Portfolio Performance EvaluationMd. Ruhul AminAssistant Professor, BIBM

Portfolio Performance Measure, Why?People are always interested in evaluating the performance of their investments.

Having spent the time and incurred the expense to design an asset allocation strategy and select the specific set of securities to form their portfolios, investors-whether they are individuals, corporations or financial institutions-must periodically determine whether their effort is worthwhile.

Investors managing their own portfolios should evaluate their performance, as should those who pay one or several professional money managers to make these decisions for them.

Portfolio Performance Measures over timeBefore the development of portfolio and capital market theories (before 1960s), consideration was on return, not on risk-peer group comparison.

After 1960s, risk-adjusted techniques-composite measures

Requirements of a portfolio managers performance Measures The ability to derive above-average returns for a given risk class

The ability to diversify the portfolio completely to eliminate all unsystematic risks, relative to the portfolios benchmark

Treynor Portfolio Performance Measure Treynor measure gives excess return per unit of systematic risk.

Risk produced by general market fluctuations (Systematic Risk) Risk resulting from unique fluctuations in the portfolio securities (Unsystematic Risk) Treynor Portfolio Performance Measure

Characteristic LineTo identify risk due to market fluctuations, he introduced the characteristic line, which defines the relationship between the rates of return for a portfolio over time and the rates of return for an appropriate market portfolio. Characteristic lines slope measures the relative volatility of the portfolios returns in relation to returns for the aggregate market.

This slope is the portfolios beta coefficient ().

Plot of Performance on SML (T Measure)

Sharpe MeasureSharpe measure divides average portfolio excess return over the sample period by the standard deviation of returns over that period.

It measures the reward to (total) volatility trade-off

This measure uses a benchmark on the ex post capital market line.

This measure indicates the risk premium return earned per unit of total risk.

In terms of capital market theory, this portfolio performance measures total risk to compare portfolios to the CML, whereas the Treynor measure examines portfolio performance in relation to SML.

Sharpe Measure

Sharpe Measure

Treynor Vs Sharpe Measures The Sharpe portfolio performance measure uses standard deviation of returns as the measure of risk whereas Treynor performance measure uses beta (systematic risk)

The Sharpe measure, therefore, evaluates the portfolio manager on the basis of both rate of return performance and diversification.

For a completely diversified portfolio, one without any unsystematic risk, the two measures give identical rankings because the total variance of the completely diversified portfolio is its systematic variance. Alternatively, a poor diversified portfolio could have a high ranking on the basis of the Treynor performance measure but a much lower ranking on the basis of the Sharpe performance measure. Any difference in rank would come directly from a difference in diversification.

Both measures produce relative not absolute rankings of performance.

Jensen Measure Jensen measure is the average return on the portfolio over and above that predicted by CAPM, given the portfolios beta and the average market return. Jensen measure is the portfolios alpha value. p = Rp [Rf + p (RM - Rf)]

p = [Rp Rf] - p [RM - Rf]

Alpha (p) is the difference between the actual excess return on portfolio P during some period and the risk premium on that portfolio that should have been earned, given its level of systematic risk and the use of the CAPM. It measures the constant return that the portfolio manager earned above, or below, the return of an unmanaged portfolio with the same (market) risk.Jensen Measure

If alpha is significantly positive, this is evidence of superior performance.

If alpha is significantly negative, this is evidence of inferior performance.

If alpha is insignificantly different from zero, this is evidence that the portfolio manager matched the market on a risk-adjusted basis. Jensen Measure

Jensen Measure

The Information Ratio (Appraisal Ratio) Performance Measure Information ratio also known as an appraisal ratio measures a portfolios average return in excess of that of a comparison or benchmark portfolio divided by the standard deviation of the excess return. Formally, the information ratio (IR) is calculated as:

Superior or Inferior Portfolio Performance results from two sourcesFirst, the manager may be able to time market turns, varying the portfolios composition in accordance with the rise and fall of the market (Superior Timing) - Bigger gain in rising markets and smaller losses in declining markets give the portfolio manager above-average risk-adjusted returns

Second, the portfolio manager may be able to select undervalued securities consistently enough to affect portfolio performance (Superior Security Selection) - A portfolio manager may try to select undervalued stocks or bonds for a given risk class and even without superior timing can earn above-average risk-adjusted returns.

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