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Lecture_Equity_Spring_2010

# Lecture_Equity_Spring_2010 - Risk and Return Past and...

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Risk and Return: Past and Prologue CHAPTER OVERVIEW This chapter introduces the concept of risk and return . That is, rational investors potentially will accept more risk if the expected returns of the investment are commensurably higher. Risk preference : Investors differ as to the degree of risk they are willing to accept. Forming portfolios with risky and risk-free asset. Rates of Return HPR = ( 29 ( 29 price Beginning P dividend Cash D price Beginning P price Ending P 0 1 0 1 ) ( ) ( + - Dollars earned per dollar invested over the investment period Assumption : The dividend is paid at the end of the holding period ( ) yield + ( ) yield Ex 5.1)

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Conventions for quoting rates of return APR(annual percentage rate) = number of periods per year × per period rate EAR = effective annual rate 1 + EAR = ( 1 + rate per period ) n = ( 1 + APR / n ) n EX) monthly return of 1% APR = 1% X 12 = 12% EAR = (1.01) 12 - 1 = 12.68% why EAR > APR ? What if n is really big? 1 + EAR = e APR ≈ ( 1 + APR / n ) n => APR = log(1+EAR) EX 5.2)
Risk and risk premiums Characteristics of Probability Distributions 1) Mean: most likely value 2) Variance or standard deviation: measures dispersion 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2 Mean: E(r) = = N s s r s p 1 ) ( ) ( Variance: Var(r) = = - N s r E s r s p 1 2 )] ( ) ( )[ ( Standard deviation: SD(r) = ) var( r Why use SD instead of VAR to measure the risk? The variance has a dimension of percent squared SD has the same dimension as expected returns

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Concept Check 2) Risk free rate: The rate of return that can be obtained without uncertainty (T-bill rate) => zero-variance => no risk premium Risk premium: An expected return in excess of risk free rate(T-bill rate) Excess return: Rate of return in excess of the T-bill rate Risk aversion: reluctance to accept risk 2 2 1 ) ( σ A r r E f = - Ex) A = 2 ~ 4 implies that to accept an increase of 0.01 in variance,investors would require an increase in the risk premium of between 0.01 ~0.02. Inflation and real rates of return 1 + r = i R r i R - = + + 1 1 where r = real interest rate, R = nominal interest rate, i= inflation rate
Asset allocation across risky and risk-free portfolios Complete portfolio: The entire portfolio including risky and risk-free assets Ex) Portfolio with two risky assets (A and B) and a risk-free asset (F) Market value of A = \$113,400 Market value of B = \$96,600 Market value of F = \$ 90,000 Market value of the portfolio = \$300,000 Market value of the risky asset = \$210,000 Weight of A in risky asset = 113,400/210,000 = 0.54 Weight of B in risky asset = 96,600/210,000 = 0.46 Weight of risky asset in the portfolio (y) = 210,000 / 300,000 = 0.70 Weight of risk-free asset in the portfolio (1-y) = 90,000 / 300,000 = 0.30 Weight of A in the portfolio = 113,400/300,000 = (113,400/210,000)(210,000/300,0000) = 0.54*0.70=0.378 Weight of B in the portfolio = 96,600/300,000 = (96,600/210,000)(210,000/300,0000) = 0.46*0.70=0.322 Suppose the investor decides to decrease risk by reducing the exposure to the risky portfolio from y = 0.7 to y=0.56 Have to leave the proportion of each asset in the risky portfolio unchanged Market value of the risky asset = \$300,000*0.56 = \$168,000 Market value of A = \$168,000*0.54 = \$90,720 Market value of B = \$168,000*0.46 = \$77,280

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