# Asset Management Lecture 12. Outline of today’s lecture Dollar- and Time-Weighted Returns Universe comparison Adjusting Returns for Risk Sharpe measure.

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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 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

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

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

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

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

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 

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

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

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

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

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

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

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%

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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