1. 7- 1 © ADMN 3116, Anton Miglo ADMN 3116: Financial Management 1 Lecture 7: Portfolio selection Anton Miglo Fall 2014

2. 7- 2 © ADMN 3116, Anton Miglo Topics Covered  Efficient Set of Portfolios  Sharpe ratio and optimal portfolio  Optimal portfolio with risk-free asset available  Excel: Solver  Additional readings: ch. 10-11 B

3. 7- 3 © ADMN 3116, Anton Miglo Diversification

4. 7- 4 © ADMN 3116, Anton Miglo Investment mistakes 1.“Put all eggs in one basket” 2.Superfluous or Naive Diversification (Diversification for diversification’s sake) a. Results in difficulty in managing such a large portfolio b. Increased costs (Search and transaction) 3.Many investors think that diversification is always associated with lower risk but also with lower return

5. 7- 5 © ADMN 3116, Anton Miglo Correlation Ontario Quebec

6. 7- 6 © ADMN 3116, Anton Miglo Portfolio of two positively correlated assets Asset A 0 15 30 -15 Asset B 0 15 30 -15 Asset C=1/2A+1/2B 0 15 30 -15

7. 7- 7 © ADMN 3116, Anton Miglo Portfolio of two negatively correlated assets -10 15 40 15 0 -10 Asset A 0 Asset B -10 0 Asset C=1/2A+1/2B

8. 7- 8 © ADMN 3116, Anton Miglo Recall: portfolios  For a portfolio of two assets, A and B, the variance of the return on the portfolio is: Where: x A = portfolio weight of asset A x B = portfolio weight of asset B such that x A + x B = 1. (Important: Recall Correlation Definition!)

9. 7- 9 © ADMN 3116, Anton Miglo The Markowitz Efficient Frontier  The Markowitz Efficient frontier is the set of portfolios with the maximum return for a given risk AND the minimum risk given a return.  For the plot, the upper left-hand boundary is the Markowitz efficient frontier.  All the other possible combinations are inefficient. That is, investors would not hold these portfolios because they could get either  more return for a given level of risk or  less risk for a given level of return.

10. 7- 10 © ADMN 3116, Anton Miglo Efficient Portfolios with Multiple Assets E[r]  0 Asset 1 Asset 2 Portfolios of Asset 1 and Asset 2 Portfolios of other assets Efficient Frontier Minimum-Variance Portfolio Investors prefer

11. 7- 11 © ADMN 3116, Anton Miglo Excel  Solver 11

12. 7- 12 © ADMN 3116, Anton Miglo Sharpe-Optimal Portfolios

13. 7- 13 © ADMN 3116, Anton Miglo Example: Solving for a Sharpe-Optimal Portfolio  From a previous chapter, we know that for a 2-asset portfolio: So, now our job is to choose the weight in asset S that maximizes the Sharpe Ratio. We could use calculus to do this, or we could use Excel.

14. 7- 14 © ADMN 3116, Anton Miglo Example: Using Excel to Solve for the Sharpe-Optimal Portfolio Suppose we enter the data (highlighted in yellow) into a spreadsheet. We “guess” that X s = 0.25 is a “good” portfolio. Using formulas for portfolio return and standard deviation, we compute Expected Return, Standard Deviation, and a Sharpe Ratio:

15. 7- 15 © ADMN 3116, Anton Miglo Example: Using Excel to Solve for the Sharpe-Optimal Portfolio, Cont.  Now, we let Excel solve for the weight in portfolio S that maximizes the Sharpe Ratio.  We use the Solver, found under Tools. Well, the “guess” of 0.25 was a tad low….