# Ratios to Evaluate Mutual Funds Performance

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Definition of the parameters for evaluation: Sharpe Ratio: It is calculated by subtracting the risk-free rate of return (return on government securities) from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns. {draw:line} {draw:frame} {draw:frame} Sharpe Ratio = Where rp = Expected portfolio rate of return rf = Risk free rate of return σp = Portfolio standard deviation Since standard deviation is a measure of the associated risk (systematic + unsystematic) of a portfolio, it helps to evaluate whether the portfolio's returns are due to smart investment decisions or a result of excess risk. Thus, the greater the Sharpe ratio of a portfolio better has been its risk-adjusted performance. {draw:frame} {draw:frame} {draw:line} Treynor Ratio: it measures returns earned in excess of that which could have been earned on a risk-less investment per each unit of market risk. Treynor Ratio = Where rp = Expected portfolio rate of return rf = Risk free rate of return β = beta of the portfolio Thus, the Treynor ratio is a risk-adjusted measure of return based on systematic risk. The difference between the Sharpe ratio and the Treynor ratio is the use of beta instead of standard deviation as the measurement of risk / volatility. Point to Remember: A completely or totally diversified portfolio of securities is the one which reduces its unsystematic risk (diversifiable risk) to zero. Thus, for a totally diversified portfolio, the total risk associated with the portfolio is just the systematic risk or the undiversified risk. Total risk of diversified portfolio = Systematic Risk ( Beta) Therefore for well diversified portfolio, Sharpe Ratio will be equal to the Treynor ratio. Fama: It measures the return given by the fund and the required returns to commensurate the risk associated with it. The difference between the returns is called ‘Net Selectivity’ and is a measure of the performance of the fund and the

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