CIO Investment Course

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CIO Investment Course June 2007

• Topic Three
• Portfolio Risk Analysis

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Notion of Tracking Error
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Notion of Tracking Error (cont.)
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Notion of Tracking Error (cont.)

• Generally speaking, portfolios can be separated
  into the following categories by the level of
  their annualized tracking errors
• Passive (i.e., Indexed) TE lt 1.0 (Note TE lt
  0.5 is normal)
• Structured 1.0 lt TE lt 3
• Active TE gt 3 (Note TE gt 5 is normal for
  active managers)

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Index Fund Example VFINX
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ETF Example SPY
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Large Blend Active Manager DGAGX
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Tracking Errors for VFINX, SPY, DGAGX
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Chile AFP Tracking Errors Fondo A(Rolling
12-month historical returns relative to Sistema)
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Chile AFP Tracking Errors Fondo E(Rolling
12-month historical returns relative to Sistema)
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Risk and Expected Return Within a Portfolio

• Portfolio Theory begins with the recognition that
  the total risk and expected return of a portfolio
  are simple extensions of a few basic statistical
  concepts.
• The important insight that emerges is that the
  risk characteristics of a portfolio become
  distinct from those of the portfolios underlying
  assets because of diversification. Consequently,
  investors can only expect compensation for risk
  that they cannot diversify away by holding a
  broad-based portfolio of securities (i.e., the
  systematic risk)
• Expected Return of a Portfolio
• where wi is the percentage investment in the i-th
  asset
• Risk of a Portfolio
• Total Risk (Unsystematic Risk) (Systematic
  Risk)

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Example of Portfolio Diversification Two-Asset
Portfolio

• Consider the risk and return characteristics of
  two stock positions
• Risk and Return of a 50-50 Portfolio
• E(Rp) (0.5)(5) (0.5)(6) 5.50
• and
• sp (.25)(64) (.25)(100) 2(.5)(.5)(8)(10)(.4
  )1/2 7.55
• Note that the risk of the portfolio is lower than
  that of either of the individual securities

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Another Two-Asset Class Example
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Example of a Three-Asset Portfolio
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Diversification and Portfolio Size Graphical
Interpretation
Total Risk
0.40
0.20
Systematic Risk
Portfolio Size
40
1
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Advanced Portfolio Risk Calculations
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Advanced Portfolio Risk Calculations (cont.)
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Advanced Portfolio Risk Calculations (cont.)
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Advanced Portfolio Risk Calculations (cont.)
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Example of Marginal Risk Contribution Calculations
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Dollar Allocation vs. Marginal Risk
ContributionUTIMCO - March 2007
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Fidelity Investments PRISM Risk-Tracking System
Chilean Pension System March 2004
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Chilean Sistema Risk Tracking Example (cont.)
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Chilean Sistema Risk Tracking Example (cont.)
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Notion of Downside Risk Measures

• As we have seen, the variance statistic is a
  symmetric measure of risk in that it treats a
  given deviation from the expected outcome the
  same regardless of whether that deviation is
  positive of negative.
• We know, however, that risk-averse investors have
  asymmetric profiles they consider only the
  possibility of achieving outcomes that deliver
  less than was originally expected as being truly
  risky. Thus, using variance (or, equivalently,
  standard deviation) to portray investor risk
  attitudes may lead to incorrect portfolio
  analysis whenever the underlying return
  distribution is not symmetric.
• Asymmetric return distributions commonly occur
  when portfolios contain either explicit or
  implicit derivative positions (e.g., using a put
  option to provide portfolio insurance).
• Consequently, a more appropriate way of capturing
  statistically the subtleties of this dimension
  must look beyond the variance measure.

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Notion of Downside Risk Measures (cont.)

• We will consider two alternative risk measures
  (i) Semi-Variance, and (ii) Lower Partial Moments
• Semi-Variance The semi-variance is calculated
  in the same manner as the variance statistic, but
  only the potential returns falling below the
  expected return are used
• Lower Partial Moment The lower partial moment
  is the sum of the weighted deviations of each
  potential outcome from a pre-specified threshold
  level (t), where each deviation is then raised to
  some exponential power (n). Like the
  semi-variance, lower partial moments are
  asymmetric risk measures in that they consider
  information for only a portion of the return
  distribution. The formula for this calculation
  is given by

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Example of Downside Risk Measures
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Example of Downside Risk Measures (cont.)
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Example of Downside Risk Measures (cont.)
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Example of Downside Risk Measures (cont.)