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Chapter 5 "History of interest rates and risk premiums" presents the following content: Factors influencing rates, level of interest rates, real vs. nominal rates, rates of return: single period, characteristics of probability distributions, mean scenario or subjective returns, variance or dispersion of returns,. | 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 Q0 Q1 r0 r1 Funds Interest Rates Supply Demand Interest Rates Supply Q0 Q1 r0 r1 Funds Demand Level of Interest 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 Real vs. Nominal Rates HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period one Rates of Return: Single Period Ending Price = 48 Beginning Price = 40 Dividend = 2 HPR = (48 - 40 + 2 )/ (40) = 25% Rates of Return: Single Period Example 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. Characteristics of Probability Distributions Symmetric distribution mean s.d. s.d. Normal Distribution Subjective returns p(s) = probability of a state r(s) = return if a state occurs 1 to s states Mean Scenario or Subjective Returns State Prob. of State r in State 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 Scenario or Subjective Returns: Example Standard deviation = [variance]1/2 Subjective or Scenario Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2.+ .1(.35-.15)2] Var= .01199 S.D.= [ .01199] 1/2 = .1095 Using Our Example: Variance or Dispersion of Returns Geom. Arith. Stan. Series Mean% Mean% Dev.% Sm Stk 11.6 17.7 39.3 Lg Stk 10.0 12.0 20.6 LT Gov 5.4 5.7 8.2 T-Bills 3.8 3.8 3.2 Inflation 3.1 3.1 4.4 Annual Holding Period Returns (Arithmetic) Risk Real Series Premiums% Returns% Sm Stk 13.9 14.6 Lg Stk 9.3 8.9 LT Gov 1.9 2.6 T-Bills --- 0.7 Inflation --- --- Risk Premiums Real Returns | 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 Q0 Q1 r0 r1 Funds Interest Rates Supply Demand Interest Rates Supply Q0 Q1 r0 r1 Funds Demand Level of Interest 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 Real vs. Nominal Rates HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period one Rates of Return: Single Period Ending Price = 48 Beginning Price = 40 Dividend = 2 HPR = (48 - 40 + 2 )/ (40) = 25% Rates of Return: Single Period Example 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the .
