Why Do Interest Rates Change? Chapter 4 Why Do Interest Rates Change?

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

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

The effect of changes in wealth: 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.

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

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%

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.

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

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?

4.1.3.2 EXAMPLE 2: Standard Deviation (b) Solution Fly-by-Night Airlines has a standard deviation of returns of 5%.

4.1.3.3 EXAMPLE 2: Standard Deviation (c) Feet-on-the-Ground Bus Company has a standard deviation of returns of 0%.

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.

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.

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.

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

4.1.5 Determinants of Asset Demand

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.

4.2.1 Derivation of Demand Curve (look at Figure 1 on P77) For one-year discount bonds (no coupon, face value $1000): Point A: Point B:

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

4.2.1.2 Supply and Demand Analysis of the Bond Market Figure 4.1 Supply and Demand for Bonds

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.

4.2.3 Market Equilibrium Occurs when Bd = Bs, at P* = 850, i* = 17.6% When P = $950, i = 5.3%, Bs > Bd (excess supply): P  to P*, i  to i* When P = $750, i = 33.0, Bd > Bs (excess demand): P  to P*, i  to i*

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.

4.2.5 Loanable (可贷出的)Funds Terminology Demand for bonds = supply of loanable funds Supply of bonds = demand for loanable funds 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

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.

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;

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. B1d to B2d .

4.3.3 Shifts in the Demand Curve Figure 4.3 Shifts in the Demand Curve for Bonds

4.3.4.1 How Factors Shift the Demand Curve - Wealth Economy , wealth , Bd , Bd shifts out to right, and the vice versa.

4.3.4.2 How Factors Shift the Demand Curve – Expected return i  in future, Re for long-term bonds , Bd shifts out to right πe , relative Re , Bd shifts out to right

4.3.4.3 How Factors Shift the Demand Curve - Risk Risk of bonds , Bd , Bd shifts out to right Risk of other assets , Bd , Bd shifts out to right

4.3.4.4 How Factors Shift the Demand Curve - Liquidity 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

4.3.5.1 Summary of Shifts in the Demand for Bonds (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 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

4.3.5.1 Summary of Shifts in the Demand for Bonds (1) 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 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

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.

4.3.6.1 Shifts in the Supply Curve Figure 4.4 Shift in the Supply Curve for Bonds

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

4.3.6.2.2 Factors that shift supply curve- Expected Inflation πe , Bs , Bs shifts out to right An increase in expected inflation causes the supply of bonds to increase

4.3.6.2.3 Factors that shift supply curve- Government Activity Government Activities Deficits , Bs , Bs shifts out to right Higher government deficits increase the supply of bonds, conversely, government surpluses decrease the supply of bonds

4.3.6.2.4 Factors That Shift Supply Curve (Table 3)

4.4 Fisher Effect and Business cycle

4.4.1 Changes in expected inflationπe If πe  Relative Re , Bd shifts in to left Bs , Bs shifts out to right P , i  Figure 4.5 Response to a Change in Expected Inflation

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)

4.4.3 Evidence on the Fisher Effect in the United States Figure 4.6 Expected Inflation and Interest Rates (Three-Month Treasury Bills), 1953–2004

4.4.4 Summary of the Fisher Effect 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 The rise in expected inflation also means that the real cost of borrowing has declined, causing the quantity of bonds supplied to increase When the demand for bonds falls and the quantity of bonds supplied increases, the equilibrium bond price falls Since the bond price is negatively related to the interest rate, this means that the interest rate will rise

4.4.5 Business Cycle Expansion Wealth , Bd , Bd shifts out to right Investment , Bs , Bs shifts right If Bs shifts more than Bd then P , i  Figure 4.7 Response to a Business Cycle Expansion

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

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)

4.5 Profiting from Interest-Rate Forecasts Methods for forecasting Supply and demand for bonds: use Flow of Funds Accounts and judgment Econometric Models: large in scale, use interlocking equations that assume past financial relationships will hold in the future

4.6 Profiting from Interest-Rate Forecasts Make decisions about assets to hold Forecast i , buy long bonds Forecast i , buy short bonds Make decisions about how to borrow Forecast i , borrow short Forecast i , borrow long

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.

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.