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ADMN 3116: Financial Management 1 Lecture 7: P ortfolio selection

ADMN 3116: Financial Management 1 Lecture 7: P ortfolio selection. Anton Miglo Fall 2014. 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. Diversification.

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ADMN 3116: Financial Management 1 Lecture 7: P ortfolio selection

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  1. ADMN 3116: Financial Management 1 • Lecture 7: Portfolio selection Anton Miglo Fall 2014

  2. 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. Diversification

  4. Investment mistakes • “Put all eggs in one basket” • 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) • Many investors think that diversification is always associated with lower risk but also with lower return

  5. Correlation Ontario Quebec

  6. Asset B Asset C=1/2A+1/2B Asset A 30 30 30 15 15 15 0 0 0 -15 -15 -15 Portfolio of two positively correlated assets

  7. Asset A Asset B Asset C=1/2A+1/2B 40 15 0 0 0 -10 -10 Portfolio of two negatively correlated assets 40 40 15 15 -10

  8. Recall: portfolios For a portfolio of two assets, A and B, the variance of the return on the portfolio is: Where: xA= portfolio weight of asset A xB = portfolio weight of asset B such that xA + xB = 1. (Important: Recall Correlation Definition!)

  9. 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. Efficient Investors prefer Frontier Portfolios of other Portfolios of assets Asset 1 and Asset 2 Minimum-Variance Portfolio Efficient Portfolios with Multiple Assets E[r] Asset 1 Asset 2 s 0

  11. Excel • Solver

  12. Sharpe-Optimal Portfolios

  13. 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. Example: Using Excel to Solve for the Sharpe-Optimal Portfolio Suppose we enter the data (highlighted in yellow) into a spreadsheet. We “guess” that Xs = 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. 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….

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