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portfolo evalution technique


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Portfolio performance evalution can be defined as a feedback and control mechanism which is used by the portfolio managers and investment analysis to make the process of portfolio/investment management more effective.


techniques Sharpe’s reward to variability model Treynor’s reward to volatility model Jensen’s differential return model

Sharpe’s reward to variability model :

Sharpe’s reward to variability model The model yield single value that can be used for investment performance ranking. it assigns highest rank to portfolio that has the best risk adjusted rate of return, his measure make a measurement of the risk premium of portfolios. the difference between a portfolio’s expected rate of return and risk less rate is called the risk premium. then each portfolio’s risk premium is divided by its standard deviation of annual return measure of the portfolio’s total risk, estimated over the evalution period. the resulting number is the rate of reward per unit of variability .

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S t= R t - R/=Reward=Risk Premium

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R t sharpe’s index Risk less rate of return


EXAMPLE Portfolio Avg return S.D. Risk free rate A 15% 3% 9% B 20% 8% 9% S A= 15-9/3=2 S B =20-9/9=1.22


TREYNOR’S REWARD TO VOLATALITY MODEL Jack L.treynor based his model on the concept of characteristic line this is the least squares regression line relating the return to the risk and Beta is the slope of the line. the slope of the line measure volatility sleep slope means that the actual rate of return for the portfolio in question is relatively sensitive to fluctuations in the general stock market whereas a gentle slope indicates that the portfolio in question is relatively insensitive to market fluctuations.treynor also pointed out that investment risk is diversified portfolio is the sum of responses to general fluctuations and fluctuations peculiar to the particular securities held in the portfolio.


Conti………….. Treynor’s measure is the portfolio's excess return per unit of portfolio’ beta coefficients(b). treynor measure relates the excess return to non diversifiable or systematic as measured by portfolio’s volatility. however, if diversified portfolios are compared the ranking will be similar irrespective of which method is used . treynor’s reward to volatility ratio is shown in the following eqution : Tt = Rt -R/ b t Tt = treynor’s measure of portfolio performance Rt =return of the portfolio R=risk less rate of return B t =beta coefficient or volatility of the portfolio

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R t Tt Risk less rate treynor’s measure ( st.deviation )


Example Portfolio return volatility risk per rate A 20% 5% 8% B 24% 8% 8% ( Portfolio A is better than portfolio B .It is all due to volatility of two portfolios.

Jensen’s differential return model:

Jensen’s differential return model Jensen’s model measure the portfolio managers predictive ability to achieve higher return than expected for the given riskness. This model is based on CAPM. jensen attempt to construct a measure of absolute performance on a risk adjusted basis that is a definite standard against which performance of various funds can be measured. R t -R= a+b ( R m -R) R t =portfolio return R=risk less return a=intercept the graph that measures the forecasting ability of the portfolio manager b=Beta coefficient, a measure of systematic risk R m =return of market portfolio

Two steps of jensen’s model:

Two steps of jensen’s model He calculate what the return of given portfolio should be on the basis of b,Rm and R. He compare that actual realized retrn of the portfolio with the calculated or predicted return. greater the excess of realized return over the calculated return, better is the performance of the portfolio

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NEGATIVE line shows that management of the performed portfolio is inferior. POSITIVE line shows that superior quality of the management funds NEUTRAL value shows that the performance of the fund is similar to the performance odf the market portfolio.

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