CHAPTER 6 RISK The Concept of Variability E(R) = Sum of (oi x pi ), The expected rate of return = E(R). E(R) = Sum of (oi x pi ), where oi is the value of the ith observation and pi is it’s probability. McGraw-Hill/Irwin

RISK PREFERENCES Risk-Averse Behavior Risk-Neutral Behavior Risk-Loving Behavior McGraw-Hill/Irwin

MEASURING PROJECT- SPECIFIC RISK McGraw-Hill/Irwin

Risk Estimates McGraw-Hill/Irwin

RISK MANAGEMENT Three primary tools may be employed by investors to minimize their expose to risk: avoid risky projects use insurance and hedging diversification McGraw-Hill/Irwin

PORTFOLIO RISK Diversifiable Risk: (unsystematic risk) can be eliminated by holding assets that are less than perfectly correlated. Nondiversifiable Risk: (systematic, or market risk) is the risk remaining in a fully-diversified portfolio. McGraw-Hill/Irwin

Diversification and Risk McGraw-Hill/Irwin

Covariance and Correlation McGraw-Hill/Irwin

OPTIMAL PORTFOLIO DECISIONS Investors base their investment decisions on its contribution to the portfolio’s risk and return. Efficient investments increase the portfolio’s expected return without adding risk. Efficient investments decrease the portfolio’s risk for a given expected return. McGraw-Hill/Irwin

Expected Risk and Returns of a Portfolio McGraw-Hill/Irwin

OPTIMAL PORTFOLIO ALLOCATIONS McGraw-Hill/Irwin

HISTORICAL RETURNS & RISK McGraw-Hill/Irwin

HISTORICAL CORRELATIONS (1979-99) McGraw-Hill/Irwin

ACCOUNTING FOR RISK The investor’s required rate of return is (E(Rj)). E(Rj) = Rf + RPj where Rf is the risk free rate and RPj is a premium for bearing risk. McGraw-Hill/Irwin

ACCOUNTING FOR RISK Asset Pricing Model to Estimate Risk Sensitivity Analysis McGraw-Hill/Irwin