1. RISK AND REAL ESTATE INVESTMENT LEARNING OBJECTIVES Calculate and interpret the basic measures of risk for individual assets and portfolios of assets. Identify the problems with, and limitations of, traditional sources of real estate risk and return data. Incorporate information regarding project riskiness into the investment decision-making process. Describe sensitivity analysis.

2. RISK The Concept of Variability The expected rate of return = E(R). E(R) = Sum of (o i x p i ), where o i is the value of the ith observation and p i is it’s probability.

3. RISK PREFERENCES Risk-Averse Behavior Risk-Neutral Behavior Risk-Loving Behavior

4. MEASURING PROJECT- SPECIFIC RISK

5. Risk Estimates

6. RISK MANAGEMENT Three primary tools may be employed by investors to minimize their expose to risk: avoid risky projects use insurance and hedging diversification

7. 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.

8. Diversification and Risk

9. Covariance and Correlation

10. 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.

11. Expected Risk and Returns of a Portfolio

12. OPTIMAL PORTFOLIO ALLOCATIONS

13. HISTORICAL RETURNS & RISK

14. HISTORICAL CORRELATIONS (1979-99)

15. ACCOUNTING FOR RISK The investor’s required rate of return is (E(R j )). E(R j ) = R f + RP j where R f is the risk free rate and RP j is a premium for bearing risk.

16. ACCOUNTING FOR RISK Asset Pricing Model to Estimate Risk Sensitivity Analysis