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Determinants of Interest Rates and Loanable Funds

This chapter explores the factors that affect interest rates in financial markets, including inflation, risk, liquidity, and special features of individual securities. It also examines the supply and demand for loanable funds and the role of foreign investments in the U.S.

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Determinants of Interest Rates and Loanable Funds

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  1. Chapter Two Determinants of Interest Rates

  2. Interest Rate Fundamentals Nominal interest rates: the interest rates actually observed in financial markets Used to determine fair present value and prices of securities Two types of components Opportunity cost on competing investments Adjustments for individual security characteristics

  3. Real Interest Rates Additional purchasing power required to forego current consumption What causes differences in nominal and realinterest 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. (1+R) = (1+r)(1+h), where R is nominal, r is real, h is inflation

  4. 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

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

  6. Determinants of Household Savings Interest rates – the higher the greater saving Tax policy – the higher, the less saving 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

  7. 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. Why is so much money coming to the US from abroad right now?

  8. Federal Government Demand for Funds (a.k.a. Deficit Financing) Source: CBO 2011 report, http://www.cbo.gov/ftpdocs/74xx/doc7492/08-17-BudgetUpdate.pdf

  9. 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

  10. Factors that Cause Supply and Demand Curves to Shift

  11. Factors that Cause Supply and Demand Curves to Shift

  12. Factors that Cause Supply and Demand Curves to Shift

  13. Determinants of Interest Rates for Individual Securities ij* = f(IP, RIR, DRPj, LRPj, SCPj, MPj) IP - inflation premium RIR – real risk-free rate DRP – default risk premium LRP – liquidity risk premium SCP – special feature premium MP maturity premium Inflation (IP) IP = [(CPIt+1) – (CPIt)]/(CPIt) x (100/1) Real Interest Rate (RIR) and the Fisher effect RIR = i – Expected (IP)

  14. Determinants of Interest Rates for Individual Securities (cont’d) Default Risk Premium (DRP) DRPj = ijt – iTt ijt = interest rate on securityj 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)

  15. Term Structure of Interest Rates:the Yield Curve • (a) Upward sloping • (b) Inverted or • downward sloping • Flat • Recessions tend to • preceded by inverted • yield curves Yield to Maturity (a) (c) (b) Time to Maturity

  16. 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

  17. 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 periodt L2 < L3 < …<LN

  18. Market Segmentation Theory Individual investors 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 Also known as Preferred Habitat Theory

  19. 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:

  20. Question The 2 year rate is 2% per year The 1 year rate is 1.5% What is the implied forward rate for year 2? Answer Then 2f1 = (1.02)2 / (1.015) – 1 = .025 or 2.5% next year

  21. Time Value of Money and Interest Rates The time value of money is based on the notion that a dollar received today is worth more than a dollar received at some future date Simple interest: interest earned on an investment is not reinvested Compound interest: interest earned on an investment is reinvested

  22. Present Value of a Lump Sum Discount future payments using current interest rates to find the present value (PV) PV = FVt[1/(1 + r)]t = FVt(PVIFr,t) PV = present value of cash flow FVt = future value of cash flow (lump sum) received in t periods r= interest rate per period t= number of years in investment horizon PVIFr,t = present value interest factor of a lump sum

  23. Future Value of a Lump Sum The future value (FV) of a lump sum received at the beginning of an investment horizon FVt = PV(1 + r)t = PV(FVIFr,t) FVIFr,t = future value interest factor of a lump sum

  24. Relation between Interest Rates and Present and Future Values Present Value (PV) Future Value (FV) Interest Rate Interest Rate

  25. Present Value of an Annuity The present value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon PMT = periodic annuity payment PVIFAr,t = present value interest factor of an annuity NOTE: PMT / i is a perpetuity, which lasts only t-periods

  26. Future Value of an Annuity The future value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon FVIFAr,t = future value interest factor of an annuity

  27. Effective Annual Return Effective or equivalent annual return (EAR) is the return earned or paid over a 12-month period taking compounding into account EAR= (1 + rper period)c – 1 c = the number of compounding periods per year

  28. Financial Calculators Setting up a financial calculator Number of digits shown after decimal point Number of compounding periods per year Key inputs/outputs (solve for one of five) N = number of compounding periods I/Y = annual interest rate PV = present value (i.e., current price) PMT = a constant payment every period FV = future value (i.e., future price) Chapter 2 Problems: On page 55, try 20, 22, and all of page 56.

  29. Chapter Three Interest Rates and Security Valuation

  30. Various Interest Rate Measures Coupon rate periodic cash flow a bond issuer contractually promises to pay a bond holder Required rate of return (r) rates used by individual market participants to calculate fair present values (PV) Expected rate of return or E(r) rates participants would earn by buying securities at current market prices(P) Realized rate of return ( r ) rate actually earned on investments

  31. Required Rate of Return The fair present value (PV) of a security is determined using the required rate of return (r) as the discount rate CF1= cash flow in period t(t= 1, …, n) ~ = indicates the projected cash flow is uncertain n= number of periods in the investment horizon

  32. Expected Rate of Return The current market price (P) of a security is determined using the expected rate of return orE(r) as the discount rate CF1 = cash flow in period t (t= 1, …, n) ~ = indicates the projected cash flow is uncertain n= number of periods in the investment horizon

  33. Realized Rate of Return The realized rate of return ( r ) is the discount rate that just equates the actual purchase price ( ) to the present value of the realized cash flows (RCFt) t (t = 1, …, n)

  34. Bond Valuation -PV of coupon payments and PV of Par or Face Value. The present value of a bond (Vb) can be written as: Par = the par or face value of the bond, usually $1,000 INT = the annual interest (or coupon) payment T = the number of years until the bond matures r = the annual interest rate (often called yield to maturity (ytm))

  35. Bond Valuation A premium bondhas a coupon rate (INT) greater than the required rate of return (r) and the fair present value of the bond (Vb) is greater than the face or par value (Par) Premium bond: If INT > r; then Vb > Par Discount bond: if INT < r, then Vb< Par Par bond: if INT = r, then Vb= Par

  36. Equity Valuation The present value of a stock (Pt) assuming zero growth in dividends can be written as: D = dividend paid at end of every year Pt = the stock’s price at the end of year t rs = the interest rate used to discount future cash flows Note: This is a Perpetuity Formula or a Consol. We find this perfect for preferred stock, which have fixed dividends.

  37. Equity ValuationThe Dividend Growth Model or Gordon Model The present value of a stock (Pt) assuming constant growth in dividends can be written as: D0 = current value of dividends Dt = value of dividends at time t = 1, 2, …, ∞ g = the constant dividend growth rate

  38. Equity Valuation The return on a stock with zero dividend growth, if purchased at current price P0, can be written as: The return on a stock with constant dividend growth, if purchased at price P0, can be written as: Dividend yield + capital gain yield

  39. Relation between Interest Rates and Bond Values Interest Rate Bond Value 12% 10% 8% 874.50 1,000 1,152.47

  40. Impact of maturity on PriceVolatility in the face of interest rate changes Absolute Value of Percent Change in a Bond’s Price for a Given Change in Interest Rates Time to Maturity

  41. Impact of Maturity on Price Volatility with increase in yields

  42. Impact of Coupon Rates onPrice Volatility Bond Value High-Coupon Bond Low-Coupon Bond Interest Rate

  43. Impact of Coupon on Price Volatility with decrease in yields

  44. Impact of r on Price Volatility Bond Price Interest Rate How does volatility change with interest rates? Price volatility is inversely related to the level of the initial interest rate r

  45. Duration Duration is the weighted-average time to maturity (measured in years) on a financial security Duration measures the sensitivity (or elasticity) of a fixed-income security’s price to small interest rate changes Duration captures the coupon and maturity effects on volatility.

  46. Duration – weighted average of coupon and Par value Duration(Dur) for a fixed-income security that pays interest annually can be written as: P0= Current price of the security t = 1 to T, the period in which a cash flow is received T = the number of years to maturity CFt = cash flow received at end of period t r= yield to maturity or required rate of return PVt= present value of cash flow received at end of period t

  47. 9% Coupon, 4 year maturity annual payment bond with a 8% ytm Duration and Volatility Duration = 3.5396 years What is the Duration if zero coupon 4 year bond?

  48. Duration Duration(Dur) (measured in years) for a fixed-income security, in general, can be written as: m= the number of times per year interest is paid, the sum term is incremented in m units

  49. Closed form duration equation: • P0 = Price • INT= Periodic cash flow in dollars, normally the semiannual coupon on a bond or the periodic monthly payment on a loan. • r = periodic interest rate = APR / m, where m = # compounding periods per year • N = Number of compounding or payment periods (or the number of years * m) • Dur = Duration = # Compounding or payment periods; Durationperiod is what you actually get from the formula

  50. Duration Duration and coupon interest the higher the coupon payment, the lower the bond’s duration Duration and yield to maturity the higher the yield to maturity, the lower the bond’s duration Duration and maturity duration increases with maturity but at a decreasing rate

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