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Asset Management Lecture 12

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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

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Text Example of Multi-period Returns 0 12 Purchase 1 share at $50 Purchase 1 share at $53 Stock pays a dividend of $2 per share Stock is sold at $54 per share

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Text Example of Multi-period Returns Dollar-Weighted ReturnTime-Weighted Return Internal Rate of Return: r G = [ (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

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

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1) Sharpe Index r p = Average return on the portfolio r f = Average risk free rate p = Standard deviation of portfolio return Risk Adjusted Performance: Sharpe

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2) Treynor Measure r p = Average return on the portfolio r f = Average risk free rate ß p = Weighted average for portfolio Risk Adjusted Performance: Treynor

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Risk Adjusted Performance: Jensen 3) Jensen’s Measure p = Alpha for the portfolio r p = Average return on the portfolio ß p = Portfolio Beta r f = Average risk free rate r m = Average return on market index portfolio

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Risk Adjusted Performance: Information Ratio Information Ratio Information Ratio divides the alpha of the portfolio by the nonsystematic risk p / (e p ) Nonsystematic risk could, in theory, be eliminated by diversification

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Risk Adjusted Performance: M 2 r p* = 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 r M = return of the market index portfolio

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Risk Adjusted Performance p / (e p ) Sharpe Treynor Jensen Information ratio M2M2

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It depends on investment assumptions If the portfolio represents the entire investment for an individual compared to the market (passive strategy) Sharpe Index or M 2 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

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

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

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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 T P line (or T Q line) Treynor measure: TP = 11% / 0.9 = 12.2% TQ = 19% / 1.6 = 11.88%

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An example of actual performance measurement

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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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