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Transcript of Performance Evaluation
Mean Return of a Portfolio
Suppose that there are n assets with rates of return 1 r , 2 r ,…, n r and these have expected values
Measuring the rate of return to a Portfolio
Measuring of portfolio performance has become an essential topic in the financial markets for the portfolio managers, investors and almost all that have something to do in the field of finance and it plays a very important role in the financial market almost all around the world. Earlier then 1950, portfolio managers and investors measured the portfolio performance almost on the rate of return basis. During that time, they knew that risk was a very important variable in determining investment success but they had no simple or clear way of measure it.
created the idea of Modern Portfolio Theory and proposed that investors expected to be compensated for additional risk and provided a framework for measuring risk .In early 1960, after the development of portfolio theory and capital asset pricing model in subsequent years, risk was included in the evaluation process.
The capital asset pricing model of
William Sharpe and John Litner
marks the birth of asset pricing theory. The attraction of capital asset pricing model was that it offered power predictions about how to measure risk and the relation between expected return and risk.
(1965) was the first researcher developing a composite measure of portfolio performance. He measured portfolio risk with beta and calculated portfolio market risk premium and later on in 1966 Sharpe developed a composite index which is similar to the Treynor measure, the only difference being the use of standard deviation instead of beta.
In 1967 Sharpe index evaluated funds performance based on both rate of return and diversification but for a completely diversified portfolio Treynor and Sharpe indices would give identical ranking. Jensen in 1968, on the other hand, attempted to construct a measure based on the security market line and he showed the difference between the expected rate of return of the portfolio and expected return of a benchmark portfolio that would be positioned on the security market line.
Prof. K. Spremann
“Portfolio measurement has not only the goal to inform about the quality of a portfolio performance__ but and that’s even more important__ to decompose and analyze the success factors of a portfolio”.
Variance of Portfolio Return
We form a portfolio of these n assets using the weights
The rate of return in terms of the individual return of the portfolio is
We find the expected rate of return by taking the weighted sum of individual expected rates of return. Using the property of linearity, we take the expected values on the both sides of equation (1)