2-1

Chapter TwoDetermination of

Interest Rates

2-2

Interest Rate Fundamentals

• Nominal interest rates: the interest rates actually observed in financial markets– Reflect the rate of exchange between monetary

assets goods across time– Affect the values (prices) of securities traded in

money and capital markets

• Real interest rates– Reflect the rate of exchange between real goods

across time

• Nominal interest rates: the interest rates actually observed in financial markets– Reflect the rate of exchange between monetary

assets goods across time– Affect the values (prices) of securities traded in

money and capital markets

• Real interest rates– Reflect the rate of exchange between real goods

across time

2-3

Loanable Funds Theory

• Loanable funds theory explains interest rates and interest rate movements

• Views level of interest rates in financial markets as a result of the supply and demand for loanable funds

• Domestic and foreign households, businesses, and governments all supply and demand loanable funds

• Loanable funds theory explains interest rates and interest rate movements

• Views level of interest rates in financial markets as a result of the supply and demand for loanable funds

• Domestic and foreign households, businesses, and governments all supply and demand loanable funds

2-4

Supply and Demand of Loanable Funds

InterestRate

Quantity of Loanable FundsSupplied and Demanded

Demand Supply

2-5

Shifts in Supply and Demand Curves change Equilibrium Interest Rates

Increased supply of loanable funds

Quantity ofFunds Supplied

InterestRate DD SS

SS*

EE*

Q*

i*

Q**

i**

Increased demand for loanable funds

Quantity of Funds Demanded

DDDD* SS

EE*

i*

i**

Q* Q**

InterestRate

2-6

Supply and Demand for Funds

Source Text Table 2-2

August 07 data

Funds        

Supplied Trill $

Demanded Trill $ Net $ Net %*

Supply %

Demand %

Households $42.52 $13.43 $ 29.09 25.4% 37.1% 11.7%

Business Nonfinancial 14.62 33.44 (18.82) -16.4% 12.8% 29.2%

Financial Intermediary 40.71 54.76 (14.05) -12.3% 35.5% 47.8%

Government 3.80 7.51 ( 3.71) -3.2% 3.3% 6.6%

Foreign 12.93 5.44 7.49 6.5% 11.3% 4.7%

Totals $114.58 $114.58 $ 0.00 0.0% 100.0% 100.0%

2-7

Shift in Supply and Demand Curves for Loanable Funds

Increase inAffect on Supply

Affect on Demand

Wealth & income Increase N/A

Risk Decrease Decrease

Near term spending needs Decrease N/A

Monetary expansion Increase N/A

Economic growth Increase Increase

Utility derived from assets Decrease Increase

Expected inflation Decrease Increase

Taxes Decrease

Currency Value Increase

Restrictive covenants Decrease

2-8

Determinants of Interest Rates for Individual Securities

• Real Interest Rate (RIR) and the Fisher effectRIR = i – Expected (IP)

• The actual Fisher Effect is given as(1+i) = (1+RIR)*(1+Expected(IP))

• Inflation (IP)IP = [(CPIt+1) – (CPIt)]/(CPIt) x (100/1)

• Real Interest Rate (RIR) and the Fisher effectRIR = i – Expected (IP)

• The actual Fisher Effect is given as(1+i) = (1+RIR)*(1+Expected(IP))

• Inflation (IP)IP = [(CPIt+1) – (CPIt)]/(CPIt) x (100/1)

2-9

Determinants of Interest Rates for Individual Securities (cont’d)

• Default Risk Premium (DRP)DRPj = ijt – iTt

ijt = interest rate on security j at time t

iTt = interest rate on similar maturity U.S. Treasury security at time t

• Liquidity Risk (LRP)

• Special Provisions (SCP)

• Term to Maturity (MP)

• Default Risk Premium (DRP)DRPj = ijt – iTt

ijt = interest rate on security j at time t

iTt = interest rate on similar maturity U.S. Treasury security at time t

• Liquidity Risk (LRP)

• Special Provisions (SCP)

• Term to Maturity (MP)

2-10

Nominal Rate of Interest

ij* = f(RIR, IP, DRPj, LRPj,MPj,, SCPj)• Riskless real rate +• Expected inflation +• Default risk premium +• Liquidity risk premium +• Maturity risk premium) +• Special covenant premium

2-11

Term Structure of Interest Rates:the Yield Curve

Yield toMaturity

Time to Maturity

(a)

(b)

(c)

(a) Upward sloping(b) Inverted or downward sloping(c) Flat

2-12

The Living Yield Curve

http://finance.yahoo.com/bonds

2-13

Unbiased Expectations Theory

• Long-term interest rates are geometric averages of current and expected future short-term interest rates

1RN = actual N-period rate today

N = term to maturity, N = 1, 2, …, 4, …

1R1 = actual current one-year rate today

E(ir1) = expected one-year rates for years, i = 1 to N

• Long-term interest rates are geometric averages of current and expected future short-term interest rates

1RN = actual N-period rate today

N = term to maturity, N = 1, 2, …, 4, …

1R1 = actual current one-year rate today

E(ir1) = expected one-year rates for years, i = 1 to N

1))](1))...((1)(1[( /1

112111 N

NN rErERR

2-14

UET Arbitrage Proof

• If the expected one year rates are 6%, 7% and 8% for the next three years respectively, and the three year rate is 5%, how could one make money on this relationship?

• Using the text’s terminology: 1R1 = 6%, 2R1=7% and 3R1 = 8% but

1R3=5%

1R1 = 6%, 2R1=7% 3R1 = 8%

1R3=5%t=0

t=0

1 2 3

3

2-15

UET Arbitrage Proof

• The average of the short term one year rates is 7%, but the three year rate is only 5%.

• One could borrow any given amount such as $1000 for the full three years and invest that money one year at a time and rolling over the investment for three years.

• The borrowing cost per year is 5% and the average rate of return is 7%. This is a riskless arbitrage.

• It would force the three year rate and the average of the one year rates to converge.

2-16

Liquidity Premium Theory

• Long-term interest rates are geometric averages of current and expected future short-term interest rates plus liquidity risk premiums that increase with maturity

Lt = liquidity premium for period t

L2 < L3 < …<LN

• Long-term interest rates are geometric averages of current and expected future short-term interest rates plus liquidity risk premiums that increase with maturity

Lt = liquidity premium for period t

L2 < L3 < …<LN

1)])(1)...()(1)(1[( /1

1212111 N

NNN LrELrERR

2-17

Liquidity Premium Theory

Liquidity Premium

Observed YC

Actual YC

Maturity

Yield to Maturity

2-18

Market Segmentation Theory

• Individual investors and FIs have specific maturity preferences

• Interest rates are determined by distinct supply and demand conditions within many maturity segments

• Investors and borrowers deviate from their preferred maturity segment only when adequately compensated to do so

• Individual investors and FIs have specific maturity preferences

• Interest rates are determined by distinct supply and demand conditions within many maturity segments

• Investors and borrowers deviate from their preferred maturity segment only when adequately compensated to do so

2-19

Market Segmentation

Maturity

Yield to Maturity

Short Intermediate Long

2-20

Implied Forward Rates

• A forward rate (f) is an expected rate on a short-term security that is to be originated at some point in the future

• The one-year forward rate for any year N in the future is:

• A forward rate (f) is an expected rate on a short-term security that is to be originated at some point in the future

• The one-year forward rate for any year N in the future is:

1])1/()1[( 1

1111

N

N

N

NN RRf

2-21

Forecasting Interest Rates

• A forward rate is a rate that can be imputed from the existing term structure.

• Given a set of long term spot rates one can find the individual one year forward rates. For instance, one year spot rate = 4% and two year spot rate = 5%

• (1+1R2)2 = (1+1R1)*(1+2F1)• (1.05)2 = (1.04)(1+2F1)•

2F1 = (1.05)2 / (1.04) -1 = 6.01%

Net Supply of Funds in U.S. in 2010

SectorNet Supply($ Billions)

Households & NPOs $ 786.9Business Nonfinancial 75.3State & Local Govt. -19.3Federal Government -1378.6Financial Sector -178.3Foreign 324.3

Totals (Discrepancy) -$389.7

Source Federal Reserve Flow of Funds Matrix Year 2010 data

Source: Federal Reserve Bank of St. Louis

Determinants of Household Savings

1. Interest rates and tax policy

2. Income and wealth: the greater the wealth or income, the greater the amount saved,

3. Attitudes about saving versus borrowing,

4. Credit availability, the greater the amount of easily obtainable consumer credit the lower the need to save,

5. Job security and belief in soundness of entitlements,

Determinants of Foreign Funds Invested in the U.S.

1. Relative interest rates and returns on global investments

2. Expected exchange rate changes

3. Safe haven status of U.S. investments

4. Foreign central bank investments in the U.S.

Determinants of Foreign Funds Invested in the U.S.

Source: Economist, February 2011

Country Foreign Currency Reserves (all $ in billions)

China $2,847 Saudi Arabia 456 Russia 444 Taiwan 382 S. Korea 292

Federal Government Demand for Funds

• Source: CBO 2011 report, http://www.cbo.gov/ftpdocs/74xx/doc7492/08-17-BudgetUpdate.pdf

Federal Government Demand for Funds

• Federal debt held by the public was at $9.0 trillion at end of 2010 (62% GDP) and is projected to grow to $17.4 trillion by 2020 (76% of projected 2020 GDP, 120% of current GDP) Large potential for crowding out and/or

dependence on foreign investment

Federal Government Demand for Funds

• Total Federal Debt is currently $14.1 trillion (97% GDP) and is projected to grow to $23.1 trillion by 2020 (64% increase)

o Interest expense is projected to grow to 3.5% of GDP by 2020