There is a very close connection between bond prices and interest rates. We will focus on interest rate calculated from prices of traded US government securities
and show how the interest rate on a particularly simple type of security can be derived solely from it price. We focus on yields derived solely from it price. We focus on yields derived from US government securities because these assets are backed by the full faith and credit of the government and, therefore, have virtually no default risk.
The US government issues securities of many different maturities: the maturity is the length of time until the final payment on the security is made by the issuer. Treasury bonds are fixed coupon security with initial maturities of more than 10 years. Treasurers note are fixed coupon securities with initial maturities of the year or less.
If we know a bonds current price and payments that the bondholder will receive over the course of the bond’s life. We can calculated the implied interest rate on the bond. This interest rate called yield-to-maturity, equates the current price of the bond to the present valve of the bond’s payment stream. The relationship between the maturity of bonds and the interest rate implied by bond prices is called the term structure of interest rates. A plot of the relationship between interest rates on short-term. Bonds are lower than interest rates on long-term. Bonds as shown for the third quarter 1989. The shape of the typical yield curve shows that interest rates often vary with maturity. We might also suspect that the volatility of interest rates varies with maturity. But before we turn to how volatility is measured and how volatility is related to maturity. It’s clarify the relationship between interest rates and the price of particularly simple type of bond. Interest rates and bond prices. Interest rates on certain types of bonds can be derived
solely from the bonds price and maturity. Let’s look at a particular type of bond called a discount, or zero. Coupon bond. A discount bond sells at a discount from its face valve and makes no interest payments over its life time. When the bond matures, the bondholder received the bond’s face valve. For example, a one- year treasury bill with a face valve of $10,000 is a discount bond that promises to pay the holder &10,000 in one year’s time. Such a bond may sell for a current price of $9434, in which case the implied interest rate on the bond is 6 percent ($10,000-$9434) $9434 = 06) clearly, as the current price of the bond changes, the implied interest rate will change. For example suppose the current price of the bond falls to $9009. The implied interest rate on the bond is 11 percent C$i0,0000-9009) 1 $9009=11).
So as the price of the bond falls, the interest rate rises, as the price of the bond falls, the interest rate falls. The US Treasury does not issue discount bonds with maturities greater than one year. However, financial market participants create pure discount bonds from long-term, coupon-paying treasure bonds by “stripping” the coupon (semi annual interest) payments from the principal payments and selling the components as separate discount securities. In February 1985, the treasury announced the STRIPS (Separate Trading of Registered Interest and Principal of Securities) program, which facilitated the “stripping” of long term treasury bonds. Under the Strips program, all newly issued treasury bonds and notes with maturities of 10 years of publications such as the wall Street journal.
Since there is a clearly defined relationship between interest rates and prices for discount bonds we need to refer to only one of those elements, not both. When we consider discount bond prices, we can easily derive the implied interest rates. Similarly, when we talk about the volatility of discount bond prices, we will easily be able to make inferences about the volatility of interest.
Trends and cycles in interest rates: we can plot the interest rate on discount bonds with a 10 year maturity from 1959 to the early 1980s, after which it generally declined.
We can discern two types of variability in interest rate and hence in discount bond prices.
Long term and short-term, long term variability refers to broad trends in interest rates, such as the upward trend until the early 1980s and the downward trend since then. Short term variability refers to how interest rates, we would like to remove that part of interest rate volatility associated with swings of longer duration than the typical business cycle.
The National Bureau of Economic Research defined minor cycles as recurrent fluctuations lasting from two or four years and major cycles as recurrent lasting about eight years. The long-term trends in interest rates that are of greater duration than typical business-cycle lengths. This long term trend is chosen in such a way that it removes the swings in interest rates associated with periods longer than about eight years. The remaining short term variability than
corresponds more closely to variability that is part of the business-cycle movement in interest rate. We will define the difference between the actual interest rate and the long-run trend as the cyclical component of the interest rate. The long swings in interest rates have been taken out, and all the variability in interest rate is around zero because of the long term trend.
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