Hence it implicitly assumes a completely diversified

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Hence, it implicitly assumes a completely diversified portfolio. Portfolios with identical systematic risk, but different total risk, will have the same Treynor ratio! Higher idiosyncratic risk should not matter in a diversified portfolio and hence is not reflected in the Treynor measure. A portfolio negative Beta will have a negative Treynor measure. Also known as the Treynor Ratio . 9
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Albert Lee Chun Portfolio Management T-Lines 10 17-10 Q has higher alpha, but P has steeper T-line. P is the better portfolio.
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Albert Lee Chun Portfolio Management Sharpe Portfolio Performance Measure 11
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Albert Lee Chun Portfolio Management Sharpe Measure 12 Similar to the Treynor measure, but uses the total risk of the portfolio, not just the systematic risk. The Sharpe Ratio is given by The larger the measure the better, as the portfolio earned a higher excess return per unit of total risk . p f p p r R = S
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Albert Lee Chun Portfolio Management Sharpe Measure It adjusts returns for total portfolio risk, as opposed to only systematic risk as in the Treynor Measure. Thus, an implicit assumption of the Sharpe ratio is that the portfolio is not fully diversified, nor will it be combined with other diversified portfolios. It is relevant for performance evaluation when comparing mutually exclusive portfolios. Sharpe originally called it the "reward-to- variability" ratio, before others started calling it the Sharpe Ratio . 13
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Albert Lee Chun Portfolio Management SML vs. CML Treynor’s measure uses Beta and hence examines portfolio return performance in relation to the SML . Sharpe’s measure uses total risk and hence examines portfolio return performance in relation to the CML . For a totally diversified portfolio, both measures give equal rankings. If it is not a diversified portfolio, the Sharpe measure could give lower rankings than the Treynor measure. Thus, the Sharpe measure evaluates the portfolio manager in terms of both return performance and diversification. 14
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Price of Risk Both the Treynor and Sharp measures, indicate the risk premium per unit of risk, either systematic risk (Treynor) or total risk (Sharpe). They measure the price of risk in units of excess returns per each unit of risk (measured either by beta or the standard deviation of the portfolio). 15 T = r R p p f p p p f p S r R
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Albert Lee Chun Portfolio Management Jensen Portfolio Performance Measure 16
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Albert Lee Chun Portfolio Management Jensen’s Alpha 17 Alpha is a risk-adjusted measure of superior performance This measure adjusts for the systematic risk of the portfolio. Positive alpha signals superior risk-adjusted returns, and that the manager is good at selecting stocks or predicting market turning points. Unlike the Sharpe Ratio, Jensen’s method does not consider the ability of the manager to diversify, as it is only accounts for systematic risk. t p t f p p r , , t M, t f, t p, R r R
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Multifactor Jensen’s Measure Measure can be extended to a multi-factor setting, for example: 18 t p p p t f p p HML SML r , 3 2 , t M, 1 t f, t p, R r R
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Albert Lee Chun Portfolio Management Information Ratio 19
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  • Winter '15
  • Charles
  • Modern portfolio theory, Albert Lee Chun

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