Performance Measures Of Mutual Funds
Mutual Fund industry today, with about 34 players and more than five hundred schemes, is one of the most preferred investment avenues in India. However, with a plethora of schemes to choose from, the retail investor faces problems in selecting funds. Factors such as investment strategy and management style are qualitative, but the funds record is an important indicator too. Though past performance alone can not be indicative of future performance, it is, frankly, the only quantitative way to judge how good a fund is at present. Therefore, there is a need to correctly assess the past performance of different mutual funds.
Worldwide, good mutual fund companies over are known by their AMCs and this fame is directly linked to their superior stock selection skills. For mutual funds to grow, AMCs must be held accountable for their selection of stocks. In other words, there must be some performance indicator that will reveal the quality of stock selection of various AMCs.
Return alone should not be considered as the basis of measurement of the performance of a mutual fund scheme, it should also include the risk taken by the fund manager because different funds will have different levels of risk attached to them. Risk associated with a fund, in a general, can be defined as variability or fluctuations in the returns generated by it. The higher the fluctuations in the returns of a fund during a given period, higher will be the risk associated with it. These fluctuations in the returns generated by a fund are resultant of two guiding forces. First, general market fluctuations, which affect all the securities present in the market, called market risk or systematic risk and second, fluctuations due to specific securities present in the portfolio of the fund, called unsystematic risk. The Total Risk of a given fund is sum of these two and is measured in terms of standard deviation of returns of the fund. Systematic risk, on the other hand, is measured in terms of Beta, which represents fluctuations in the NAV of the fund vis--vis market. The more responsive the NAV of a mutual fund is to the changes in the market; higher will be its beta. Beta is calculated by relating the returns on a mutual fund with the returns in the market. While unsystematic risk can be diversified through investments in a number of instruments, systematic risk can not. By using the risk return relationship, we try to assess the competitive strength of the mutual funds vis--vis one another in a better way.
In order to determine the risk-adjusted returns of investment portfolios, several eminent authors have worked since 1960s to develop composite performance indices to evaluate a portfolio by comparing alternative portfolios within a particular risk class. The most important and widely used measures of performance are:
The Treynor Measure
The Sharpe Measure
Jenson Model
Fama Model
The Treynor Measure
Developed by Jack Treynor, this performance measure evaluates funds on the basis of Treynor's Index. This Index is a ratio of return generated by the fund over and above risk free rate of return (generally taken to be the return on securities backed by the government, as there is no credit risk associated), during a given period and systematic risk associated with it (beta). Symbolically, it can be represented as:
Treynor's Index (Ti) = (Ri - Rf)/Bi.
Where, Ri represents return on fund, Rf is risk free rate of return and Bi is beta of the fund.
All risk-averse investors would like to maximize this value. While a high and positive Treynor's Index shows a superior risk-adjusted performance of a fund, a low and negative Treynor's Index is an indication of unfavorable performance.
The Sharpe Measure
In this model, performance of a fund is evaluated on the basis of Sharpe Ratio, which is a ratio of returns generated by the fund over and above risk free rate of return and the total risk associated with it. According to Sharpe, it is the total risk of the fund that the investors are concerned about. So, the model evaluates funds on the basis of reward per unit of total risk. Symbolically, it can be written as:
Sharpe Index (Si) = (Ri - Rf)/Si
Where, Si is standard deviation of the fund.
While a high and positive Sharpe Ratio shows a superior risk-adjusted performance of a fund, a low and negative Sharpe Ratio is an indication of unfavorable performance.
Comparison of Sharpe and Treynor
Sharpe and Treynor measures are similar in a way, since they both divide the risk premium by a numerical risk measure. The total risk is appropriate when we are evaluating the risk return relationship for well-diversified portfolios. On the other hand, the systematic risk is the relevant measure of risk when we are evaluating less than fully diversified portfolios or individual stocks. For a well-diversified portfolio the total risk is equal to systematic risk. Rankings based on total risk (Sharpe measure) and systematic risk (Treynor measure) should be identical for a well-diversified portfolio, as the total risk is reduced to systematic risk. Therefore, a poorly diversified fund that ranks higher on Treynor measure, compared with another fund that is highly diversified, will rank lower on Sharpe Measure.
Jenson Model
Jenson's model proposes another risk adjusted performance measure. This measure was developed by Michael Jenson and is sometimes referred to as the Differential Return Method. This measure involves evaluation of the returns that the fund has generated vs. the returns actually expected out of the fund given the level of its systematic risk. The surplus between the two returns is called Alpha, which measures the performance of a fund compared with the actual returns over the period. Required return of a fund at a given level of risk (Bi) can be calculated as:
Ri = Rf + Bi (Rm - Rf)
Where, Rm is average market return during the given period. After calculating it, alpha can be obtained by subtracting required return from the actual return of the fund.
Higher alpha represents superior performance of the fund and vice versa. Limitation of this model is that it considers only systematic risk not the entire risk associated with the fund and an ordinary investor can not mitigate unsystematic risk, as his knowledge of market is primitive.
Fama Model
The Eugene Fama model is an extension of Jenson model. This model compares the performance, measured in terms of returns, of a fund with the required return commensurate with the total risk associated with it. The difference between these two is taken as a measure of the performance of the fund and is called net selectivity.
The net selectivity represents the stock selection skill of the fund manager, as it is the excess return over and above the return required to compensate for the total risk taken by the fund manager. Higher value of which indicates that fund manager has earned returns well above the return commensurate with the level of risk taken by him.
Required return can be calculated as: Ri = Rf + Si/Sm*(Rm - Rf)
Where, Sm is standard deviation of market returns. The net selectivity is then calculated by subtracting this required return from the actual return of the fund.
Among the above performance measures, two models namely, Treynor measure and Jenson model use systematic risk based on the premise that the unsystematic risk is diversifiable. These models are suitable for large investors like institutional investors with high risk taking capacities as they do not face paucity of funds and can invest in a number of options to dilute some risks. For them, a portfolio can be spread across a number of stocks and sectors. However, Sharpe measure and Fama model that consider the entire risk associated with fund are suitable for small investors, as the ordinary investor lacks the necessary skill and resources to diversified. Moreover, the selection of the fund on the basis of superior stock selection ability of the fund manager will also help in safeguarding the money invested to a great extent. The investment in funds that have generated big returns at higher levels of risks leaves the money all the more prone to risks of all kinds that may exceed the individual investors' risk appetite.
Source: Mutualfundsindia Research Team
Mutual Fund industry today, with about 34 players and more than five hundred schemes, is one of the most preferred investment avenues in India. However, with a plethora of schemes to choose from, the retail investor faces problems in selecting funds. Factors such as investment strategy and management style are qualitative, but the funds record is an important indicator too. Though past performance alone can not be indicative of future performance, it is, frankly, the only quantitative way to judge how good a fund is at present. Therefore, there is a need to correctly assess the past performance of different mutual funds.
Worldwide, good mutual fund companies over are known by their AMCs and this fame is directly linked to their superior stock selection skills. For mutual funds to grow, AMCs must be held accountable for their selection of stocks. In other words, there must be some performance indicator that will reveal the quality of stock selection of various AMCs.
Return alone should not be considered as the basis of measurement of the performance of a mutual fund scheme, it should also include the risk taken by the fund manager because different funds will have different levels of risk attached to them. Risk associated with a fund, in a general, can be defined as variability or fluctuations in the returns generated by it. The higher the fluctuations in the returns of a fund during a given period, higher will be the risk associated with it. These fluctuations in the returns generated by a fund are resultant of two guiding forces. First, general market fluctuations, which affect all the securities present in the market, called market risk or systematic risk and second, fluctuations due to specific securities present in the portfolio of the fund, called unsystematic risk. The Total Risk of a given fund is sum of these two and is measured in terms of standard deviation of returns of the fund. Systematic risk, on the other hand, is measured in terms of Beta, which represents fluctuations in the NAV of the fund vis--vis market. The more responsive the NAV of a mutual fund is to the changes in the market; higher will be its beta. Beta is calculated by relating the returns on a mutual fund with the returns in the market. While unsystematic risk can be diversified through investments in a number of instruments, systematic risk can not. By using the risk return relationship, we try to assess the competitive strength of the mutual funds vis--vis one another in a better way.
In order to determine the risk-adjusted returns of investment portfolios, several eminent authors have worked since 1960s to develop composite performance indices to evaluate a portfolio by comparing alternative portfolios within a particular risk class. The most important and widely used measures of performance are:
The Treynor Measure
The Sharpe Measure
Jenson Model
Fama Model
The Treynor Measure
Developed by Jack Treynor, this performance measure evaluates funds on the basis of Treynor's Index. This Index is a ratio of return generated by the fund over and above risk free rate of return (generally taken to be the return on securities backed by the government, as there is no credit risk associated), during a given period and systematic risk associated with it (beta). Symbolically, it can be represented as:
Treynor's Index (Ti) = (Ri - Rf)/Bi.
Where, Ri represents return on fund, Rf is risk free rate of return and Bi is beta of the fund.
All risk-averse investors would like to maximize this value. While a high and positive Treynor's Index shows a superior risk-adjusted performance of a fund, a low and negative Treynor's Index is an indication of unfavorable performance.
The Sharpe Measure
In this model, performance of a fund is evaluated on the basis of Sharpe Ratio, which is a ratio of returns generated by the fund over and above risk free rate of return and the total risk associated with it. According to Sharpe, it is the total risk of the fund that the investors are concerned about. So, the model evaluates funds on the basis of reward per unit of total risk. Symbolically, it can be written as:
Sharpe Index (Si) = (Ri - Rf)/Si
Where, Si is standard deviation of the fund.
While a high and positive Sharpe Ratio shows a superior risk-adjusted performance of a fund, a low and negative Sharpe Ratio is an indication of unfavorable performance.
Comparison of Sharpe and Treynor
Sharpe and Treynor measures are similar in a way, since they both divide the risk premium by a numerical risk measure. The total risk is appropriate when we are evaluating the risk return relationship for well-diversified portfolios. On the other hand, the systematic risk is the relevant measure of risk when we are evaluating less than fully diversified portfolios or individual stocks. For a well-diversified portfolio the total risk is equal to systematic risk. Rankings based on total risk (Sharpe measure) and systematic risk (Treynor measure) should be identical for a well-diversified portfolio, as the total risk is reduced to systematic risk. Therefore, a poorly diversified fund that ranks higher on Treynor measure, compared with another fund that is highly diversified, will rank lower on Sharpe Measure.
Jenson Model
Jenson's model proposes another risk adjusted performance measure. This measure was developed by Michael Jenson and is sometimes referred to as the Differential Return Method. This measure involves evaluation of the returns that the fund has generated vs. the returns actually expected out of the fund given the level of its systematic risk. The surplus between the two returns is called Alpha, which measures the performance of a fund compared with the actual returns over the period. Required return of a fund at a given level of risk (Bi) can be calculated as:
Ri = Rf + Bi (Rm - Rf)
Where, Rm is average market return during the given period. After calculating it, alpha can be obtained by subtracting required return from the actual return of the fund.
Higher alpha represents superior performance of the fund and vice versa. Limitation of this model is that it considers only systematic risk not the entire risk associated with the fund and an ordinary investor can not mitigate unsystematic risk, as his knowledge of market is primitive.
Fama Model
The Eugene Fama model is an extension of Jenson model. This model compares the performance, measured in terms of returns, of a fund with the required return commensurate with the total risk associated with it. The difference between these two is taken as a measure of the performance of the fund and is called net selectivity.
The net selectivity represents the stock selection skill of the fund manager, as it is the excess return over and above the return required to compensate for the total risk taken by the fund manager. Higher value of which indicates that fund manager has earned returns well above the return commensurate with the level of risk taken by him.
Required return can be calculated as: Ri = Rf + Si/Sm*(Rm - Rf)
Where, Sm is standard deviation of market returns. The net selectivity is then calculated by subtracting this required return from the actual return of the fund.
Among the above performance measures, two models namely, Treynor measure and Jenson model use systematic risk based on the premise that the unsystematic risk is diversifiable. These models are suitable for large investors like institutional investors with high risk taking capacities as they do not face paucity of funds and can invest in a number of options to dilute some risks. For them, a portfolio can be spread across a number of stocks and sectors. However, Sharpe measure and Fama model that consider the entire risk associated with fund are suitable for small investors, as the ordinary investor lacks the necessary skill and resources to diversified. Moreover, the selection of the fund on the basis of superior stock selection ability of the fund manager will also help in safeguarding the money invested to a great extent. The investment in funds that have generated big returns at higher levels of risks leaves the money all the more prone to risks of all kinds that may exceed the individual investors' risk appetite.
Source: Mutualfundsindia Research Team
