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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 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.


The term duration has a special meaning in the context of bonds. It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows.

It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations.


Duration changes as the coupons are paid to the bondholder. As the bondholder receives a coupon payment, the amount of the cash flow is no longer on the time line, which means it is no longer counted as a future cash flow that goes towards repaying the bondholder.

Duration increases immediately on the day a coupon is paid, but throughout the life of the bond, the duration is continually decreasing as time to the bond’s maturity decreases.

But duration also increases momentarily on the day a coupon is paid and removed from the series of future cash flows ‑ all this occurs until duration, eventually converges with the bond’s maturity. The same is true for a zero‑coupon bond.


Besides the movement of time and the payment of coupons, there are other factors that affect a bond’s duration: the coupon rate and its yield.

Bonds with high coupon rates and, in turn, high yields will tend to have lower durations than bonds that pay low coupon rates or offer low yields.

This makes empirical sense, because when a bond pays a higher coupon rate or has a high yield, the holder of the security receives repayment for the security at a faster rate.


More than once throughout this tutorial, we have established that when interest rates rise, bond prices fall, and vice versa. But how does one determine the degree of a price change when interest rates change?

Generally, bonds with a high duration will have a higher price fluctuation than bonds with a low duration. But it is important to know that there are also three other factors that determine how sensitive a bond’s price is to changes in interest rates.

These factors are term to maturity, coupon rate and yield to maturity. Knowing what affects a bond’s volatility is important to investors who use duration‑based immunization strategies, which we discuss below, in their portfolios.


If term to maturity and a bond’s initial price remain constant, the higher the coupon, the lower the volatility, and the lower the coupon, the higher the volatility.

If the coupon rate and the bond’s initial price are constant, the bond with a longer term to maturity will display higher price volatility and a bond with a shorter term to maturity will display lower price volatility.

Therefore, if you would like to invest in a bond with minimal interest rate risk, a bond with high coupon payments and a short term to maturity would be optimal.

An investor who predicts that interest rates will decline would best potentially capitalize on a bond with low coupon payments and a long term to maturity, since these factors would magnify a bond’s price increase.


The sensitivity of a bond’s price to changes in interest rates also depends on its yield to maturity.

A bond with a high yield to maturity will display lower price volatility than a bond with a lower yield to maturity, but a similar coupon rate and term to maturity.

Yield to maturity is affected by the bond’s credit rating, so bonds with poor credit ratings will have higher yields than bonds with excellent credit ratings.

Therefore, bonds with poor credit ratings typically display lower price volatility than bonds with excellent credit ratings.

All three factors affect the degree to which bond price will change in the face of a change in prevailing interest rates. These factors work together and against each other.

If a bond has both a short term to maturity and a low coupon rate, its characteristics have opposite effects on its volatility: the low coupon raises volatility and the short term to maturity lowers volatility. The bond’s volatility would then be an average of these two opposite effects.

Understanding what duration is, how it is used and what factors affect it will help you to determine a bond’s price volatility. Volatility is an important factor in determining your strategy for capitalizing on interest rate movements.

Furthermore, duration will also help you to determine how you can protect your portfolio from interest rate risk.


For any given bond, a graph of the relationship between price and yield is convex. This means that the graph forms a curve rather than a straight‑line (linear). The degree to which the graph is curved shows how much a bond’s yield changes in response to a change in price.


Convexity is also useful for comparing bonds. If two bonds offer the same duration and yield but one exhibits greater convexity, changes in interest rates will affect each bond differently.

A bond with greater convexity is less affected by interest rates than a bond with less convexity.

Also, bonds with greater convexity will have a higher price than bonds with a lower convexity, regardless of whether interest rates rise or fall.


Here is a summary of the different kinds of convexities produced by different types of bonds:

  1. The graph of the price‑yield relationship for a plain vanilla bond exhibits positive convexity. The price‑yield curve will increase as yield decreases, and vice versa. Therefore, as market yields decrease, the duration increases (and vice versa).
  2. In general the higher the coupon rate, the lower the convexity of a bond. Zero‑coupon bonds have the highest convexity.
  3. Callable bonds will exhibit negative convexity at certain price‑yield combinations. Negative convexity means that as market yields decrease, duration decreases as well.

Convexity is the final major concept you need to know for gaining insight into the more technical aspects of the bond market.

Understanding even the most basic characteristics of convexity allows the investor to better comprehend the way in which duration is best measured and how changes in interest rates affect the prices of both plain vanilla and callable bonds.


Most bond transactions can be completed through a full service or discount brokerage. You can also open an account with a bond broker.

If you do decide to purchase a bond through your broker, he or she may tell you that the trade is commission free. Don’t be fooled.

What typically happens is that the broker will mark up the price slightly; this markup is really the same as a commission.

To make sure that you are not being taken advantage of, simply look up the latest quote for the bond and determine whether the markup is acceptable. Remember, you should research bonds just as you would stocks.


Investing in the municipal, corporate and government bonds can become very complicated and oftentimes bond brokers are not as knowledgeable or trustworthy as one might be led to believe.

As a result, investments in the bond markets can be mismanaged, misrepresented and unsuitable investments offered and sold in violation of federal and state securities law and in breach of a bond broker’s fiduciary duty.

Bond brokers can also be held responsible for their negligence and failure to abide by commodities industry rules and regulations.

At the Law Offices of Robert Wayne Pearce, P.A. we know the nature, mechanics and risks of investing in the bond markets as well as the applicable laws, rules and regulations governing those investments.

Please contact us for a free consultation if you believe you have been harmed by brokers misconduct in connection with your municipal, corporate and government bond market investments.


Contact The Law Offices of Robert Wayne Pearce, P.A., in Boca Raton to discuss your fraud or misrepresentation claim. The firm can be reached by phone at 561-338-0037, toll free at 800-732-2889 or via e-mail.

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Robert Wayne Pearce

Robert Wayne Pearce has been a trial attorney for more than 40 years and is the founding partner of The Law Offices of Robert Wayne Pearce. You can learn more about Robert and his accomplishments by clicking here.

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