Chapter 6: Bonds, Bond Prices and the Determination of Interest Rates, Part II

In the second part of chapter 6 we focus on the bond market and how the overall level of interest rates is determined. Now that we know how to measure interest rates, we want to examine why interest rates fluctuate up and down. The answer lies with the laws of supply and demand in financial markets. That's right, there is no escaping supply and demand in an economics class.

The Bond Market

Now let's take a look at how bond buyers and bond sellers determine the level of interest rates, and how changes in market conditions result in changing interest rates. Our discussion of asset demand above is important in deriving the supply and demand curves.

The Demand for Bonds

Bond demand is based on the behavior of those who buy bonds, or lenders/savers.

Consider a zero coupon bond with a face value of $1000. Suppose the bond has 1 year until maturity, and the expected holding period is one year. Then the bond's expected return is equal to its yield to maturity:

Using the formula above, we can calculate the expected return for various prices:

Bond Price			i = exp. return
700			42.86%
750			33.33%
800			25%
850			17.65%
900			11.11%
950			5.26%

As the bond price rises, both the yield to maturity and the expected return fall. As the expected return falls, the quantity demanded of the bond will fall. So the bond demand curve looks like this:

At higher prices, the quantity demanded of bonds falls. Also, note that higher bond prices are associated with lower interest rates because bond prices and interest rates are negatively related.

The Supply of Bonds

To determine the level of interest rates, we also need the bond supply curve, which models the behavior of those who issue bonds, or borrowers. Higher bond prices mean lower interest rates, which encourage borrowing, holding other factors constant. So the bond supply curve slopes up with respect to bond prices:

In the bond market above, the equilibrium interest rate is 17.65%.

However, to understand why interest rates are always changing, we need to understand why equilibrium changes, or why supply and demand curves shift in the bond market.

What shifts the bond demand curve?

A change in wealth. As wealth increases, people will buy more bonds at each and every price, and the demand for bonds rises, or shifts right. So when an expanding economy increases both income and wealth, we expect bond demand to increase too.
A change in expected interest rates/returns. For bonds with more than a year to maturity, rising interest rates in the future will decrease the value of the bond (and hence the expected return). At each and every price, fewer bonds will be demanded. Bond demand will fall, or shift left when expected future interest rates fall. The size of the decrease will be larger for longer term bonds.
A change in expected inflation. If investors expect the inflation rate to rise, then they expect the real return on their bond to fall, as future payments are able to buy less. Higher inflation expectations decrease bond demand.
A change in the relative risk of bonds. At any given price or expected return, if bonds become riskier than other assets, people will switch to less risky assets. An increase in the relative risk of bonds with decrease bond demand.
A change in the relative liquidity of bonds. If it becomes harder to resell bonds in the bond market relative to other assets, people will switch to assets that are easier to resell. A decrease in the relative liquidity of bonds will decrease bond demand.

What shifts the bond supply curve?

A change in business conditions. Firms issue bonds to finance the purchase of capital equipment and the expansion of production. This makes sense only if this expansion is expected to be profitable. As economic conditions become more favorable, expected profitability rises and bond supply will increase or shift right. Also tax incentives for borrowing can also be considered a business condition.
A change in expected inflation. While rising inflation decreases the real return for those who buy bonds, it decreases the real cost of borrowing for those who issue bonds: For a given nominal interest rate (and bond price), higher inflation means a lower real interest rate. Thus, higher expected inflation increases bond supply.
A change in government borrowing. If the government runs budget deficits, the U.S. Treasury must issue additional bonds to finance the shortfall in tax revenue. At each and every bond price, the quantity supplied increases, so the bond supply curve shifts right. Conversely, federal budget surpluses could lead the U.S. Treasury to buy back and retire bonds with the excess revenue and decrease bond supply.

Two things to remember about the bond market:

The demand for bonds is the same as the supply of loanable funds. Those who buy bonds are providing loans to others and are receiving interest.
The supply of bonds is the same as the demand for loanable funds. Those who supply or issue bonds are borrowing money and paying interest.

Equilibrium Interest Rates

Any shift in the bond demand and/or bond supply curves implies a new equilibrium interest rate. Thus, when we observe fluctuating interest rates in the economy, the root cause is changes in the factors affecting bond supply and bond demand. Let's look a couple of applications.

Example 1: An increase in expected inflation (The Fisher Effect)

Suppose expected inflation is initially at about 3% with initial bond supply and demand curves of Bs and Bd (blue). The equilibrium interest rate is 5% (point 1):

Now suppose inflation expectations rise to 4%. Bond demand decreases (along with the expected real return) and bond supply increases (as the real cost of borrowing declines) to Bs' and Bd' (red). The new equilibrium interest rate is definitely higher (and the bond price lower):

The total impact on the quantity of bonds here is zero, but in general depends on the size of the shifts in the bond demand and supply curves. So the Fisher effect is this: when expected inflation rises, nominal interest rates will rise. This prediction of our model is validated by time series data on interest rates.

Example 2: An economic slowdown

Let's start again with initial bond supply and demand curves of Bs and Bd (blue). The equilibrium interest rate is 5% (point 1):

Now suppose we are in the first quarter of 2001, in the midst of an economic slowdown and concern about a recession. Again this condition will affect both the bond demand and bond supply curves. With the slowdown comes a decline in income and wealth the demand for bonds will decrease to Bd''. The slowdown also has negative implications for profits, so bond supply also declines to Bs'':

In general, where both bond supply and bond demand decrease, the total effect on the equilibrium interest rate is uncertain. Here the shift in bond supply is larger than the shift in bond demand, so the interest rate falls. This is consist with the data on interest rates and the business cycle: nominal interest rates tend to fall during recessions and rise during expansions. In other words, interest rates are procyclical.

The table below summarizes that impact of various factors and the bond market and the equilibrium level of interest rates:

The Effect of Selected Variables on the Bond Market and Equilibrium Interest Rates.

Variable

Change in Variable

Change in Bd

Change in Bs

Change in i

Wealth

increase

decrease

Expected Interest Rates

increase

decrease

increase

Expected Inflation

increase

decrease

increase

Relative Risk

increase

decrease

increase

Relative Liquidity

increase

decrease

Business Conditions

increase

Government Borrowing

increase

The Risks Associated with Holding Bonds

While bonds promise fixed cash flows over times, these financial instruments are not without risk. The risk varies depending on the issuer and current economic conditions, but all bonds carry some type of risk. There are three major risks:

Default Risk

This is the risk that the bond issuer will fail to make the promised payments in full and on time. One bond issuer, The United States government, is considered to have no default risk, so default risk is not applicable for U.S. Treasury securities. However all other issuers such as private corporations, state and local governments, and foreign governments carry some risk of default. The higher the default risk, the greater the bond yield. Why? Recall that investors are risk average and will demand a higher yield in order to hold an assets with greater risk.

Default risk can vary quite a bit among issuers, so there are rating systems used to assess this risk. We will look at this in greater detail in chapter 7.

Inflation Risk

Most bonds promise a fixed dollar payments (there are some bonds out there where payments are indexed to inflation). However, with any inflation, those fixed dollar payments will buy fewer goods and services in the future. Bond yields reflect both a real interest rate and an expected inflation rate. The risk is that future inflation is uncertain and could be much higher than expected, which drives down the real return for bondholders. All fixed rate bonds will carry inflation risk. Inflation risk is minimal in countries like the U.S. but it can be huge in developing countries.

Interest Rate Risk

Any bond price moves in the opposite direction of interest rates. Therefore a bond's price or value will fluctuate over the life of the bond as interest rates move up and down. This fluctuation in value again exposes the bondholder to risk, especially if the bondholder expects to sell the bond prior to its maturity. Let's reconsider the bond table from part I, example 3:

Look at each bond's price (the 2-year, 5-year, and 10-year bonds) as the yield to maturity rises from 6% to 8%. The prices fall for all of the bonds, but by different amounts. The price on the 2-year bond falls less than $400 or less than 4%. The price on the 10-year bond falls by more than $1300 or more than 13%. Maturity is a principle bond characteristic that affects price volatility: Prices (and thus returns) are more volatile for long-term bonds than short-term bonds. In other words, long-term bonds have greater interest-rate risk.

Why is this the case? Intuitively, with a long-term bond, you are "locked in" to a coupon rate for a longer period of time. So if newer bonds are issued with lower coupon rates, your long-term bond becomes much more valuable. If new bonds have higher coupon rates, your long-term bond becomes much less valuable. For a bond with less than 1 year left until maturity, the change in interest rates will not matter that much. The consequences of changing interest rates are much more serious for bonds with longer times left until maturity.

ALL BONDS HAVE SOME INTEREST-RATE RISK. So no bond, even Treasuries, are completely risk-free. U.S. Treasury Bills are the closest to a riskfree bond given their issuer and short time to maturity.

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