Chapter 4

Why Do Interest Rates Change?

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Chapter Preview

Interest rates might fluctuate time and time and affect business activities. We will examine the forces that move interest rates and the theories behind those movements. Topics include: Determining Asset Demand Supply and Demand in the Bond Market Changes in Equilibrium Interest Rates

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4.1 Determinants of Asset Demand

An asset is a piece of property that is a store of value.

Facing the question of whether to buy and hold an asset or whether to buy one asset rather than another, an individual must consider the following factors:

Wealth, expected return, risk and liquidity

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4.1.1 Wealth (财富 )

Wealth, the total resources owned by the individual, including all assets;

The effect of changes in wealth:

Other things being equal, an increase in wealth raises the quantity demanded of an asset.

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4.1.2 Expected Return (预期收益 )

Expected return: the return expected over the next period, on one asset relative to alternative assets;

The expected return on an asset is the weighted average of all possible returns, where the weights are the probabilities of occurrence (发生事件 ) of that return:

Re = p1R1 + p2R2, Where

p1 = probability of occurrence of return 1; R1 = return in state 1

p2 = probability of occurrence return 2; R2 = return in state 2

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4.1.2.1 EXAMPLE 1: Expected Return (P72)

What is the expected return on the Mobil Oil bond if the return is 12% two-thirds of the time and 8% one-third of the time?

Solution

The expected return is 10.68%.

Re = p1R1 + p2R2 ， where

p1 = probability of occurrence of return 1 = 2/3 = .67

R1 = return in state 1 = 12% = 0.12

p2 = probability of occurrence return 2 = 1/3 = .33

R2 = return in state 2 = 8% = 0.08

Thus

Re = (.67)(0.12) + (.33)(0.08) = 0.1068 = 10.68%

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4.1.2.2 Effect of changes in expected return

An increase in an asset’s expected return relative to that of an alternative asset, holding everything else unchanged, raises the quantity demanded of the asset.

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4.1.3 Risk

Risk: the degree of uncertainty associated with the return on one asset relative to alternative assets;

In finance, we use standard deviation of return as a measure of risk;

The formula for the standard deviation is shown as on P73

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4.1.3.1 EXAMPLE 2: Standard Deviation (a) What is the standard deviation of the returns

on the Fly-by-Night Airlines stock and Feet-on-the Ground Bus Company, with the same return outcomes and probabilities described as on P73?

Of these two stocks, which is riskier?

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4.1.3.2 EXAMPLE 2: Standard Deviation (b)

Solution Fly-by-Night Airlines has a standard deviation of returns of

5%.

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4.1.3.3 EXAMPLE 2: Standard Deviation (c) Feet-on-the-Ground Bus Company has a standard

deviation of returns of 0%.

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4.1.3.4 EXAMPLE 2: Standard Deviation (d) Fly-by-Night Airlines has a standard deviation of

returns of 5%; Feet-on-the-Ground Bus Company has a standard deviation of returns of 0%

Clearly, Fly-by-Night Airlines is a riskier stock because its standard deviation of returns of 5% is higher than the zero standard deviation of returns for Feet-on-the-Ground Bus Company, which has a certain return.

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4.1.3.5 Conclusion on the above example A risk-averse （厌恶风险） person prefers stock in

the Feet-on-the-Ground (the sure thing) to Fly-by-Night stock (the riskier asset), even though the stocks have the same expected return, 10%.

By contrast, a person who prefers risk is a risk lover. Most people are risk-averse, especially in their

financial decisions.

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4.1.3.6 Effect of changes in risk Holding everything else constant,

if an asset’s risk rises relative to that of alternative assets, its quantity demanded will fall.

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4.1.4 Liquidity

Liquidity: the ease and speed with which an asset can be turned into cash, relative to alternative assets;

Effect of changes in liquidity: The more liquid an asset is relative to alternative assets, holding everything else unchanged, the more desirable it is, and the greater will be the quantity demanded.

Government bond VS company bond

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4.1.5 Determinants of Asset Demand

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4.2 Supply and demand in the bond market

We want to study the interest-rate determination by examining the supply of and demand for bonds;

Since interest rates on different markets tend to move together, we first of all study by supposing that there is only one type of securities and a single interest rate in the entire economy.

In next chapter, we will discuss why interest rates on different securities differ.

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Point B:

i Re F P P

P$950 i $1000 $950

$950.053 5.3% Bd 100

P$900 i $1000 $900

$900.111 11.1% Bd 200

4.2.1 Derivation of Demand Curve (look at Figure 1 on P77)

Point A:

For one-year discount bonds (no coupon, face value $1000):

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4.2.1.1 Derivation of Demand Curve Point C: P = $850 i = 17.6% Bd = 300

Point D: P = $800 i = 25.0% Bd = 400

Point E: P = $750 i = 33.0% Bd = 500

Demand Curve is Bd in Figure 1 which connects points A, B, C, D, E. Has usual downward slope

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Figure 4.1 Supply and Demand for Bonds

4.2.1.2 Supply and Demand Analysis of the Bond Market

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4.2.2 Derivation of Supply Curve Point F: P = $750 i = 33.0% Bs = 100 Point G: P = $800 i = 25.0% Bs = 200 Point C: P = $850 i = 17.6% Bs = 300 Point H: P = $900 i = 11.1% Bs = 400 Point I: P = $950 i = 5.3% Bs = 500 Supply Curve is Bs that connects points F, G, C, H,

I, and has upward slope: the higher the interest rate, the less willingness to issue new bonds.

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4.2.3 Market Equilibrium

1. Occurs when Bd = Bs, at P* = 850, i* = 17.6%

2. When P = $950, i = 5.3%, Bs > Bd (excess supply): P to P*, i to i*

3. When P = $750, i = 33.0, Bd > Bs (excess demand): P to P*, i to i*

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4.2.4 Market Demand Conditions

Market equilibrium occurs when the amount that people are willing to buy (demand) equals the amount that people are willing to sell (supply) at a given price

Excess supply occurs when the amount that people are willing to sell (supply) is greater than the amount people are willing to buy (demand) at a given price

Excess demand occurs when the amount that people are willing to buy (demand) is greater than the amount that people are willing to sell (supply) at a given price.

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4.2.5 Loanable (可贷出的 )Funds Terminology

1. Demand for bonds = supply of loanable funds

2. Supply of bonds = demand for loanable funds

3. Therefore we can use the Figure 4.2 to express interest rates value in the usual direction.

Figure 4.2 A Comparison of Terminology: Loanable Funds and Supply and Demand for Bonds

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4.3 Changes in Equilibrium Interest Rates

It is important to distinct between movements along a demand (or supply) curve and a shifts in a demand (or supply) curve.

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4.3.1 Movement along the demand curve When quantity demanded changes as a

result of a change in the price of the bond, we have a movement along the demand curve, e.g., from Point A to B;

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4.3.2 Shift in the demand curve When quantity demanded changes at each

given price of the bond in response to a change in some other factor besides the bond’s price or interest rate, we have a shift in the demand curve, e.g. B1

d to B2d .

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4.3.3 Shifts in the Demand Curve

Figure 4.3 Shifts in the Demand Curve for Bonds

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4.3.4.1 How Factors Shift the Demand Curve - WealthWealth

Economy , wealth , Bd , Bd shifts out to right, and the vice versa.

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4.3.4.2 How Factors Shift the Demand Curve – Expected return1. Expected Return

i in future, Re for long-term bonds , Bd shifts out to right

πe , relative Re , Bd shifts out to right

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4.3.4.3 How Factors Shift the Demand Curve - RiskRisk

Risk of bonds , Bd , Bd shifts out to right Risk of other assets , Bd , Bd shifts out to right

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4.3.4.4 How Factors Shift the Demand Curve - LiquidityLiquidity

Liquidity of bonds , Bd , Bd shifts out to right Liquidity of other assets , Bd ,Bd shifts out to

right

4.3.4.5 Factors That Shift Demand Curve

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4.3.5.1 Summary of Shifts in the Demand for Bonds (1)1. Wealth: in a business cycle expansion with

growing wealth, the demand for bonds rises, conversely, in a recession, when income and wealth are falling, the demand for bonds falls

2. Expected returns: higher expected interest rates in the future decrease the demand for long-term bonds, conversely, lower expected interest rates in the future increase the demand for long-term bonds

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4.3.5.1 Summary of Shifts in the Demand for Bonds (1)3. Risk: an increase in the riskiness of bonds causes

the demand for bonds to fall, conversely, an increase in the riskiness of alternative assets (like stocks) causes the demand for bonds to rise

4. Liquidity: increased liquidity of the bond market results in an increased demand for bonds, conversely, increased liquidity of alternative asset markets (like the stock market) lowers the demand for bonds

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4.3.6 Changes in Supply

Certain factors can cause the supply curve for bonds to shift:

Expected profitability of investment opportunities;

Expected inflation; Government activities.

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4.3.6.1 Shifts in the Supply Curve

Figure 4.4 Shift in the Supply Curve for Bonds

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4.3.6.2.1 Factors that shift supply curve- Profitability

Profitability of Investment Opportunities Business cycle expansion, investment

opportunities , Bs , Bs shifts out to right

In a business cycle expansion, the supply of bonds increases, conversely, in a recession, when there are far fewer expected profitable investment opportunities, the supply of bonds falls

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4.3.6.2.2 Factors that shift supply curve- Expected InflationExpected Inflation

πe , Bs , Bs shifts out to right

An increase in expected inflation causes the supply of bonds to increase

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4.3.6.2.3 Factors that shift supply curve- Government ActivityGovernment Activities

Deficits , Bs , Bs shifts out to right

Higher government deficits increase the supply of bonds, conversely, government surpluses decrease the supply of bonds

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4.3.6.2.4 Factors That Shift Supply Curve (Table 3)

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4.4 Fisher Effect and Business cycle Fisher Effect Business cycle

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4.4.1 Changes in expected inflationπe

If πe 1. Relative

Re , Bd shifts in to left

2. Bs , Bs shifts out to right

3. P , i

Figure 4.5 Response to a Change in Expected Inflation

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4.4.2 Fisher Effect

Our analysis on demand and supply has brought an important observation: when expected inflation rises, interest rates will rise.

This observation was firstly pointed out by Irving Fisher, and therefore called Fisher Effect.

Irving Fisher, famous economist( (1867-1947)

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Figure 4.6 Expected Inflation and Interest Rates (Three-Month Treasury Bills), 1953–2004

4.4.3 Evidence on the Fisher Effect in the United States

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4.4.4 Summary of the Fisher Effect

1. If expected inflation rises from 5% to 10%, the expected return on bonds relative to real assets falls and, as a result, the demand for bonds falls

2. The rise in expected inflation also means that the real cost of borrowing has declined, causing the quantity of bonds supplied to increase

3. When the demand for bonds falls and the quantity of bonds supplied increases, the equilibrium bond price falls

4. Since the bond price is negatively related to the interest rate, this means that the interest rate will rise

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4.4.5 Business Cycle Expansion1. Wealth , Bd , Bd

shifts out to right

2. Investment , Bs , Bs shifts right

3. If Bs shifts more than Bd then P , i

Figure 4.7 Response to a Business Cycle Expansion

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4.4.6 Evidence on Business Cycles and Interest Rates

Figure 4.8 Business Cycle and Interest Rates (Three-Month Treasury Bills), 1951–2004

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4.4.7 Business cycle and Interest rates

Interest rates rise during business expansions;

Interest rates fall during contractions (as shown in the shaded areas indicating periods of recession in Figure 4.8)

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4.5 Profiting from Interest-Rate Forecasts

Methods for forecasting1. Supply and demand for bonds: use Flow of

Funds Accounts and judgment

2. Econometric Models: large in scale, use interlocking equations that assume past financial relationships will hold in the future

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4.6 Profiting from Interest-Rate Forecasts Make decisions about assets to hold

1. Forecast i , buy long bonds

2. Forecast i , buy short bonds

Make decisions about how to borrow1. Forecast i , borrow short

2. Forecast i , borrow long

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Chapter Summary

Determining Asset Demand: We examined the forces that affect the demand and supply of assets.

Supply and Demand in the Bond Market: We examine those forces in the context of bonds, and examined the impact on interest rates.

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Chapter Summary (cont.)

Changes in Equilibrium Interest Rates: We further examined the dynamics of changes in supply and demand in the bond market, and the corresponding effect on bond prices and interest rates.