more risk. Some investors, however, interpret an inverted curve as an indication that the economy will soon experience a slowdown, which causes future interest rates to give even lower yields. Before a slowdown, it is better to lock money into long-term investments at present prevailing yields, because future yields will be even lower.




The Theoretical Spot Rate Curve
Unfortunately, the basic yield curve does not account for securities that have varying coupon rates. When the yield to maturity was calculated, we assumed that the coupons were reinvested at an interest rate equal to the coupon rate, therefore, the bond was priced at par as though prevailing interest rates were equal to the bond's coupon rate.

The spot-rate curve addresses this assumption and accounts for the fact that many Treasuries offer varying coupons and would therefore not accurately represent similar noncallable fixed-income securities. If for instance you compared a 10-year bond paying a 7% coupon with a 10-year Treasury bond that currently has a coupon of 4%, your comparison wouldn't mean much. Both of the bonds have the same term to maturity, but the 4% coupon of the Treasury bond would not be an appropriate benchmark for the bond paying 7%. The spot-rate curve, however, offers a more accurate measure as it adjusts the yield curve so it reflects any variations in the interest rate of the plotted benchmark. The interest rate taken from the plot is known as the spot rate.


The spot-rate curve is created by plotting the yields of zero-coupon Treasury bills and their corresponding maturities. The spot rate given by each zero-coupon security and the spot-rate curve are used together for determining the value of each zero-coupon component of a noncallable fixed-income security. Remember, in this case, that the term structure of interest rates is graphed as though each coupon payment of a noncallable fixed-income security were a zero-coupon bond.

T-bills are issued by the government, but they do not have maturities greater than one year. As a result, the bootstrapping method is used to fill in interest rates for zero-coupon securities greater than one year. Bootstrapping is a complicated and involved process and will not be detailed in this section (to your relief!); however, it is important to remember that the bootstrapping method equates a T-bill's value to the value of all zero-coupon components that form the security.




The Credit Spread

The credit spread, or quality spread, is the additional yield an investor receives for acquiring a corporate bond instead of a similar federal instrument. As illustrated in the graph below, the spread is demonstrated as the yield curve of the corporate bond and is plotted with the term structure of interest rates. Remember that the term structure of interest rates is a gauge of the direction of interest rates and the general state of the economy. Corporate fixed-income securities have more risk of default than federal securities and, as a result, the prices of corporate securities are usually lower, while corporate bonds usually have a higher yield.



When inflation rates are increasing (or the economy is contracting) the credit spread between corporate and Treasury securities widens. This is because investors must be offered additional compensation (in the form of a higher coupon rate) for acquiring the higher risk associated with corporate bonds.

When interest rates are declining (or the economy is expanding), the credit spread between Federal and corporate fixed-income securities generally narrows. The lower interest rates give companies an opportunity to borrow money at lower rates, which allows them to expand their operations and also their cash flows. When interest rates are declining, the economy is expanding in the long run, so the risk associated with investing in a long-term corporate bond is also generally lower.

Now you have a general understanding of the concepts and uses of the yield curve. The yield curve is graphed using government securities, which are used as benchmarks for fixed income investments. The yield curve, in conjunction with the credit spread, is used for pricing corporate bonds. Now that you have a better understanding of the relationship between interest rates, bond prices and yields, we are ready to examine the degree to which bond prices change with respect to a change in interest rates.
Advanced Bond Concepts: Duration

  1. Advanced Bond Concepts: Introduction
  2. Advanced Bond Concepts: Bond Type Specifics
  3. Advanced Bond Concepts: Bond Pricing
  4. Advanced Bond Concepts: Yield and Bond Price
  5. Advanced Bond Concepts: Term Structure of Interest Rates
  6. Advanced Bond Concepts: Duration
  7. Advanced Bond Concepts: Convexity
  8. Advanced Bond Concepts: Formula Cheat Sheet
  9. Advanced Bond Concepts: Conclusion
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