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V0 (1+GAR)n W HICH METHOD SHOULD BE USED?
In order to generate unbiased outcomes, AAR CCR GAR DR In annual reports or prospectus issued by a managed fund, it is common to find the historical performance in
the form of 3, 5, or 7 years ago, and the geometric average annual return of the fund achieved over the
To look at the historical performance of managed funds, we look at risk adjusted measures: Sharpe index
Appraisal ratio P ERFORMANCE MEASURES
T HE SHARPE (REWARD TO VARIABILITY) INDEX ̅̅̅
The Sharpe index measures the average excess return per unit of total risk.
The Sharpe index of a portfolio is the slope of the capital allocation line that shows the risk return
combinations of a new set of portfolios formed by combining the portfolio and the risk free asset. Since the
Sharpe index is a measure of risk-adjusted return, between 2 portfolios, the one with the larger index is
preferred. 2 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 According to the CAPM, the market portfolio offers the largest Sharpe index, and the CML is the new efficient
frontier so that no portfolio is expected to sit above the CML. Fund managers are said to have beaten the
market if their portfolios achieve a larger Sharpe index than the market portfolio.
The Sharpe index uses the standard deviation of returns (composed of both systematic and unsystematic risk)
to measure risks, which means that it penalizes portfolios that are not well diversified. T HE TREYNOR INDEX ̅̅̅
The Treynor index measures the average excess return per unit of systematic risk.
The Treynor index of a portfolio is the slope of the line that joins the portfolio and the risk free asset. If the
market index is representative of the market portfolio, then the Treynor index is used to test if the portfolio’s
slope is higher than the slope of the SML. If the Treynor index of the portfolio is higher than that of the SML,
the point will lie above the SML. As CAPM assumes that all assets are priced as equilibrium, this reflects the
fund manager’s ability to identify and invest in underpriced assets before mispricing is corrected.
The Treynor index measures risk using beta (systematic risk). Portfolio held by in...
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