The most important and widely used measures of performance are:
Ø The Treynor Measure
Ø The Sharpe Measure
Ø Jenson Model
Ø Fama Model

**PERFORMANCE EVALUATION**

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:

Ø
The Treynor Measure

Ø
The Sharpe Measure

Ø
Jenson Model

Ø
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),b 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.

**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.

**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.

**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.

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.

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Business Science : Security Analysis and Portfolio Management : Portfolio Analysis : Performance Evaluation |

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