Chapter Two Determination of Interest Rates

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

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

Supply and Demand of Loanable Funds Interest Rate Quantity of Loanable Funds Supplied and Demanded

Shifts in Supply and Demand Curves change Equilibrium Interest Rates Increased supply of loanable funds Increased demand for loanable funds Interest Rate DD* Interest Rate SS SS DD DD SS* i** E* E i* E i* E* i** Q* Q** Q* Q** Quantity of Funds Supplied Quantity of Funds Demanded

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 $ 0.00 0.0% 100.0%

Shift in Supply and Demand Curves for Loanable Funds Increase in Affect on Supply Affect on Demand Wealth & income Increase N/A Risk Decrease Near term spending needs Monetary expansion Economic growth Utility derived from assets Expected inflation Taxes Currency Value Restrictive covenants

Determinants of Interest Rates for Individual Securities Real Interest Rate (RIR) and the Fisher effect RIR = 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)

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)

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

Term Structure of Interest Rates: the Yield Curve (a) Upward sloping (b) Inverted or downward sloping (c) Flat Yield to Maturity (a) (c) (b) Time to Maturity

http://finance.yahoo.com/bonds The Living Yield Curve

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

UET Arbitrage Proof 1R1 = 6%, 2R1=7% 3R1 = 8% 1R3=5% 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% 2 3 t=0 1 1R3=5% 3 t=0

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.

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

Liquidity Premium Theory Yield to Maturity Observed YC Liquidity Premium Actual YC Maturity

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

Market Segmentation Yield to Maturity Short Intermediate Long Maturity

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:

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 Sector Net Supply ($ Billions) Households & NPOs $ 786.9 Business Nonfinancial 75.3 State & Local Govt. -19.3 Federal Government -1378.6 Financial Sector -178.3 Foreign 324.3 Totals (Discrepancy) -$389.7 A negative number represents net demand for funds. The biggest supplier was households and non-profits (reported together). The second largest source of funds was the Foreign sector. The biggest demander was the Federal Government. The column should sum to zero but large discrepancies are typical. Source Federal Reserve Flow of Funds Matrix Year 2010 data

Notice that household personal savings rates (% of income saved) have increased since the financial crisis.

Determinants of Household Savings Interest rates and tax policy Income and wealth: the greater the wealth or income, the greater the amount saved, Attitudes about saving versus borrowing, Credit availability, the greater the amount of easily obtainable consumer credit the lower the need to save, Job security and belief in soundness of entitlements,

Determinants of Foreign Funds Invested in the U.S. Relative interest rates and returns on global investments Expected exchange rate changes Safe haven status of U.S. investments Foreign central bank investments in the U.S. Foreign funds suppliers examine the same factors as U.S. suppliers except that they must also factor in expected changes in currency values, global interest rates, different tax rates and sovereign risk. There is typically some built in demand for U.S. investments however because the U.S. is considered a safe haven, i.e., a country with relatively low political and economic risk and a stable currency. High levels of reserves are indicative of foreign central bank activity to limit the growth in the value of their currencies against the dollar. This may be done to stimulate their export sectors. The dollars are often reinvested in the U.S., typically in Treasuries. This provides an additional source of financing to the U.S. and helps remove a market discipline from U.S. borrowers.

Determinants of Foreign Funds Invested in the U.S. Source: Economist, February 2011 Note: Not all of these reserves are in dollars. The IMF estimates about 60% of total foreign currency reserves are in dollars. High levels of reserves are indicative of foreign central bank activity to limit the growth in the value of their currencies against the dollar. This may be done to stimulate their export sectors. The dollars are often reinvested in the U.S., typically in Treasuries. This provides an additional source of financing to the U.S. and helps remove a market discipline from U.S. borrowers.

Federal Government Demand for Funds Source: CBO 2011 report, http://www.cbo.gov/ftpdocs/74xx/doc7492/08-17-BudgetUpdate.pdf Note: Government demand for funds is expected to remain high over the next 10 years.

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 Crowding out: When debt held by public (which is the measure that affects the credit markets) hits about 90% it is thought (in theory) to begin to significantly retard growth, perhaps hold back GDP growth by up to 1%! … But nobody knows for sure, and it depends on interest rates and ability to get foreign source money.

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) Interest expense is projected to grow to 3.5% of GDP by 2020 Note: Total Federal debt includes debt owed to trust funds and other government entities. While touted a lot in the press, debt held by the public (see prior slide) is the number that affects the credit markets. The point however is that the projected debt growth is unsustainable and will begin to curtail other necessary spending and growth.