Chap002

Chapter Two

Determinants of Interest Rates

McGraw-Hill/Irwin

Copyright Š 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Interest Rate Fundamentals  Nominal interest rates: the interest rates Nominal interest rates: the interest rates

actually actually observed observed in in financial financial markets markets  

Used Used to to determine determine fair fair present present value value and and prices prices of of securities securities Two Two types types of of components components  Opportunity cost Opportunity cost  Adjustments for individual security characteristics Adjustments for individual security characteristics

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Real Interest Rates 

Additional purchasing power required to forego current consumption 





What causes differences in nominal and real interest rates?

If you wish to earn a 3% real return and prices are expected to increase by 2%, what rate must you charge?

Irving Fisher first postulated that interest rates contain a premium for expected inflation.

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Loanable Funds Theory Loanable Loanable funds funds theory theory explains explains interest interest rates rates and and interest interest rate rate movements movements  Views level of interest rates in financial markets Views level of interest rates in financial markets as as aa result result of of the the supply supply and and demand demand for for loanable loanable funds funds  Domestic and foreign households, businesses, Domestic and foreign households, businesses, and and governments governments all all supply supply and and demand demand loanable loanable funds funds 

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Supply and Demand of Loanable Funds Interest Rate

Demand

Supply

Quantity of Loanable Funds Supplied and Demanded 2-5

Net Supply of Funds in U.S. in 2010 Source Federal Reserve Flow of Funds Matrix Net Supply in Billions Year 2010 data of Dollars 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

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Source: Federal Reserve Bank of St. Louis

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Determinants of Household Savings 1.

2.

3.

4.

5.

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,

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Determinants of Foreign Funds Invested in the U.S. 1.

2.

3.

4.

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.

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Determinants of Foreign Funds Invested in the U.S. Country China Saudi Arabia Russia Taiwan S. Korea

Foreign Currency Reserves (all $ in billions) $2,847 456 444 382 292

Source: Economist, February 2011

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Federal Government Demand for Funds

ď Ź

Source: CBO 2011 report

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

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Federal Government Demand for Funds ď Ź

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

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Federal Government Demand for Funds ď Ź

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

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Shifts in Supply and Demand Curves change Equilibrium Interest Rates Increased supply of loanable funds Increased demand for loanable funds Interest Rate

Interest Rate

SS

DD

SS*

DD

DD*

i** i*

E

i*

E*

i** Q* Q**

Quantity of Funds Supplied

SS

E* E

Q* Q**

Quantity of Funds Demanded

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Factors that Cause Supply and Demand Curves to Shift Increase in Affect on Supply Affect on Demand Wealth & income Increase N/A As wealth and income increase, funds suppliers are more willing to supply funds to markets. Result: lower interest rates Risk Decrease Decrease As the risk of an investment decreases, funds suppliers are less willing to purchase the claim. All else equal, demanders of funds would be less willing to borrow as well. Result: higher interest rates Near term spending needs Decrease N/A As current spending needs increase, funds suppliers are less willing to invest.

Result: higher interest rates Monetary expansion Increase N/A As the central bank increases the supply of money in the economy, this directly increases the supply of funds available for lending. Result: lower interest rates

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Factors that Cause Supply and Demand Curves to Shift Increase in Affect on Supply Affect on Demand Economic growth Increase Increase With stronger economic growth, wealth and incomes rise, increasing the supply of funds available. As U.S. economic strength improves relative to the rest of the world, foreign supply of funds is also increased. Business demand for funds increases as more projects are profitable. Result: indeterminate effect on interest rates, but at more rapid growth rates interest rates tend to rise.

Utility derived from assets Decrease Increase As utility from owning assets increases, funds suppliers are less willing to invest and postpone consumption whereas funds demanders are more willing to borrow. Result: higher interest rates Restrictive covenants Increase Decrease As loan or bond covenants become more restrictive, borrowers reduce their demand for funds. Result: lower interest rates

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Factors that Cause Supply and Demand Curves to Shift Increase in Affect on Supply Affect on Demand Tax Increase Decrease Increase Taxes on interest and capital gains reduce the returns to savers and the incentive to save.

The tax deductibility of interest paid on debt increases borrowing demand. Result: Higher interest rates Currency Appreciation Increase N/A Foreign suppliers of funds would earn a higher rate of return if the currency appreciates and a lower rate of return measured in their own currency if the dollar depreciates.

Foreign central banks often buy U.S. Treasury securities as part of their attempts to prevent their currency from appreciating against the dollar.

Result: Lower interest rates Expected inflation Decrease Increase An increase in expected inflation implies that suppliers will be repaid with dollars that will have less purchasing power than originally anticipated. Suppliers lose purchasing power and borrowers gain more than originally anticipated. This implies that supply will be reduced and demand increased. Result: Higher interest rates

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Determinants of Interest Rates for Individual Securities  iij** = f(IP, RIR, DRP , LRP , SCP , MP ) j = f(IP, RIR, DRPj j, LRPj j, SCPj j, MPj j)  Inflation (IP) Inflation (IP)

IP ) x (100/1) IP == [(CPI [(CPIt+1t+1)) –– (CPI (CPIt)]/(CPI )]/(CPI ) x (100/1) t t t

 Real Interest Rate (RIR) and the Fisher Real Interest Rate (RIR) and the Fisher

effect effect

RIR RIR == ii –– Expected Expected (IP) (IP)

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Determinants of Interest Rates for Individual Securities (cont’d)  Default Risk Premium (DRP) Default Risk Premium (DRP)

DRP DRPj j == iijtjt –– iiTtTt iijt jt == interest interest rate rate on on security security jj at at time time tt iiTtTt == interest interest rate rate on on similar similar maturity maturity U.S. U.S. Treasury Treasury security security at at time time tt  Liquidity Risk (LRP) Liquidity Risk (LRP)  Special Provisions (SCP) Special Provisions (SCP)  Term to Maturity (MP) Term to Maturity (MP)

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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

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Unbiased Expectations Theory 

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

RN = [(1+ 1 R1 )(1 + E ( 2 r1 ))...(1 + E ( N r1 ))]

1/ N

1

−1

RR ==actual actualN-period N-periodrate ratetoday today NN==term termto tomaturity, maturity,NN==1, 1,2, 2,…, …,4, 4,… …

1R R1 ==actual actualcurrent currentone-year one-yearrate ratetoday today 1 1 NN

1

1

E( E(irir1)1)==expected expectedone-year one-yearrates ratesfor foryears, years,ii==11to toNN

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Liquidity Premium Theory 

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

1/ N R = [( 1 + R )( 1 + E ( r ) + L )...( 1 + E ( r ) + L )] −1 1 N 1 1 2 1 2 N 1 N

LLt ==liquidity liquiditypremium premiumfor forperiod periodtt t LL2 <<LL3 <<…<L …<LN 2

3

N

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Market Segmentation Theory Individual Individual investors investors and and FIs FIs have have specific specific maturity maturity preferences preferences  Interest rates are determined by distinct supply Interest rates are determined by distinct supply and and demand demand conditions conditions within within many many maturity maturity segments segments  Investors and borrowers deviate from their Investors and borrowers deviate from their preferred preferred maturity maturity segment segment only only when when adequately adequately compensated compensated to to do do so so 

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Implied Forward Rates AA forward forward rate rate (f) (f) is is an an expected expected rate rate on on aa shortshortterm term security security that that is is to to be be originated originated at at some some point point in in the the future future  The one-year forward rate for any year N in the The one-year forward rate for any year N in the future future is: is: 

f1 = [(1+1 RN ) /(1+1 RN −1 ) N

N

N −1

] −1

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Time Value of Money and Interest Rates  The time value of money is based on the The time value of money is based on the

notion notion that that aa dollar dollar received received today today is is worth worth more more than than aa dollar dollar received received at at some some future future date date 

Simple Simple interest: interest: interest interest earned earned on on an an

investment investment is is not not reinvested reinvested  Compound interest: interest earned on an Compound interest: interest earned on an investment investment is is reinvested reinvested

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Present Value of a Lump Sum ď Źď Ź

Discount Discount future future payments payments using using current current interest interest rates rates to to find find the the present present value value (PV) (PV) tt PV + r)] == FV ) PV == FV FVt[1/(1 [1/(1 + r)] FVt(PVIF t t(PVIFr,tr,t) PV PV==present presentvalue valueof ofcash cashflow flow FV FVt t==future futurevalue valueof ofcash cashflow flow(lump (lumpsum) sum)received receivedin intt periods periods rr==interest interestrate rateper perperiod period tt==number numberof ofyears yearsin ininvestment investmenthorizon horizon PVIF PVIFr,t ==present presentvalue valueinterest interestfactor factorof ofaalump lumpsum sum r,t

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Future Value of a Lump Sum ď Źď Ź The future value (FV) of a lump sum The future value (FV) of a lump sum

received received at at the the beginning beginning of of an an investment investment horizon horizon tt FV = PV (1 + r) FVt t = PV (1 + r) == PV(FVIF PV(FVIFr,tr,t))

FVIF FVIFr,tr,t == future future value value interest interest factor factor of of aa lump lump sum sum

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Relation between Interest Rates and Present and Future Values Present Value (PV)

Future Value (FV) Interest Rate Interest Rate

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Present Value of an Annuity 

The The present present value value of of aa finite finite series series of of equal equal cash cash flows flows received received on on the the last last day day of of equal equal intervals intervals throughout throughout the the investment investment horizon horizon 1 − (1 + i )− t  PV = PMT ∑ [1/(1 + r )] = PMT ×   i   j =1 PMT payment PMT==periodic periodicannuity annuity payment t

j

PVIFA PVIFAr,tr,t==present presentvalue valueinterest interestfactor factorof ofan anannuity annuity

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Future Value of an Annuity 

The The future future value value of of aa finite finite series series of of equal equal cash cash flows flows received received on on the the last last day day of of equal equal intervals intervals throughout throughout the the investment investment horizon horizon t −1

 (1 + i )t − 1 FVt = PMT ∑ (1 + r ) = PMT ×   i   j =0 FVIFA FVIFAr,t ==future futurevalue valueinterest interestfactor factorof ofan anannuity annuity j

r,t

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Effective Annual Return  Effective or equivalent annual return Effective or equivalent annual return

(EAR) (EAR) is is the the return return earned earned or or paid paid over over aa 12-month 12-month period period taking taking compounding compounding into into account account cc EAR = (1 + r ) –1 EAR = (1 + rperperperiod period) – 1 cc==the thenumber numberof ofcompounding compoundingperiods periodsper peryear year

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Financial Calculators 

Setting Setting up up aa financial financial calculator calculator  



Number Numberof ofdigits digitsshown shownafter afterdecimal decimalpoint point Number Numberof ofcompounding compoundingperiods periodsper peryear year

Key Key inputs/outputs inputs/outputs (solve (solve for for one one of of five) five) NN==number numberof ofcompounding compoundingperiods periods I/Y I/Y==annual annualinterest interestrate rate PV PV==present presentvalue value(i.e., (i.e.,current currentprice) price) PMT PMT==aaconstant constantpayment paymentevery everyperiod period FV FV==future futurevalue value(i.e., (i.e.,future futureprice) price)

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