Asset Management

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

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Risk Aversion and utility values

• Risk aversion a risk-averse investor will reject
  a fair gamble.
• Utility value
• Risk-neutral investors
• A0
• Risk lover
• Alt0

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Risk Aversion and utility values
A4
E(r)
U1
A2
U0.5
s
6
Risk Aversion and utility values
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Risk Aversion and utility values
Certainty equivalent rate
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Estimating A

• Consider an insurance policy with a cost of v
• Expected return
• Variance
• Utility
• -vU

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risk premium v
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Two-Security Portfolios with Various Correlations
100 Stock B
return
? -1.0
? 1.0
? 0.2
100 Stock A
?

• Relationship depends on correlation coefficient
• -1.0 lt r lt 1.0
• If r 1.0, no risk reduction is possible
• If r 1.0, complete risk reduction is possible

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Markowitz portfolio selection model
return
efficient frontier
minimum variance portfolio
Individual Assets
?P
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Markowitz portfolio selection model
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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
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Markowitz portfolio selection model

• Sharpe ratio
• Excess return / SD of excess return
• Reward to volatility
• The tangency portfolio has the highest Sharpe
  ratio

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Markowitz portfolio selection model

Indifference curve
Capital market line
return
rf
?
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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 ltsergio.gaspar_at_fe.unl.ptgt