1. Chapter 4 The Meaning of Interest Rates

2. Measuring Interest Rates
Present value: a dollar paid to you one year from now is less valuable than a dollar paid to you today.
Why: a dollar deposited today can earn interest and become $1 x (1+i) one year from today.

3. Present Value

4. Simple Present Value

5. Simple Present Value
What is the present value of $250 to be pain in two years if i=15%
CF=250
i=0.15
N=2
PV=(250)/(1.3225)=$189.4

6. Simple Present Value
Suppose that you won $20 million lottery which promises payment of $1 million for the next 20 years. Hove you won $20 million?
If I = 10%
You won
PV=(1/1.1)+(1/1.1^2)+…+(1/1.1^20)
=$9.4 million ONLY

7. Simple Present Value
Cannot directly compare payments scheduled in different points in the time line
$100
$100
$100
$100
Year 1 2 n PV
100
100/(1+i)
100/(1+i)2
100/(1+i)n

8. Four Types of Credit Market Instruments
Simple Loan
Fixed Payment Loan (making the same payment every period to the owner of the loan)
Coupon Bond(pays a fixed interest payment to the owner of the bond)
Discount Bond or zero coupon bond(bought at a price less than the face value)

9. Yield to Maturity
Yield to maturity: the interest rate that equates the present value of cash flow payments received from a debt instrument with its value today

10. Yield to Maturity on a Simple Loan

11. Fixed-Payment Loan

12. Coupon Bond

13. Coupon Bond
When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate.
The price of a coupon bond and the yield to maturity are negatively related.
The yield to maturity is greater than the coupon rate when the bond price is below its face value.

14. Coupon Bond
Consol or perpetuity: a bond with no maturity date that does not repay principal but pays fixed coupon payments forever
For coupon bonds, this equation gives the current yield, an easy to calculate approximation to the yield to maturity

15. Discount Bond

16. The Distinction Between Interest Rates and Returns
Rate of Return:

17. The Distinction Between Real and Nominal Interest Rates
Nominal interest rate makes no allowance for inflation.
Real interest rate is adjusted for changes in price level so it more accurately reflects the cost of borrowing.
Ex ante real interest rate is adjusted for expected changes in the price level
Ex post real interest rate is adjusted for actual changes in the price level

18. Fisher Equation

19. Figure 1 Real and Nominal Interest Rates (Three-Month Treasury Bill), 1953–2014
Sources: Nominal rates from Federal Reserve Bank of St. Louis FRED database: The real rate is
constructed using the procedure outlined in Frederic S. Mishkin, “The Real Interest Rate: An Empirical Investigation,” Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151–200. This procedure involves estimating expected inflation as a function of past interest rates, inflation, and time trends, and then subtracting the expected inflation measure from the nominal interest rate.

20. Determinants of Asset Demand
Wealth: the total resources owned by the individual, including all assets
Expected Return: the return expected over the next period on one asset relative to alternative assets
Risk: the degree of uncertainty associated with the return on one asset relative to alternative assets
Liquidity: the ease and speed with which an asset can be turned into cash relative to alternative assets

21. Theory of Portfolio Choice
Holding all other factors constant:
The quantity demanded of an asset is positively related to wealth
The quantity demanded of an asset is positively related to its expected return relative to alternative assets
The quantity demanded of an asset is negatively related to the risk of its returns relative to alternative assets
The quantity demanded of an asset is positively related to its liquidity relative to alternative assets

22. Theory of Portfolio Choice

23. Supply and Demand in the Bond Market
At lower prices (higher interest rates), ceteris paribus, the quantity demanded of bonds is higher: an inverse relationship
At lower prices (higher interest rates), ceteris paribus, the quantity supplied of bonds is lower: a positive relationship

24. Figure 1 Supply and Demand for Bonds (p-f)/p
Price of Bonds, P ($) Bs
With excess supply, the bond price falls to P * A I B H C
P * = 850 (i * = 17.6%) G D
With excess demand, the bond price rises to P * F E Bd
100
200
400
500
Quantity of Bonds, B
($ billions)
300

25. 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
Bd = Bs defines the equilibrium (or market clearing) price and interest rate.
When Bd > Bs , there is excess demand, price will rise and interest rate will fall
When Bd < Bs , there is excess supply, price will fall and interest rate will rise

26. Changes in Equilibrium Interest Rates
Shifts in the demand for bonds:
Wealth: in an expansion with growing wealth, the demand curve for bonds shifts to the right
Expected Returns: higher expected interest rates in the future lower the expected return for long-term bonds, shifting the demand curve to the left
Expected Inflation: an increase in the expected rate of inflations lowers the expected return for bonds, causing the demand curve to shift to the left
Risk: an increase in the riskiness of bonds causes the demand curve to shift to the left
Liquidity: increased liquidity of bonds results in the demand curve shifting right

27. Figure 2 Shift in the Demand Curve for Bonds
Price of Bonds, P A′
An increase in the demand for bonds shifts the bond demand curve rightward. A B D E C B′ C′ D′ E′
Quantity of Bonds, B

28. Shifts in the Demand for Bonds

29. Shifts in the Supply of Bonds
Shifts in the supply for bonds:
Expected profitability of investment opportunities: in an expansion, the supply curve shifts to the right
Expected inflation: an increase in expected inflation shifts the supply curve for bonds to the right
Government budget: increased budget deficits shift the supply curve to the right

30. Shifts in the Supply of Bonds

31. Figure 3 Shift in the Supply Curve for Bonds
Price of Bonds, P I H G F C I′ H′
An increase in the supply of bonds shifts the bond supply curve rightward. C′ G′ F′
Quantity of Bonds, B

32. Figure 4 Response to a Change in Expected Inflation
Price of Bonds, P
Step 1. A rise in expected inflation shifts the bond demand curve leftward . . . 1 P1
Step 2. and shifts the bond supply curve rightward . . .
Step 3. causing the price of bonds to fall and the equilibrium interest rate to rise. 2 P2
Quantity of Bonds, B

33. Figure 5 Expected Inflation and Interest Rates (Three-Month Treasury Bills), 1953–2014
Sources: Federal Reserve Bank of St. Louis FRE D database: Expected inflation calculated using procedures outlined in Frederic S. Mishkin, “The Real Interest Rate: An Empirical Investigation,” Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151–200. These procedures involve estimating expected inflation as a function of past interest rates, inflation, and time trends.

34. Figure 6 Response to a Business Cycle Expansion
Price of Bonds, P
Step 1. A business cycle expansion
shifts the bond supply curve
rightward . . .
Step 2. and shifts the bond demand
curve rightward, but by a lesser
amount . . . P1 1
Step 3. so the price of bonds falls
and the equilibrium interest rate
rises. 2 P2
Quantity of Bonds, B

35. Figure 7 Business Cycle and Interest Rates (Three-Month Treasury Bills), 1951–2014
Source: Federal Reserve Bank of St. Louis FRE D database:

36. Supply and Demand in the Market for Money: The Liquidity Preference Framework

37. Figure 8 Equilibrium in the Market for Money
Interest Rate, i (%) 30 25 20 10 5 Ms A
With excess supply, the interest rate falls to i *. B C
i * =15 D
With excess demand,
the interest rate rises
to i *. E Md
100
200
400
500
600
300
Quantity of Money, M
($ billions)

38. Demand for money in the liquidity preference framework:
Supply and Demand in the Market for Money: The Liquidity Preference Framework
Demand for money in the liquidity preference framework:
As the interest rate increases:
The opportunity cost of holding money increases…
The relative expected return of money decreases…
…and therefore the quantity demanded of money decreases.

39. Shifts in the demand for money:
Changes in Equilibrium Interest Rates in the Liquidity Preference Framework
Shifts in the demand for money:
Income Effect: a higher level of income causes the demand for money at each interest rate to increase and the demand curve to shift to the right
Price-Level Effect: a rise in the price level causes the demand for money at each interest rate to increase and the demand curve to shift to the right

40. Shifts in the supply of money:
Changes in Equilibrium Interest Rates in the Liquidity Preference Framework
Shifts in the supply of money:
Assume that the supply of money is controlled by the central bank.
An increase in the money supply engineered by the Federal Reserve will shift the supply curve for money to the right.

41. Changes in Equilibrium Interest Rates in the Liquidity Preference Framework

42. Figure 9 Response to a Change in Income or the Price Level
Interest Rate, i Ms
Step 1. A rise in income or the price level shifts the money demand curve rightward . . . i2 2
Step 2. and the equilibrium interest rate rises. i1 1
Quantity of Money, M

43. Figure 10 Response to a Change in the Money Supply
Interest rates, i i1 1
Step 2. and the equilibrium
interest rate falls. i2 2
Quantity of Money, M

44. Money and Interest Rates
A one time increase in the money supply will cause prices to rise to a permanently higher level by the end of the year. The interest rate will rise via the increased prices.
Price-level effect remains even after prices have stopped rising.
A rising price level will raise interest rates because people will expect inflation to be higher over the course of the year. When the price level stops rising, expectations of inflation will return to zero.
Expected-inflation effect persists only as long as the price level continues to rise.

45. Does a Higher Rate of Growth of the Money Supply Lower Interest Rates?
Liquidity preference framework leads to the conclusion that an increase in the money supply will lower interest rates: the liquidity effect.
Income effect finds interest rates rising because increasing the money supply is an expansionary influence on the economy (the demand curve shifts to the right).

46. Does a Higher Rate of Growth of the Money Supply Lower Interest Rates?
Price-Level effect predicts an increase in the money supply leads to a rise in interest rates in response to the rise in the price level (the demand curve shifts to the right).
Expected-Inflation effect shows an increase in interest rates because an increase in the money supply may lead people to expect a higher price level in the future (the demand curve shifts to the right).

47. Figure 11 Response over Time to an Increase in Money Supply Growth
Interest Rate, i i1 i2
Figure 11 Response over Time to an Increase in Money Supply Growth
(a) Liquidity effect larger than other effects T
Income, Price-Level, and Expected- inflation Effects
Liquidity Effect
Time
Interest Rate, i i2 i1
(b) Liquidity effect smaller than other effects and slow adjustment of expected inflation T
Liquidity Effect
Income, Price-Level, and Expected- inflation Effects
Time
Interest Rate, i i2 i1
(c) Liquidity effect smaller than expected-inflation effect and fast adjustment of expected inflation T
Liquidity and expected- inflation Effect
Income and Price-Level Effects
Time

48. Figure 12 Money Growth (M2, Annual Rate) and Interest Rates (Three-Month Treasury Bills), 1950–2014
Source: Federal Reserve Bank of St. Louis FRE D database: