Term Structure of Interest Rates – Definitions and Theories

2024-09-23Last Updated: 2024-09-23

The term structure of interest rates, commonly known as the yield curve, shows the nominal interest rates on default free, pure discount bonds of all maturities. The Treasury yield curve and the term structure of interest rates are almost the same thing. The only difference is that the term structure is based on pure discount bonds whereas the yield curve is based on coupon bond yields.

The yield curve may be upward sloping, downward sloping or humped. When the interest rate increases at a decreasing rate and the inflation premium is expected to rise gradually,the combined effect is an upward sloping yield curve. When the rate of inflation is expected to decrease in the future and the the expected decline is large enough to offset the interest risk premium, it produces a downward sloping term structure.

The shape of the yield curve depends on two factors:

Expectations about future inflation
The relative riskiness of securities with different maturities

Generally, the yield curve is upward sloping because short-term securities have less interest rate risk than long-term rates, hence smaller market risk premiums. An upward sloping term structure may be a reflection of anticipated increases in inflation. Therefore, short-term rates are normally lower than long-term rates.

TERM STRUCTURE THEORIES

1. Expectations Theory

The expectations theory states that the yield curve depends on expectations concerning future inflation ratios. Under the expectations theory, maturity risk premium and liquidity risk premium are zero.

In this theory, the investors are indifferent with respect to maturity in the sense that they don’t view long-term bonds riskier than short-term bonds. So, market risk premium is zero and long-term rates are a weighted average of expected and current short-term interest rates. Assuming that market risk premium is zero, a bond trader is just as willing to buy a 30-year bond to pick up a short-term profit as he would be to buy a 3-month security.

2. Liquidity Preference Theory

Liquidity preference theory states that long-term bonds yield more than short-term bonds for two reasons:

All else equal, investors prefer to hold short-term securities since they can be converted to cash with little danger of loss of capital.Supply of short-term funds increases.

Borrowers prefer long-term debt because short-term debt exposes them to the risk of having to repay the debt under adverse conditions. So, the demand for long-term funds increases causing long-term rates to rise. The borrowers may want to lock in long-term funds and are willing to pay a higher rate for long-term funds. So, this also leads short-term rates to decrease and long-term rates to rise.

3. Market Segmentation Theory

Each lender and borrower has a preferred maturity. Differences exist between savers and borrowers. So, market segmentation theory implies that the slope of the yield curve depends on supply and demand conditions in the long and short-term markets.

An upward slooping would occur when there is a large supply of funds in the short-term market relative to demand but a shortage of long-term funds.

A downward sloping curve would indicate relatively strong demand in short-term market relative to demand but a shortage of long-term funds.

Given the rich set of fixed-income securities traded in the market, their prices provide the information needed to value riskless cash flows at hand.

In the market, this information on the time value of money is given in several different forms:

1. Spot interest rates
2. Prices of discount bonds
3. Prices of coupon bonds
4. Forward interest rates

The form in which this information is expressed depends on the particular market.

1. Spot Interest Rates

Spot interest rate, rt, is the interest rate for maturity date t.

rt is for payments only on date t.
rt is the “average” rate of interest between now and date t.
rt is different for each different date t.

The set of spot interest rates for different dates gives the term structure of interest rates, which refers to the relation between spot rates and their maturities.

2. Discount Bonds

Discount bonds (zero coupon bonds) are the simplest fixed-income securities. Definition: A discount bond with maturity date t is a bond which pays $1 only at t.

3. Coupon Bonds

A coupon bond pays a stream of regular coupon payments and a principal at maturity.

4. Forward Interest Rates

Forward interest rates depict a transaction between two future dates, for instance, t1 and t2. For a forward transaction to borrow money in the future terms of transaction is agreed on today, loan is received on a future date t1, repayment of the loan occurs on date t2.