Casual observation and formal research both suggest that investment risk is as important to investors as expected return. while we have theories about the relationship between risk and expected return that would prevail in rational capital markets, there is no theory about the levels of risk we should find in the marketplace. we can at best estimate the level of risk likely to confront investors by analyzing historical experience. | 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) = (9%-6%) / () 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 . . 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 2 .2 .05 3 .4 .15 4 .2 .25 5 .1 .35 E(r) = (.1)() + (.2)(.05).+ (.1)(.35) E(r) = .15 Scenario or Subjective Returns: Example Standard deviation = [variance]1/2 Subjective or Scenario Var =[(.1)()2+(.2)(.05- .15)2.+ .1(.)2] Var= .01199 [ .01199] 1/2 = .1095 Using Our Example: Variance or Dispersion of Returns Geom. Arith. Stan. Series Mean% Mean% Dev.% Sm Stk Lg Stk LT Gov T-Bills Inflation Annual Holding Period Returns (Arithmetic) Risk Real Series Premiums% Returns% Sm Stk Lg Stk LT Gov T-Bills --- 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) = (9%-6%) / () 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 .
