Interest rates influence the stock market, but they are most closely related to the bond market. The bond market incorporates bond prices, which moves our understanding from interest rates as a form of payment to interest rates as a form of market return.
A debt contract is defined by interest payments and maturity. Another word for maturity is term. The principal is the amount borrowed and it is repaid at maturity. Many personal loans are amortizing (meaning principal is slowly repaid), but most sovereign and corporate bonds have a single principal repayment at maturity. In the bond market, the face value of the bond is the amount borrowed at origination and repaid at maturity. A discount bond is a bond that does not make interest payments. Discount bonds are issued at a discount to face value. The buyer pays less than face value for the bond and then receives the face value at maturity. In this way, the discounted prices serves as the functional equivalent of interest. For instance, a $1000 discount bond might be issued at $950. A coupon bond is a bond that makes regular interest payments called coupon payments. The coupon rate is a percentage of the face value that determines the coupon payment. For example, a $1000 bond with a coupon rate of 5% makes a coupon payment of $50. The coupon rate is a form of interest on a coupon bond that is unchanging. It is a feature of the bond contract itself that obligates the borrower to make the regular coupon payments. Coupon bonds make regular payments of a fixed amount, which is why bonds are referred to as fixed-income.
If you understand discount bond and coupon bond, you can understand that there are multiple ways to make money in the bond market. Money can be made on the value of the bond (like a discount bond) or the interest payments (like a coupon bond).
In the bond market, interest rates are referred to as yield. Yield is another term for interest or return. A return on investment is often referred to as the yield. The most important form on interest rate to understand in the bond market is the yield to maturity. The yield to maturity incorporates the value of the bond, the interest payments on the bond, and the maturity of the bond. In other words, it is the total return to the bond investor from the present to maturity that incorporates both the value of the bond and interest payments on the bond. Yield to maturity is a market interest rate that changes with market trading, not a contractual interest rate that is fixed at issuance.
A basic form of a coupon-bond valuation formula that includes yield to maturity. Here is the formula for a two-period coupon bond:
Note that this is a variation of the present value calculation. Here, we are using price as present value and yield to maturity (YTM) as the interest rate in the denominator. The FV in this equation can be thought of as future value, but more specifically as face value. The face value is the principal returned at maturity. The C is the coupon payment, which is coupon rate multiplied by face value. The contractual features of the bond are the face value, the maturity, and the coupon rate. Let’s say that this is a $1000 two-year bond that makes annual coupon payments at a coupon rate of 4%. This would result in the following equation:
Note that we have now have one equation with two unknowns: price and yield to maturity. This means that price and yield to maturity are mechanically linked. One could say that price determines yield to maturity or, alternatively, that yield to maturity determines price. In other words, they are two sides of the same coin. If you know the price of the bond, you can calculate the YTM and, if you know YTM, you can calculate the price. This highlights that yield to maturity is a market interest rate. It is not a fixed, contractual interest rate like the coupon rate. It changes with price. In the example above, suppose that the yield to maturity is 6%. We can calculate that the price is $963.33. Similarly, if we know that the price is $963.33, we can calculate that the yield to maturity is 6%. Price and yield to maturity are co-determined.
Note that price is on the left hand side of the equation and yield to maturity is in the denominator on the right hand side of the equation. This implies that price and yield to maturity have an inverse relationship. A higher price means lower yield to maturity and a lower price means a higher yield to maturity. This is a fundamental relationship that is critical to understanding the bond market. One does not cause the other and it is not a negative correlation. The inverse relationship is just math, an outcome of the bond pricing equation.
Prices in the bond market are constantly changing just like stock prices. When there is greater demand for a bond the price will rise and with less demand the price of a bond will fall. A bond with a price below face value is trading at a discount and a bond with a price above face value is trading at a premium.
Now consider again how to understand yield to maturity. Yield to maturity is a market interest rate that incorporates price. Consider an investor who buys a bond at a discount. This means that the investor pays a price that is less than face value. If the investor holds the bond to maturity, the investor will be paid the coupon payments and the full face value of the bond at maturity. This means that the total return to the investor will be greater than just the coupon payments. The investor will also be earning the difference between the discounted price and the face value. The yield to maturity incorporates this additional return from the discounted price. Therefore, bonds trading at a discount have a yield to maturity that is greater than the coupon rate. In contrast, bonds trading at a premium will return less to the investor at maturity than what was paid. Therefore, premium bonds have a yield to maturity that is less than the coupon rate.
As explained in the introduction to interest rates, interest rates tend to rise in a growing economy and fall in a slowing economy. Similarly, yield to maturity rises in a growing economy and falls in a slowing economy. Yield to maturity is a nominal interest rate, so it also includes inflation. As inflation expectations rise, yield to maturity will rise.
When yields in the bond market increase, the price of existing bonds will fall. This is interest rate risk. Think about an investor holding a bond that pays a 4% coupon rate and has a 4% yield to maturity. Suppose that the economy improves and interest rates start rising. A new bond is issued that pays a 5% coupon rate. How will this affect the value of the bond paying 4%? It will decline. The price of the initial bond will decline until the bond has a yield to maturity of 5%, which is equivalent to the new bonds paying a 5% coupon. Therefore, when rates rise, the value of existing bonds fall. On the flip side, when rates fall, the value of existing bonds rise. If new bonds are being issued at 3%, the price of the initial bond will increase until the bond has a yield to maturity of 3%, which is equivalent to to the new bonds paying a 3% coupon. Interest rate risk is two sided. Rising rates will cause bond prices to fall and falling rates will cause bond prices to rise.
Recall that yields reflect the time value of money. When interest rates rise, this will increase the time value of money, which increases the discount factor in the bond pricing equation. This is why rising rates cause bond prices to fall (interest rate risk). Now think about bond maturity. Bonds will longer maturity have coupon payments and principal repayment that are further in the future. How do you think this will affect interest rate risk? Interest rate risk is greater for bonds with longer maturity. Mechanically, the exponents on the discount factor highlight this fact. Cash flows that occur further in the future are discounted more. When the discount factor increases in these ratios, it will have an even more powerful effect. In other words, the effect of rising yield on price is greater for bonds with longer maturity. A small change in yield has a proportionately larger negative impact on price for long-term bonds. Conversely, short-term debt is relatively more insulated from interest rate risk.
This brings us to the sovereign bond market.
Before understanding corporate bonds, you need to understand sovereign bonds. Sovereign bonds are bonds issued by governments. For instance, “Treasuries” are securities issued by the U.S. government. Sovereign bonds form a benchmark for corporate bonds in any country, so it is impossible to understand corporate bonds without understanding sovereign bonds.
Sovereign bonds serve as a debt benchmark because they are the risk-free rate. U.S. Treasury securities are backed by the full faith and credit of the U.S. government. The government has the power to tax the people, which means that it should have sufficient cash flow to pay the obligations as long as the power of taxation holds. The term “risk-free” specifically means that U.S. Treasuries will not default (they do not have credit risk). As such, there is no credit risk premium in Treasuries. They are often viewed as a the safest security on the planet due to the global strength of the U.S. government. This makes Treasuries the ideal financial security for studying the other concepts of interest rate risk. Treasuries do not have credit risk (risk-free), but they do have interest rate risk.
The U.S. Treasury issues short-term debt securities and long-term debt securities. Treasury bills are the government debt component of the money market, which is the part of the debt market with short-term maturities. Common maturities of Treasury bills are 1 month, 2 month, 3 month, 6 month, and 1 year. Treasury bills are discount securities that do not make any interest payments. They are issued by the U.S. Treasury at a discount to face value. Treasury notes and bonds (I will refer to them jointly as Treasury bonds) are Treasury securities with maturities of 2 years or more. Common maturities are 2, 3, 5, 7, 10, and 30 years. For instance, the 10-year Treasury note is a debt obligation issued by the United States Department of the Treasury with a maturity of 10 years upon initial issuance. Treasury bonds are coupon bonds that make semi-annual coupon payments to the bond holder.
Treasuries are debt securities that each have a yield to maturity. This yield to maturity is determined by price, coupon payment, and maturity as explained above.
The combination of yields to maturity on Treasury securities of different maturities is called the yield curve. The yield curve includes information on the yields of short-term securities all the way up through the yields of long-term securities. This provides a benchmark government yield for securities of any maturity. This functions as a the key baseline yield for corporate bonds of various maturities. Their yield will be compared to a Treasury security of comparable maturity. The origin of the yield curve is the overnight interest rate which is set by the central bank. Yields up to one year closely reflect the rates set by monetary policy. Yields at maturities greater than a year are determined more by investors in the bond market. Changes in investor demand will drive changes in longer-term yields, like the 10-year yield.
The term premium is the difference in yield to maturity between long-term and short-term debt securities. It measures how much more investors are compensated for buying longer-term securities. For instance, suppose that the 10-year Treasury yield is 5% and the 2-year Treasury yield is 3%. The “10 minus 2” term premium is 2%.
The yield curve is typically upward sloping. This means that longer-term Treasury securities typically have higher yield than shorter-term Treasury securities. A yield curve in which all Treasuries have roughly the same yield is a flat yield curve. An inverted (downward sloping) yield curve means that longer-term Treasury securities have a lower yield than shorter-term Treasury securities. An upward sloping yield curve has a positive term premium and an inverted yield curve has a negative term premium.
The yield on long-term securities reflect expectations of future short-term yields. An investor can invest money in long-term securities or an investor can roll over a sequence of short-term securities. For instance, one two-year bond or a sequence of two one-year bonds. Prices reflect market expectations, so these strategies should expect to have the same yield. If long-term yields are greater than short-term yields, the market must expect short-term rates to rise. Conversely, if long-term yields are less than short-term yields, the market must expect short-term rates to fall.
Based on the expectations hypothesis, the shape of the yield curve depicts the outlook for short-term interest rates. We know that rates tend to rise in a growing economy and fall in a slowing economy. This is a why an upward-sloping yield curve indicates a positive outlook for the economy and an inverted yield curve indicates a negative outlook for the economy. An inverted yield curve historically has been a predictor of recessions.