Determining Interest Rates C H A P T E R 4 4.1 4.2 4.3 Discuss the most important factors in building an investment portfolio LEARNING OBJECTIVES After

Determining Interest Rates

C H A P T E R 4

4.1

4.2

4.3

Discuss the most important factors in building an investment portfolio

LEARNING OBJECTIVES

After studying this lesson, you should be able to:

Use a model of demand and supply to determine market interest rates for bondsUse the bond market model to explain changes in interest rates

4.4 Use the loanable funds model to analyze the international capital market

IF INFLATION INCREASES, ARE BONDS A GOOD INVESTMENT?

•Recently, interest rates on U.S. Treasury notes and corporate bonds have been falling relative to their 30-year averages.

•If interest rates on these securities rose back to their historical averages, holders of bonds would suffer losses.

•Not surprisingly, many financial advisers have warned investors that buying bonds could be risky.

•In this lesson, we study how investors take into account expectations of inflation, as well as other factors, such as risk and information costs, when making investment decisions.

•An Inside Look at Policy on page 116 discusses movements in interest rates during 2010.

Determining Interest Rates

C H A P T E R 4

Key Issue and Question

Issue: Federal Reserve policies to combat the recession of 2007–2009 led some economists to predict that inflation would rise and make long-term bonds a poor investment.

Question: How do investors take into account expected inflation and other factors when making investment decisions?

4.1Learning Objective

Discuss the most important factors in building an investment portfolio.

How to Build an Investment Portfolio

The Determinants of Portfolio Choice

The determinants of portfolio choice, sometimes referred to as determinants of asset demand, are:

1.The saver’s wealth or total amount of savings to be allocated among investments

2. The expected rate of return from an investment compared with the expected rates of return on other investments

3. The degree of risk in the investment compared with the degree of risk in other investments

4. The liquidity of the investment compared with the liquidity of other investments

5. The cost of acquiring information about the investment compared with the cost of acquiring information about other investments

In general, when we view financial markets as a whole, we can assume that an increase in wealth will increase the quantity demanded for most financial assets.

Wealth

Expected Rate of Return

Expected return The return expected on an asset during a future period; also known as expected rate of return.

We calculate the expected return on an investment using this formula:

Expected return = [(Probability of event 1 occurring) X (Value of event 1)]+ [(Probability of event 2 occurring) X (Value of event 2)].

For example, with equal probability of a rate of return of 15% or a rate of return of 5%:

Expected return = (0.50)(15%) + (0.50)(5%) = 10%.


Risk

Risk The degree of uncertainty in the return on an asset.

• For example, if there is a probability of 50% that a bond will have a return of 12% or a probability of 50% that the bond will have a return of 8%, then the expected return on the bond is(0.50)(12%) + (0.50)(8%) = 10%.

• Most investors are risk averse, which means that in choosing between two assets with the same expected returns, they would choose the asset with the lower risk. For this reason, there is a trade-off between risk and return.

• There are also risk-loving investors who prefer to hold risky assets with the possibility of maximizing returns, and risk-neutral investors, who make their decisions on the basis of expected returns, ignoring risk.


Making the Connection

Fear the Black Swan!• The table below illustrates the trade-off between risk and return.

• Investors in stocks of small companies during these years experienced the highest average returns but also accepted the most risk.

• Investors in U.S. Treasury bills experienced the lowest average returns but also the least risk.

• The term black swan event refers to rare events that have a large impact on society or the economy. Some economists see the financial crisis as a black swan event because before it occurred, few believed it was possible.


Liquidity

The Cost of Acquiring Information

• All else being equal, investors will accept a lower return on an asset that has lower costs of acquiring information.

• We saw in lesson 2 that liquidity is the ease with which an asset can be exchanged for money.

• The greater an asset’s liquidity, the more desirable the asset is to investors.

We can summarize our discussion of the determinants of portfolio choice by noting that desirable characteristics of a financial asset cause the quantity of the asset demanded by investors to increase, and undesirable characteristics of a financial asset cause the quantity of the asset demanded to decrease.



Diversification

Diversification Dividing wealth among many different assets to reduce risk.

Market (or systematic) risk Risk that is common to all assets of a certain type, such as the increases and decreases in stocks resulting from the business cycle.

Idiosyncratic (or unsystematic) risk Risk that pertains to a particular asset rather than to the market as a whole, as when the price of a particular firm’s stock fluctuates because of the success or failure of a new product.



How Much Risk Should You Tolerate in Your Portfolio?

One important factor in deciding on the degree of risk to accept is your time horizon.


• In addition to your time horizon, you must consider the effects of inflation and taxes in building a portfolio.

• We saw in lesson 3 the important difference between real and nominal interest rates.

• Depending on the investment, your real, after-tax return may be considerably different from your nominal pretax return.

• In lesson 5, we will look further at how differences in tax treatment can affect the returns on certain investments.

• Understanding how risk, inflation, and taxation affect your investments will help you reduce emotional reactions to market volatility and make better-informed investment decisions.



Use a model of demand and supply to determine market interest rates for bonds.

Market Interest Rates and the Demand and Supply for Bonds

• Because the coupon payment and the face value do not change, once we have determined the equilibrium price in the bond market, we have also determined the equilibrium interest rate.

• In the analysis that follows, remember that the bond market approach is most useful when considering how the factors affecting the demand and supply for bonds affect the interest rate.

• The market for loanable funds approach, which treats the funds being traded as the good, is most useful when considering how changes in the demand and supply of funds affect the interest rate.

• The price of a bond, P, and its yield to maturity, i, are linked by the arithmetic of the equation showing the price of a bond with coupon payments C that has a face value FV and that matures in n years:

A Demand and Supply Graph of the Bond Market

Figure 4.1

The Market for Bonds

The equilibrium price of bonds is determined in the bond market.By determining the price of bonds, the bond market also determines the interest rate on bonds. In this case, a one-year discount bond with a face value of $1,000 has an equilibrium price of $960, which means it has an interest rate (i) of 4.2%.The equilibrium quantity of bonds is $500 billion.•


Figure 4.2

Equilibrium in Markets for Bonds

At the equilibrium price of bonds of $960, the quantity of bonds demanded by investors equals the quantity of bonds supplied by borrowers.At any price above $960, there is an excess supply of bonds, and the price of bonds will fall.At any price below $960, there is an excess demand for bonds, and the price of bonds will rise. The behavior of bond buyers and sellers pushes the price of bonds to the equilibrium of $960.•

The interest rate on the bond is:


Explaining Changes in Equilibrium Interest Rates

In drawing the demand and supply curves for bonds in Figure 4.1, we held constant everything that could affect the willingness of investors to buy bonds—or firms and investors to sell bonds—except for the price of bonds.

If the price of bonds changes, we move along the demand (or supply) curve, but the curve does not shift, so we have a change in quantity demanded (or supplied).

If any other relevant variable—such as wealth or the expected rate of inflation—changes, then the demand (or supply) curve shifts, and we have a change in demand (or supply).


Factors That Shift the Demand Curve for Bonds

Five factors cause the demand curve for bonds to shift:

1. Wealth

2. Expected return on bonds

3. Risk

4. Liquidity

5. Information costs


Figure 4.3 (1 of 2)

Shifts in the DemandCurve for Bonds

An increase in wealth, holding all other factors constant, will shift the demand curve for bonds to the right.As the demand curve for bonds shifts to the right, the equilibrium price of bonds rises from $960 to $980, and the equilibrium quantity of bonds increases from $500 billion to $600 billion. •

Wealth


Figure 4.3 (2 of 2)

Shifts in the DemandCurve for Bonds (continued)

A decrease in wealth, holding all other factors constant, will shift the demand curve for bonds to the left, reducing both the equilibrium price and equilibrium quantity. As the demand curve for bonds shifts to the left, the equilibrium price falls from $960 to $940, and the equilibrium quantity of bonds decreases from $500 billion to $400 billion.•

Wealth


Expected return on bondsIf the expected return on bonds rises relative to expected returns on other assets,

investors will increase their demand for bonds, and the demand curve for bonds will shift to the right.

RiskA decrease in the riskiness of bonds relative to the riskiness of other assets

increases the willingness of investors to buy bonds and causes the demand curve for bonds to shift to the right.

LiquidityIf the liquidity of bonds increases, investors demand more bonds at any given

price, and the demand curve for bonds shifts to the right.

Information costsAs a result of the lower information costs, the demand curve for bonds shifts to

the right.


Table 4.2 (1 of 3) Factors That Shift the Demand Curve for Bonds






Factors That Shift the Supply Curve for Bonds

Four factors are most important in explaining shifts in the supply curve for bonds:

1. Expected pretax profitability of physical capital investments

2. Business taxes

3. Expected inflation

4. Government borrowing


Expected pretax profitability of physical capital investments

Shifts in the SupplyCurve for Bonds

An increase in firms’ expectations of the profitability of investments in physical capital will, holding all other factors constant, shift the supply curve for bonds to the right as firms issue more bonds at any given price.As the supply curve for bonds shifts to the right, the equilibrium price of bonds falls from $960 to $940, and the equilibrium quantity of bonds increases from $500 billion to $575 billion.•

Figure 4.4 (1 of 2)


Expected pretax profitability of physical capital investments

Figure 4.4 (2 of 2)

Shifts in the SupplyCurve for Bonds (continued)

If firms become pessimistic about the profits they could earn from investing in physical capital, then, holding all other factors constant, the supply curve for bonds will shift to the left.As the supply for bonds shifts to the left, the equilibrium price increases from $960 to $975, and the equilibrium quantity of bonds decreases from $500 billion to $400 billion.•


Business taxes

When business taxes are raised, the profits firms earn on new investments in physical capital decline, and firms issue fewer bonds. The result is that the supply curve for bonds will shift to the left.

Expected inflation

An increase in the expected rate of inflation reduces investors’ demand for bonds by reducing the expected real interest rate that investors receive for any given nominal interest rate.

From the point of view of a firm issuing a bond, a lower expected real interest rate is attractive because it means the firm pays less in real terms to borrow funds.


Government borrowing

Figure 4.5 The Federal Budget

With the exception of a few years in the late 1990s, the federal government has typically run a budget deficit. The recession of 2007–2009 led to record deficits that required the federal government to borrow heavily by selling bonds.•


Government borrowing


When the government runs a deficit, households may look ahead and conclude that at some point the government will have to raise taxes to pay off the bonds issued to finance the deficit.

To prepare for those future higher tax payments, households may begin to increase their saving. This increased saving will shift the demand curve for bonds to the right at the same time that the supply curve for bonds shifts to the right because of the deficit.

If nothing else changes, an increase in government borrowing shifts the bond supply curve to the right, reducing the price of bonds and increasing the interest rate. A fall in government borrowing shifts the bond supply curve to the left, increasing the price of bonds and decreasing the interest rate.

Table 4.3 (1 of 2) Factors That Shift the Supply Curve for Bonds


Table 4.3 (2 of 2) Factors That Shift the Supply Curve for Bonds



Use the bond market model to explain changes in interest rates.

The Bond Market Model and Changes in Interest Rates

In this section, we consider two examples of using the bond market model to explain changes in interest rates:

(1) The movement of interest rates over the business cycle, which refers to the alternating periods of economic expansion and economic recession experienced by the United States and most other economies; and

(2) The Fisher effect, which describes the movement of interest rates in response to changes in the rate of inflation.

Why Do Interest Rates Fall during Recessions?

Interest Rate Changes in an Economic Downturn

1. From an initial equilibrium at E1, an economic downturn reduces household wealth and decreases the demand for bonds at any bond price. The bond demand curve shifts to the left, from D1 to D2.

2. The fall in expected profitability reduces lenders’ supply of bonds at any bond price. The bond supply curve shifts to the left, from S1 to S2.

3. In the new equilibrium, E2, the bond price rises from P1 to P2.•

Figure 4.6


How Do Changes in Expected Inflation Affect Interest Rates?The Fisher Effect

Fisher effect The assertion by Irving Fisher that the nominal interest rises or falls point-for-point with changes in the expected inflation rate.

The discussion of the Fisher effect alerts us to two important facts about the bond market:

1. Higher inflation rates result in higher nominal interest rates, and lower inflation rates result in lower nominal interest rates.

2. Changes in expected inflation can lead to changes in nominal interest rates before a change in actual inflation has occurred.


Expected Inflation and Interest Rates

1. From an initial equilibrium at E1, an increase in expected inflation reduces investors’ expected real return, reducing investors’ willingness to buy bonds at any bond price. The demand curve for bonds shifts to the left, from D1 to D2.

2. The increase in expected inflation increases firms’ willingness to issue bonds at any bond price. The supply curve for bonds shifts to the right, from S1 to S2.

3. In the new equilibrium, E2, the bond price falls from P1 to P2.•

Figure 4.7


Solved Problem 4.3

Why Worry About Falling Bond Prices When the Inflation Rate Is Low?


The inflation rate in late 2009 was quite low, but financial advisor Bill Tedford forecast that inflation would increase to 5% by 2011. He argued that this increase in inflation made bonds a bad investment. Tedford was hardly alone in offering this advice. For instance, in its March 2010 issue, Consumer Reports magazine advised its readers to “steer clear of long-term Treasury bonds.”

a. Explain why an increase in expected inflation will make bonds a bad investment. Include a demand and supply graph of the bond market.

b. If inflation was not expected to increase until 2011, should investors have waited until then to sell their bonds? Briefly explain.

c. In its advice, Consumer Reports singles out “long-term bonds” as an investment for its readers to avoid. Why would long-term bonds be a worse investment than short-term bonds if expected inflation was increasing?

Solved Problem


Solving the Problem

Step 1 Review the lesson material.

Step 2 Answer part (a) by explaining

why an increase in expected

inflation may make bonds a

bad investment and illustrate

your response with a graph.


4.3

Solved Problem 4.3 (continued)


Solving the Problem

Step 3 Answer part (b) by discussing the difference in the effects of actual and

expected inflation on changes in bond prices.


Changes in bond prices result from changes in the expected rate of inflation. If Tedford was correct that future inflation was going to be significantly higher, investors would be wise to sell bonds right away. Waiting until the nominal interest rate had risen and bond prices had fallen would be too late to avoid the capital losses from owning bonds.

Step 4 Explain why long-term bonds are a particularly bad investment if expected

inflation increases.

An increase in expected inflation will increase the nominal interest rate on both short-term and long-term bonds. The longer the maturity of a bond, the greater the change in price. So, the capital losses on long-term bonds will be greater than the ones on short-term bonds.


Use the loanable funds model to analyze the international capital market.

The Loanable Funds Model and the International Capital Market

In the loanable funds approach, the borrower is the buyer because the borrower purchases the use of the funds. The lender is the seller because the lender provides the funds being borrowed.

Although the demand and supply of bonds approach and the loanable funds approach are equivalent, the loanable funds approach is more useful when looking at the flow of funds between the U.S. and foreign financial markets.

Table 4.4 summarizes the two views of the bond market.

The Demand and Supply of Loanable Funds

Figure 4.8 The Demand for Bonds and the Supply of Loanable Funds

In panel (a), the bond demand curve, Bd, shows a negative relationship between the quantity of bonds demanded by lenders and the price of bonds, all else being equal.In panel (b), the supply curve for loanable funds, Ls, shows a positive relationship between the quantity of loanable funds supplied by lenders and the interest rate, all else being equal.•


The Demand and Supply of Loanable Funds

Figure 4.9 The Supply of Bonds and the Demand for Loanable Funds

In panel (a), the bond supply curve, Bs, shows a positive relationship between the quantity of bonds supplied by borrowers and the price of bonds, all else being equal.In panel (b), the demand curve for loanable funds, Ld, shows a negative relationship between the quantity of loanable funds demanded by borrowers and the interest rate, all else being equal.•


Equilibrium in the Bond Market from the Loanable Funds Perspective

Equilibrium in the Market for Loanable Funds

At the equilibrium interest rate, the quantity of loanable funds supplied by lenders equals the quantity of loanable funds demanded by borrowers.At any interest rate below the equilibrium, there is an excess demand for loanable funds. At any interest rate above equilibrium, there is an excess supply of loanable funds. The behavior of lenders and borrowers pushes the interest rate to 4.2%.•

Figure 4.10


The International Capital Market and the Interest Rate

Closed economy An economy in which households, firms, and governments do not borrow or lend internationally.

Open economy An economy in which households, firms, and governments borrow and lend internationally.

The foreign sector influences the domestic interest rate and the quantity of funds available in the domestic economy.

The loanable funds approach provides a good framework for analyzing the interaction between U.S. and foreign bond markets.


Small Open Economy

Small open economy An economy in which total saving is too small to affect the world real interest rate.

The key ideas to remember about a small economy are as follows:

•The real interest rate in a small open economy is the same as the interest rate in the international capital market.

•If the quantity of loanable funds supplied domestically exceeds the quantity of funds demanded domestically at that interest rate, the country invests some of its loanable funds abroad.

•If the quantity of loanable funds demanded domestically exceeds the quantity of funds supplied domestically at that interest rate, the country finances some of its domestic borrowing needs with funds from abroad.


Small Open Economy

Determining the Real Interest Rate in a Small Open EconomyThe domestic real interest rate in a small open economy is the world real interest rate, (rw), which in this case is 3%.•

Figure 4.11


Large Open Economy

Large open economy An economy in which shifts in domestic saving and investment are large enough to affect the world real interest rate.

In the case of a large open economy, we cannot assume that the domestic real interest rate is equal to the world real interest rate.


Figure 4.12 Determining the Real Interest Rate in a Large Open Economy

Saving and investment shifts in a large open economy can affect the world real interest rate. The world real interest rate adjusts to equalize desired international borrowing and desired international lending.At a world real interest rate of 4%, desired international lending by the domestic economy equals desired international borrowing by the rest of the world.•



Did a Global “Saving Glut” Cause the U.S. Housing Boom?

Some economists have argued that the Fed persisted in a low-interest-rate policy for too long a period, thereby fueling the housing boom.Fed Chairman Ben Bernanke disagreed, arguing that “a significant increase in the global supply of saving—a global saving glut— . . . helps to explain . . . the relatively low level of long-term interest rates in the world today.”


Answering the Key Question

At the beginning of this lesson, we asked the question:“How do investors take into account expected inflation and other factors when making investment decisions?”

We have seen in this lesson that investors increase or decrease their demand for bonds as a result of changes in a number of factors.

When expected inflation increases, investors reduce their demand for bonds because, for every nominal interest rate, the higher the inflation rate, the lower the real interest rate investors will receive.

We have seen that increases in expected inflation lead to higher nominal interest rates and capital losses for investors who hold bonds in their portfolios.

AN INSIDE LOOK AT POLICY

Investors Forecast Lower Bond Prices, Higher Interest Rates

Wall Street Journal, Interest Rates Have Nowhere to Go but Up

• As the U.S. economy recovered from recession in 2010, analysts forecast a period of rising interest rates.

• Higher interest rates would damage the housing market, which had begun to recover from the recession.

• Analysts expected interest rate increases because the federal government was forced to sell more bonds to finance its budget deficits, and the rate of inflation was likely to increase.

• Because low interest rates helped to fuel the growth of stock prices, higher interest rates were likely to slow the growth of stock prices in the future.

• The figure in the next slide shows the impact of an increase in expected inflation on the markets for bonds and loanable funds.

Key Points in the Article

AN INSIDE LOOK AT POLICY

Documents

Determining Interest Rates C H A P T E R 4 4.1 4.2 4.3 Discuss the most important factors in building an investment portfolio LEARNING OBJECTIVES After