1. QDai for FEUNL Finanças November 2

2. QDai for FEUNL Topics covered  Minimum variance portfolio  Efficient frontier  Systematic risk vs. Unsystematic risk  Seperation principle of investment  Security market line

3. QDai for FEUNL Previously  Single stock Expected return Variance  Portfolio Expected Variance Correlation

4. QDai for FEUNL Portfolio: diversification effect Superteck R A Slowpoke R B Portfolio with 60% in R A and 40% in R B Expected return 17.5%5.5%12.7% SD0.25860.11500.1544 Weighted average SD= 0.6*0.2586+0.4*0.1150=0.2012

5. QDai for FEUNL Portfolio: diversification effect  Variance of portfolio = =0.36*0.066875 +2*0.6*0.4*(-0.004875) +0.16*0.013225 =0.023851 OR =

6. QDai for FEUNL Portfolio: diversification effect  Conclusion:

7. QDai for FEUNL The opportunity set of two assets 100% Stock A 100% Stock B

8. QDai for FEUNL Two-Security Portfolios with Various Correlations 100% Stock A return  100% Stock B  Relationship depends on correlation coefficient

9. QDai for FEUNL The Efficient Set for Many Securities The opportunity set of risk-return combinations of various portfolios. return PP Individual Assets

10. QDai for FEUNL Portfolio Risk as a Function of the Number of Stocks in the Portfolio n  Diversification can not eliminate all of the risk of individual securities. Portfolio risk

11. QDai for FEUNL Risk of a security  Total risk of an individual security =  Systematic risk:  Unsystematic risk:  Why do we care about risk diversification?

12. QDai for FEUNL Risk aversion  Example: Suppose you have a saving of €2,000. There is a gamble with a 50% chance of doubling your money, and a 50% chance that you will lose all.

13. QDai for FEUNL Optimal Risky Portfolio with a Risk-Free Asset In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills rfrf return 

14. QDai for FEUNL Separation Principle  The investor’s investment decision consists of two separate steps

15. QDai for FEUNL Definition of Risk When Investors Hold the Market Portfolio  Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta ()of the security.

16. QDai for FEUNL Security Returns Return on market %

17. QDai for FEUNL Definition of Risk When Investors Hold the Market Portfolio  Beta measures

18. QDai for FEUNL Capital asset pricing model (CAPM)  Expected market return  Expected return of an individual security  The expected return on a security is linearly related to its beta.  The relationship also holds for portfolios.

19. QDai for FEUNL Relationship Between Risk & Expected Return Expected return  )(β F M iF i RRRR  F R 1.0 M R