Chapter 17RISK AND DIVERSIFICATION

• What is risk aversion, and why are investors, as a group, risk averse?

• What are the general investment implications of risk aversion?

• Why is standard deviation a good measure of risk, and how does an investor compute standard deviations for both individual securities and portfolios?

RISK AND DIVERSIFICATION-Cont.

• What is the impact of security correlations impact portfolio risk?

• What are the benefits of diversification, and how investors achieve them?

• What is the meaning of efficient diversification and modern portfolio theory

What is risk aversion?

• Risk aversion

• Risk aversion and expected returns

• Relative risk aversion and expected returns

Figure 17.1 – Distribution of Yearly Returns of Stocks and T-Bills, 1926-2002

Figure 17.2 – Risk Aversion and Expected Returns

Measuring risk and return: Individual securities

• Measuring returns– Ex-ante or expected returns– Ex-post or historical returns

• Measuring risk– Range– Number of negative outcomes– Standard deviation (or variance)

Calculating standard deviations and security selection

• Ex-ante or expected risk

• Ex-post or historical risk

• Security selection

Figure 17.3 – Risk/Return Graph for Security Selection

Portfolio risk and return

• Portfolio return.– Ex-ante portfolio return, ERp

– Ex-post portfolio return, Mp

Standard deviation of atwo-security portfolio

• Covariance (COV(A,B))

• Correlation coefficient CORR(A,B)

• CORR(A,B) = COV(A,B)/ (SDA)(SDB)

• Standard deviation for a two-security portfolio

• Correlation and portfolio standard deviation

Figure 17.4 – Two-Security Portfolio Combinations with Various Correlations

Investment opportunity set for two-security portfolio

• Minimum variance portfolio

• Standard Deviation of an N-Security Portfolio.

Figure 17.5 – Two-Security Portfolio Combinations of Securities A and E

Diversification

• Diversification across securities• Two types of portfolio risk• Mathematical effects of diversification• Diversification across time• Efficient diversification• How to find an efficient frontier

• Implications for Investors

Figure 17.6 – Example of Diversification Across Securities

Figure 17.7 – Efficient Frontier for Three Stocks

Figure 17.8 – Full-Market Efficient Frontier