文档介绍：INVESTMENTSFourth Edition
ChapterChapter 22
RiskRisk
andand
RiskRisk AversionAversion
INVESTMENTSFourth Edition
RiskyRisky InvestmentsInvestments
withwith RiskRisk--FreeFree InvestmentInvestment
p = .6 W1 = 150 Profit = 50
Risky Inv.
1-p = .4
100 W2 = 80 Profit = -20
Risk Free T-bills Profit = 5
Risk Premium = 17
INVESTMENTSFourth Edition
AssetAsset ReturnsReturns
Asset returns over a given period are often uncertain.
D + P − P
R = 1 1 0
P 0
D + P
= 1 1 − 1
P 0
P0 is the price at the beginning of period
P1 is the price at the end of the period--Uncertain
D1 is the dividend at the end of the period—Uncertain
So return on a asset is a random variable, characterized by:
• All possible es
• Probability of each e
INVESTMENTSFourth Edition
ExpectedExpected raterate ofof returnreturn onon aa investmentinvestment
E 0 ( D 1 + P 1 ) − P 0
E 0 R =
P 0
E D + E P
= 0 1 0 1 − 1
P 0
Expected rate of pensates for time-
value and risk
E0 (R) = R f + Risk premium
For example:
E 0 ( D 1 + P 1 ) − P 0
E 0 R =
P 0
122
= − 1 = 22 %
100
INVESTMENTSFourth Edition
VarianceVariance onon aa investmentinvestment
Fro example
σ 2 (R) = ×(50% − 22%)2 + ×(−20% − 22%)2
=
σ(R) = ×(50% − 22%)2 + ×(−20% − 22%)2
=
INVESTMENTSFourth Edition
MeasuringMeasuring expectedexpected returnreturn andand riskrisk----
exampleexample
Moments of return distributions
state 1 2 3 Mean
Asset probability 1/3 1/3 1/3
Asset 0 R0(%) 5 5 5 5
Asset 1 R1 -10 5 20 5
Asset 2 R2 -5 5 15 5
Asset 3 R3 - 6 5
Between asset 0 and 1,which one would you choose?
Between asset 1 and 2……
Between asset 2 and 3……
INVESTMENTSFourth Edition
TheseThese returnsreturns havehave thethe followingfollowing
momentsmoments
Mean St D Skewness
R0(%) 5 0
R1 5 0
R2 5 0
R3 5 -
1/ 3
Skewness = {E[( x − Ex ]3 } / St .D of x
INVESTMENTSFourth Edition
RiskRisk Ave