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In Part 1 of a series on modern portfolio theory, we look at beta to determine the level of a fund's index-related risk.

Individual mutual fund reports on Morningstar.in feature a Ratings & Risk tab, which lists a number of quantitative risk/return measures.

These measures include Morningstar's risk-adjusted ratings, several measures of volatility, such as standard deviation, and various modern portfolio theory statistics, such as beta, for the three-, five-, 10-, and 15-year periods, wherever available.

Each of these measures provides a different look at a fund's risk, volatility, return, or a combination of those factors.

MPT is rooted in the assertion that there's no free lunch--you'll only obtain higher returns if you're willing to take on more risk. At the same time, MPT holds that diversifying a portfolio across multiple assets can help decrease its risk level.

Modern portfolio statistics such as alpha and beta attempt to show how an investment's volatility and return characteristics compare with those of a given index.

And Morningstar provides four MPT statistics for each fund during the past three-, five, 10- and 15-year periods, wherever available: beta, R-squared, alpha, and Treynor ratio. Today, we'll focus on Beta.

**How it works**

Understanding beta will serve as a helpful foundation in deciphering and using the other MPT statistics. Beta attempts to gauge an investment's sensitivity to market movements.

When the market is up on a given day, will the fund gain even more than the benchmark? And when the market is down, will the fund lose even more than its benchmark?

A lower beta not only indicates that an investment has been less volatile than the market itself, but also implies that the fund takes on less risk with lower potential return. Contrarily, a higher beta implies a higher-risk investment with greater return potential.

The starting point for beta is measuring the volatility of a benchmark's returns in excess of what Treasury bills return--that's the baseline. The benchmark's beta is always 1.0.

We then calculate the beta for the investment by comparing its excess return over Treasury bills during a given time period with the benchmark's excess return over Treasury bills during that same time period.

So a fund like Reliance Equity with a three-year beta of 0.91, would be expected to gain 9% less, on average, than the benchmark in up markets and expected to lose, on average, 9% less in down markets.

In contrast, JM Core 11 has a three-year beta of 1.34, indicating that it is expected to gain, on average, 34% more than the benchmark in up markets, and expected to lose, on average, 34% more in down markets.

**How to use it (and how not to)**

In theory, beta is a relatively straightforward, quantifiable measure of relative risk. Investors can use it, along with other risk and volatility data points, to help compare multiple investments and determine how, if at all, a specific investment might fit in the context of a broadly diversified portfolio.

At the same time, it is not a foolproof measure for practical application.

First, investors should keep in mind that because beta is a relative figure, it is not appropriate to assume that a low beta implies low volatility or that a high beta implies high volatility.

For example, a fund may have a fairly low beta, but if the benchmark used to calculate that beta is ultra-volatile and features aggressive holdings, the fund won't necessarily exhibit low volatility in an absolute sense.

Secondly, though beta is based on an investment's past behavior, it is used to determine how a fund is likely to behave in the future. However, historical performance can be unreliable in predicting future performance or future relative volatility.

And because beta is derived from a formula that only takes into account fund and benchmark returns and correlation, the statistic paints an overly simplistic and incomplete picture. For example, beta does not take into consideration macroeconomic developments.

Moreover, beta assumes that going forward, a fund's potential for upside and downside risk is virtually equal, but in practice, investments rarely exhibit perfectly symmetrical risk/return profiles. The beta statistic also removes from the equation the additional risk that investors' behavior can impose on their holdings.

Finally, and most important, the usefulness of a fund's beta (and other MPT statistics, for that matter) is completely dependent on the relevance of its market benchmark.

A fund might have a very low beta, but if it's not closely correlated with the index used to calculate that beta, the statistic is close to meaningless.

That's why investors using MPT statistics should do so in conjunction with the fund's R-squared, which measures its correlation with a given benchmark. In the next article in this series, we'll explore R-squared and how to use it when building a portfolio.

*Other articles in this series*

**Investment Ratios**

- Sharpe Ratio: Are Your Fund's Returns Worth the Risk?
- Sortino Ratio: Are Your Fund's Return Worth the Downside Risk?
- Treynor Ratio: Is This the Best Way to Judge Risk/Return?

**Modern Portfolio Theory**

*This article first appeared on Morningstar.com, our sister US site, and has been formatted for India.*

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