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Asset Management

Asset Management. Lecture 12. Outline of today’s lecture. Dollar- and Time-Weighted Returns Universe comparison Adjusting Returns for Risk Sharpe measure Treynor measure Jensen measure Information ratio M 2 measure The choice of measure. Text Example of Multi-period Returns. 1. 2.

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Asset Management

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  1. Asset Management Lecture 12

  2. Outline of today’s lecture • Dollar- and Time-Weighted Returns • Universe comparison • Adjusting Returns for Risk • Sharpe measure • Treynor measure • Jensen measure • Information ratio • M2 measure • The choice of measure

  3. Text Example of Multi-period Returns 1 2 0 Stock pays a dividend of $2 per share Stock is sold at $54 per share Purchase 1 share at $53 Stock pays a dividend of $2 per share Purchase 1 share at $50

  4. Text Example of Multi-period Returns Internal Rate of Return: rG = [ (1.1) (1.0566) ]1/2 - 1 = 7.83% • Internal rate of return considering the cash flow from or to investment; • Returns are weighted by the amount invested in each stock • Equal weighting

  5. Universe comparison Comparison with other managers of similar investment style May be misleading Portfolio characteristics are not comparable Survivorship bias Universe comparison 95th percentile The median 5th percentile

  6. 1) Sharpe Index Risk Adjusted Performance: Sharpe • rp = Average return on the portfolio • rf = Average risk free rate = Standard deviation of portfolio return p 

  7. 2) Treynor Measure Risk Adjusted Performance: Treynor • rp = Average return on the portfolio • rf = Average risk free rate • ßp = Weighted average for portfolio

  8. Risk Adjusted Performance: Jensen 3) Jensen’s Measure  = Alpha for the portfolio p rp = Average return on the portfolio ßp= Portfolio Beta rf = Average risk free rate rm = Average return on market index portfolio

  9. Risk Adjusted Performance: Information Ratio Information Ratio ap / s(ep) Information Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification

  10. Risk Adjusted Performance: M2 • rp* = return of a hypothetical portfolio made up of T-bills and the managed portfolio that has the same standard deviation as the market index portfolio • rM = return of the market index portfolio

  11. Risk Adjusted Performance ap / s(ep)

  12. It depends on investment assumptions If the portfolio represents the entire investment for an individual compared to the market (passive strategy) Sharpe Index or M2 If the portfolio is one of many portfolios combined in a large fund There exist many alternative portfolios Jensen  The Treynor measure: more complete because it adjusts for risk The choice of measure

  13. Example: comparing two risky portfolios Jensen’s measure: Portfolio Q is preferred.

  14. Example: comparing two risky portfolios Nonsystematic risk will be diversified away in a well diversified fund.

  15. Example: comparing two risky portfolios Suppose that you form a portfolio with risk-free assets and portfolio P (or Q), then all possible portfolios lie along the TP line (or TQ line) Treynor measure: TP = 11% / 0.9 = 12.2% TQ = 19% / 1.6 = 11.88%

  16. An example of actual performance measurement

  17. An example of actual performance measurement • Which portfolio to choose? • If the portfolio stands for the entire investment fund • If the portfolio is only a subportfolio of a larger fund • If this is an active portfolio to be mixed with the index

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