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Chapter 5

Chapter 5. History of Interest Rates and Risk Premiums. Factors Influencing Rates. Supply Households Demand Businesses Government’s Net Supply and/or Demand Federal Reserve Actions. Interest Rates. Supply. r 1. r 0. Demand. Q 0. Q 1. Funds. Level of Rates. Real vs. Nominal Rates.

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Chapter 5

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  1. Chapter 5 History ofInterest Rates andRisk Premiums

  2. Factors Influencing Rates • Supply • Households • Demand • Businesses • Government’s Net Supply and/or Demand • Federal Reserve Actions

  3. Interest Rates Supply r1 r0 Demand Q0 Q1 Funds Level of Rates

  4. Real vs. Nominal Rates Fisher effect: Approximation nominal rate = real rate + inflation premium R = r + i or r = R - i Example r = 3%, i = 6% R = 9% = 3% + 6% or 3% = 9% - 6% Fisher effect: Exact r = (R - i) / (1 + i) 2.83% = (9%-6%) / (1.06) Empirical Relationship: Inflation and interest rates move closely together

  5. Rates of Return: Single Period HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period one

  6. Rates of Return: Single Period Example Ending Price = 48 Beginning Price = 40 Dividend = 2 HPR = (48 - 40 + 2 )/ (40) = 25%

  7. Characteristics of Probability Distributions 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2

  8. Normal Distribution s.d. s.d. r Symmetric distribution

  9. E ( r ) = p ( s ) r ( s ) s Measuring Mean: Scenario or Subjective Returns Subjective returns p(s) = probability of a state r(s) = return if a state occurs 1 to s states

  10. Numerical Example: Subjective or Scenario Distributions StateProb. of State r in State 1 .1 -.05 2 .2 .05 3 .4 .15 4 .2 .25 5 .1 .35 E(r) = (.1)(-.05) + (.2)(.05)...+ (.1)(.35) E(r) = .15

  11. 2 Variance = p ( s ) [ r - E ( r )] s s Measuring Variance or Dispersion of Returns Subjective or Scenario Standard deviation = [variance]1/2 Using Our Example: Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2...+ .1(.35-.15)2] Var= .01199 S.D.= [ .01199] 1/2 = .1095

  12. Annual Holding Period ReturnsFrom Figure 6.1 of Text Geom. Arith. Stan. Series Mean% Mean% Dev.% Lg Stk 10.5 12.5 20.4 Sm Stk 12.6 19.0 40.4 LT Gov 5.0 5.3 8.0 T-Bills 3.7 3.8 3.3 Inflation 3.1 3.2 4.5

  13. Annual Holding Period Risk Premiums and Real Returns Risk Real Series Premiums% Returns% Lg Stk 8.7 9.3 Sm Stk 15.2 15.8 LT Gov 1.5 2.1 T-Bills --- 0.6 Inflation --- ---

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