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Performance Evaluation of Mutual Fund/ Portfolio
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Standard Deviation
Reports a fund's volatility, which indicates thetendency of the returns to rise or fall drastically in
a short period of time.
Measuring the degree to which the fund
fluctuates in relation to its mean return of a fundover a period of time.
A stable past performance of a fund is not
necessarily a guarantee of future stability.
Compare the fund to another with a similarinvestment strategy and similar returns
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Determines the volatility, or risk, of a fund in
comparison to that of its index or benchmark
A fund with a beta very close to 1 means the
fund's performance closely matches the index or
benchmark
If, for example,
A fund has a beta of 1.03 in relation to the BSE
Sensex, the fund has been moving 3% more thanthe index. Therefore, if the BSE Sensex increased
10%, the fund would be expected to increase
10.30%.
Beta
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R-Squared
R-squared describes the level of associationbetween the fund's volatility and market risk
R-squared values range between 0 and 1
If a fund's beta has an R-squared value that isclose to 1, the beta of the fund should be trusted
R-squared value that is less than 0.5 indicates
that the beta is not particularly useful
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AlphaAlpha = (Fund return-Risk free return) - Funds beta
*(Benchmark return- risk free return)Alpha is the risk-adjusted return on an investment
Alpha is the difference between the returns one wouldexpect from a fund, given its beta, and the return it
actually produces
A positive alpha of 1.0 means the fund hasoutperformed its benchmark index by 1%.
A negative alpha would indicate an underperformanceof 1%.
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AlphaA measure of performance on a risk-adjusted basis. Alphatakes the volatility (price risk) of a mutual fund andcompares its risk-adjusted performance to a benchmarkindex.
The excess return of the fund relative to the return of thebenchmark index is a fund's alpha.
The abnormal rate of return on a security or portfolio in excessof what would be predicted by an equilibrium model like
the capital asset pricing model (CAPM).
If a CAPM analysis estimates that a portfolio should earn 10%based on the risk of the portfolio but the portfolio actuallyearns 15%, the portfolio's alpha would be 5%. This 5% isthe excess return over what was predicted in the CAPM
model.
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The Treynor Measure
This Index is a ratio of return generated by
the fund over and above risk free rate ofreturn 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 or portfolioRf is risk free rate of return
Bi
is beta of the fund.
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Jenson Model This measure involves evaluation of the
returns that the fund has generated vs. thereturns actually expected out of the fundgiven the level of its systematic risk.
Required return of a fund at a given level ofrisk (Bi) can be calculated as:
Ri = Rf + Bi (Rm - Rf)
Where, Rm = average market return during the
given period.Ri= average rate of return on portfolio p or the
fund
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Fama Model
Compares the performance, measured in termsof returns, of a fund with the required return
commensurate with the total risk associated with
it.
Required return can be calculated as:
Ri = Rf + Si/Sm*(Rm - Rf)
Where, Sm = standard deviation of market returnsSi = standard deviation of the portfolio or fund
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The sources of tracking are transaction costs, feescharged by the AMC, fund expenses and cash
holdings. One of the reasons for tracking error in
passively managed funds is the sampling bias.
In order to reduce trading and transaction costs,
fund managers hold a selection of securities that is
statistically likely to replicate the performance of
the index. The sample does not exactly perform asthe index, which leads to differential returns or
tracking error.
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