History of Interest Rates and Risk Premiums Chapter 5.

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Presentation transcript:

History of Interest Rates and Risk Premiums Chapter 5

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

Level of Rates Q0Q0 Q1Q1 r0r0 r1r1 Funds Interest Rates Supply Demand

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 P 0 = Beginning price P 1 = Ending price D 1 = Dividend during period one Rates of Return: Single Period

Ending Price = 48 Beginning Price = 40 Dividend = 2 HPR = ( )/ (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 r s.d. Normal Distribution

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

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

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

Geom.Arith.Stan. SeriesMean%Mean%Dev.% Lg Stk Sm Stk LT Gov T-Bills Inflation Annual Holding Period Returns From Figure 6.1 of Text

Risk Real SeriesPremiums%Returns% Lg Stk Sm Stk LT Gov T-Bills Inflation Annual Holding Period Risk Premiums and Real Returns