Written by P Saravanan | Updated: Nov 1 2013, 02:27am hrs

With the Sensex touching new highs, the most common question on the mind of investors is how their equity portfolio is performing. Often, investors simply define a successful portfolio by a positive return on investment, ignoring the risk factor.

Investors need to classify their portfolios into similar risk classes based on a measure of risk and, then, compare the rates of return for alternative portfolios directly within these risk classes. Here are four major composite equity portfolio performance measures that combine risk and return performance into a single value.

Peer group comparison

This is the most common manner of evaluating portfolio. This is computed by calculating a portfolios relative return ranking compared to a collection of similar funds or portfolios. The major advantage of a peer group comparison is that it is relatively simple to compute. The objective here is to compare the returns generated by a given portfolio relative to other portfolios, which follow more or less a similar mandate. This comparison can be captured easily through a boxplot graph. Though it is simple and easy to compute, it is often difficult to find a peer group and the assumption of peer portfolios following a similar mandate is a doubtful one.

Treynor Portfolio Performance measure

Treynor developed the first composite measure of portfolio performance that included risk. He postulated two components of risks, namely risk produced by general market fluctuations and that resulting from unique fluctuations in portfolio securities. To identify risk due to market fluctuations, he introduced the concept of beta, which defines the relationship between the rates of return for a portfolio over time and the rates of return for an appropriate market portfolio. A higher beta indicates the portfolio that is more sensitive to market returns and has greater market risk and vice versa.

In a completely diversified portfolio, these unique risks for individual stocks should cancel out. As the correlation of the portfolio with the market increases, unique risk declines and diversification improves. Treynor ratio exhibits the risk-adjusted performance of the portfolio or fund. His formula goes as follows: (Portfolio Return Risk Free Rate of Return )/Beta. Treynor's ratio is also known as 'rewards to volatility ratio'. The higher the Treynor measure, the better the portfolio.

Sharpe Portfolio Performance measure

Sharpe conceived of a composite measure to evaluate the performance of portfolios or mutual funds. His formula goes as follows: (Portfolio Return Risk Free Rate of Return )/Standard deviation of portfolio returns. It is computed by subtracting the risk-free rate from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns. This ratio indicates whether a portfolios return is owing to smart and correct investment decisions or due to excess risk. Higher the ratio, the better the portfolio.

Sharpe or Treynor which one to use

The Sharpe portfolio performance measure uses the standard deviation of returns as the measure of total risk, whereas the Treynor performance measure uses beta. The Sharpe measure, therefore, evaluates the portfolio on the basis of both rate of return performance and diversification.

For a completely diversified portfolio, the two measures give identical rankings. Alternatively, a poorly diversified portfolio could have a high ranking on the basis of the Treynor performance measure, but much lower on the basis of the Sharpe performance measure. Any difference in rank would come directly from a difference in diversification. Therefore, these two performance measures provide complementary yet different information and both measures should be used. If investors are dealing with a group of well-diversified portfolios, as like the many mutual funds are, the two measures provide similar rankings.

Jensens Portfolio Performance measure

Basically, Jensens measure calculates the excess return that a portfolio generates over its expected return. This measure of return is also known as Jensen's Alpha. The formula is: Portfolio Return Benchmark return. The benchmark return is computed as Risk Free Rate of Return + Beta (Market Rate of Return Risk Free Rate of Return). This ratio measures how much of the portfolio's rate of return is attributable to the investor's ability to deliver above-average returns, adjusted for market risk. The higher the ratio, the better the risk-adjusted returns.

Portfolio performance measures are key aspect of the investment decision process. These tools provide the necessary information for investors to assess how effectively their money has been invested.

The writer is an associate professor in finance and accounting at IIM Shillong

A comparative study

Peer group comparison

* This is computed by calculating a portfolios relative return ranking compared to a collection of similar funds or portfolios.

* The major advantage of a peer group comparison is that it is relatively simple to compute. But the assumption of peer portfolios following a similar mandate is a doubtful one.

Treynor Portfolio

Performance measure

* Treynor introduced the concept of beta, which defines the relationship between the rates of return for a portfolio over time and the rates of return for an appropriate market portfolio. A higher beta indicates the portfolio that is more sensitive to market returns and has greater market risk and vice versa.

* Treynor ratio exhibits the risk-adjusted performance of the portfolio or fund. The formula goes as follows: (Portfolio Return Risk Free Rate of Return )/Beta

Sharpe Portfolio

Performance measure

* Sharpes formula is: (Portfolio Return Risk Free Rate of Return )/Standard deviation of portfolio returns. It is computed by subtracting the risk-free rate from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns . This ratio indicates whether a portfolios return is owing to smart investment decisions or excess risk

Jensens Portfolio

Performance measure

* This calculates the excess return that a portfolio generates over expected returns. The formula is: Portfolio Return Benchmark return. The benchmark return is computed as Risk Free Rate of Return + Beta (Market Rate of Return Risk Free Rate of Return). This ratio measures how much of the portfolio's rate of return is attributable to the investor's ability to deliver above-average returns, adjusted for market risk

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