1. F303 Intermediate Investments1 Inside the Optimal Risky Portfolio New Terms: –Co-variance –Correlation –Diversification Diversification – the process of adding assets to a portfolio in order to reduce the risk of the overall portfolio

2. F303 Intermediate Investments2 Types of Risk Systematic Risk – This risk is part of the economic system (it is systemic!). It is non- diversifiable and is a/k/a market risk Non-Systematic Risk is firm specific. It can be diversified away How can we tell if adding assets to a portfolio will reduce the overall risk of the portfolio? –Covariance –Correlation

3. F303 Intermediate Investments3 Diversification and Risk: An Example Two stock funds –Avers: A fund made up of Pizza Companies –Zagrebs: A fund made up of beef producing companies –What is the expected return on each fund?

4. F303 Intermediate Investments4 Diversification and Risk: An Example What is the individual deviation, variance and standard deviation for each fund?

5. F303 Intermediate Investments5 Diversification and Risk: An Example What would happen if these two assets were combined in a single portfolio? What is the Variance? What is the Standard Deviation?

6. F303 Intermediate Investments6 Diversification and Risk: An Example How do we measure the Covariance and Correlation Coefficient? The Covariance = the product of the deviations:

7. F303 Intermediate Investments7 Diversification and Risk: An Example Correlation Coefficient = Covariance SD A * SD Z If the Correlation Coefficient is < 1, the addition of the asset has diversification benefits, regardless of the other risk/return characteristics of the asset!

8. F303 Intermediate Investments8 Three Rules for Portfolios Made Up of Two Risky Assets! 1.The rate of return on the portfolio is a weighted average of the returns on the component securities, with the investment proportions as weights r p = w a r a + w z r z 2.The same holds true for the Expected rate of return R p = w a E(r a ) + w z E(r z ) 3.The variance of the rate of return on the two risky asset portfolio is V = (w a SD a ) 2 + (w z SD z ) 2 +2(w a SD a )(W z SD z )Corr az