1. Qdai for FENUL Finanças October 31

2. Qdai for FENUL Topics covered  Expected return  Variance, standard deviation  Covariance  Correlation  Portfolio: return and risk

3. Qdai for FENUL Previously  NPV: find appropriate discount rate  The discount rate is related to the risk level of the project  Measure the risk level with standard deviation.  This class: the relationship between risk and return.

4. Qdai for FENUL Individual securities  Expected return: The return that an individual expects a stock to earn over the next period.

5. Qdai for FENUL Individual securities  Variance and Standard Deviation: the volatility of a stock’s return  Covariance and Correlation: the interrelationship between two securities

6. Qdai for FENUL Expected return and Variance Superteck returns R AT Slowpoke Returns R BT Depression-20%5% Recession10%20% Normal30%-12% Boom50%9%

7. Qdai for FENUL Covariance and Correlation Superteck R AT Dev.Slowpoke R BT Dev.Product of deviations Depression -20%5% Recession 10%20% Normal 30%-12% Boom 50%9% Expected return Variance SD Covariance Correlation

8. Qdai for FENUL Portfolio: expected return  Expected return of a portfolio: the weighted average of the expected returns on the individual securities  Example. R A =17.5% R B =5.5% Expected return on portfolio =  If invest $60 in A and $40 in B, then Expected return on portfolio =

9. Qdai for FENUL Portfolio: variance  Variance of a portofolio Var(portfolio)=

10. Qdai for FENUL Portfolio: variance  The variance of a portofolio depends on  For given variances of securities, a positive relationship (covariance) the variance of the portfolio  A negative relationship (covariance) the portfolio variance.

11. Qdai for FENUL Portfolio: variance Example: X A =60%, X B =40%, = 0.066875, = 0.013225, Cov (A,B)=-0.004875

12. Qdai for FENUL Portoflio: variance  The matrix approach AB A B

13. Qdai for FENUL Portfolio: Standard Deviation  Standard deviation of a portfolio = SD(portfolio)  In the previous example, var(portfolio)=0.023851  SD(portfolio) =

14. Qdai for FENUL 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