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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