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Asset Management

In this lecture, we will explore key concepts in asset management, focusing on risk aversion, utility, and the Markowitz portfolio selection model. We will examine how to determine an investor's risk tolerance and the effect of risk on utility values. The session will also cover constructing efficient portfolios using Excel, including calculating expected returns, variance, and correlations among assets. Students will have the opportunity to apply these principles by creating their own portfolios with a set of financial assets.

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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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