INVESTMENTS Risk and Risk aversion
INVESTMENTS Fourth Edition Risk and Risk Aversion Risk Aversion Chapter 2 Chapter 2
Risky investments -ree lryestrrier p=6 W,=150 Profit=50 Risky iny 1-p=4 Wo=80 Profit=-20 Risk Free t-bills Profit =5 Risk Premium =17
INVESTMENTS Fourth Edition W1 = 150 Profit = 50 W2 = 80 Profit = -20 p = .6 1-p = .4 100 Risky Inv. Risk Free T-bills Profit = 5 Risk Premium = 17 Risky Investments Risky Investments with Risk with Risk-Free Investment Free Investment
IIITOTMATNTO Asset reture a Asset returns over a given period are often uncertain D t p P R P D + p Po is the price at the beginning of period PI is the price at the end of the period--Uncertain DI is the dividend at the end of the period--Uncertain So return on a asset is a random variable, characterized by All possible outcomes Probability of each outcome
INVESTMENTS Fourth Edition Asset Returns Asset Returns Asset returns over a given period are often uncertain. 1 0 1 1 0 1 1 0 − + = + − = P D P P D P P R P 0 is the price at the beginning of period P 1 is the price at the end of the period--Uncertain D 1 is the dividend at the end of the period—Uncertain So return on a asset is a random variable, characterized by: • All possible outcomes • Probability of each outcome
INVESTMENTS Expected rate of return on a! inyestment E。R E0(D1+P1)-P E。D,+E。P Expected rate of return compensates for time- k value and r1s」 Eo(R=R+ Risk premium For example E R E(D1+P1) 122 1=22
INVESTMENTS Fourth Edition Expected rate of return on a investment Expected rate of return on a investment 1 ( ) 0 0 1 0 1 0 0 1 1 0 0 − + = + − = P E D E P P E D P P E R Expected rate of return compensates for timevalue and risk E0 (R) = R f + Risk premium For example: 1 22 % 100 122 ( ) 0 0 1 1 0 0 = − = + − = P E D P P E R
INVESTMENTS Variance on a inyestment Fro example (R)=0.6×(50%-22%)2+0.4×(-20%-22 =0.1176 (R)=06×(50%-299+04×(20%-292 0.3429
INVESTMENTS Fourth Edition Variance on a investment Variance on a investment Fro example 0.1176 ( ) 0.6 (50 % 22%) 0.4 ( 20 % 22%) 2 2 2 = σ R = × − + × − − 0.3429 ( ) 0.6 (50 % 22%) 0.4 ( 20 % 22%) 2 2 = σ R = × − + × − −