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Asset Management

Asset Management. Lecture Two. I will more or less follow the structure of the textbook “Investments” with a few exceptions. These parts of the textbook are omitted: Part IV (fixed income) Part V (security analysis) Part VI (options and other derivatives). Outline for today.

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Asset Management

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  1. Asset Management Lecture Two

  2. I will more or less follow the structure of the textbook “Investments” with a few exceptions. • These parts of the textbook are omitted: • Part IV (fixed income) • Part V (security analysis) • Part VI (options and other derivatives)

  3. Outline for today • Risk aversion and utility • Estimating risk aversion • Markowitz portfolio selection model • How to find the efficient frontier and the optimal risky portfolio with Excel

  4. Risk Aversion and utility values • Risk aversion: a risk-averse investor will reject a fair gamble. • Utility value • Risk-neutral investors • A=0 • Risk lover • A<0

  5. Risk Aversion and utility values A=4 E(r) U=1 A=2 U=0.5 σ

  6. Risk Aversion and utility values

  7. Risk Aversion and utility values Certainty equivalent rate

  8. Estimating A • Consider an insurance policy with a cost of v: • Expected return • Variance • Utility • -v=U

  9. risk premium v

  10. Two-Security Portfolios with Various Correlations • Relationship depends on correlation coefficient -1.0 <r< +1.0 • If r = +1.0, no risk reduction is possible • If r = –1.0, complete risk reduction is possible 100% Stock B return  = -1.0  = 1.0  = 0.2 100% Stock A 

  11. Markowitz portfolio selection model return efficient frontier minimum variance portfolio Individual Assets P

  12. Markowitz portfolio selection model

  13. Markowitz portfolio selection model Indifference curve Capital market line return Separation property: the portfolio manager offers the same risky portfolio to all investors Market portfolio rf  Investors allocate their money across the risk-free asset and the market portfolio Investors borrow at the risk-free rate and invest in the market portfolio

  14. Markowitz portfolio selection model • Sharpe ratio • Excess return / SD of excess return • Reward to volatility • The tangency portfolio has the highest Sharpe ratio

  15. Markowitz portfolio selection model Indifference curve Capital market line return rf 

  16. Markowitz portfolio selection model • How to find the efficient frontier and the optimal portfolio? • Find E(r) for each asset • Find SD for each asset • Find covariance between each pair of assets • As a starting point, assume a weight for each asset • Use Excel Solver as an optimizer

  17. Individual Homework • Construct a portfolio of assets with 5 financial assets • Explain briefly why you choose these assets for your portfolio. • Use recent 36 monthly data to calculate E(r), var(r), and cov. • Report for your minimum variance portfolio and the tangency portfolio: • the weights of assets • expected return, SD and the Sharpe ratio • Repeat the exercise with no-short-sale constraint. • Due on Feb 13. Sent your excel file to Sérgio Gaspar <sergio.gaspar@fe.unl.pt>

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