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In our series on modern portfolio theory, we discuss the alpha data point's reliability in determining a fund's risk/reward profile.

Fund managers often tout the fact that they've generated positive alpha. Should an investor be be impressed?

The answer is: yes, in some circles, being able to generate alpha is touted as the holy grail of investing--it's an indication that a manager has been able to generate an above-average return relative to the risk that he or she is taking on.

But like beta, alpha has some useful applications as well as some limitations. Before you put too much stock in the statistic, it's important to know exactly what alpha is telling you and how it's calculated.

**How alpha works**

Although alpha precedes beta in the Greek alphabet, a fund's beta is a necessary precursor to calculating its alpha. Beta measures an investment's volatility, or more specifically, its sensitivity to the movements of a market index.

On days when a market index generates a positive return, a fund with a high beta would be expected to gain even more than the index. On the flip side, the high-beta fund would be expected to lose more than the index during market downdrafts.

Alpha attempts to show whether a fund has adequately compensated investors for its volatility level, as reflected by its beta. For example, the aforementioned high-beta fund might have experienced extreme performance gyrations relative to its benchmark.

But if its returns have been even higher than its beta would predict, the fund has generated positive alpha. A low-beta fund can also generate positive alpha by generating higher returns than its beta would suggest.

The starting point for calculating alpha is to find how much a fund and its benchmark have returned (on a monthly basis) over the return of a guaranteed risk-free investment such as a government bond.

You then find the expected return for the investment by multiplying the fund's beta by the benchmark's excess returns. The difference between the fund's actual return and its expected return is its alpha.

If alpha is positive, it means that the fund returned more than its expected return, whereas a negative alpha indicates that the fund returned less.

For example, let's say a stock fund generated an excess return of 10% in a given time frame and the index generated an excess return of 8%. If the fund had a beta of 0.5, its expected return would be just 4%. (0.5 times 8%). But given the fund's actual excess return of 10%, the fund's alpha is 0.6 (10% minus 4%).

Bear in mind that a higher beta (higher risk relative to an index) does not necessarily equate to higher alpha (greater return for that risk); a high-beta fund may well sport a negative alpha.

That's because the greater the risk the fund assumes, the higher the hurdle the fund must jump over in order to outperform the benchmark.

Moreover, because alpha is determined by both a fund's return and risk, two funds could have the same returns but their differing risk levels will lead to two distinct alphas.

**Don't ignore these caveats**

Given that alpha attempts to measure an active fund manager's worth versus a market benchmark, it may be tempting to single-mindedly pursue only the funds with the highest alphas and ignore the rest.

But the limitations of this statistic are numerous. For starters, alpha and beta are of limited use if a fund doesn't have a high correlation to the benchmark to which it's being compared.

That's why it's important to check that a fund has a high R-squared with a benchmark before putting any weight on its alpha or beta.

If a fund has a low correlation with its index, its corresponding alpha statistic is not reliable, nor is the beta statistic from which the alpha is derived.

Moreover, all modern portfolio theory statistics are based on an investment's past return history; alpha, like beta, is a backward-looking measure and its predictive ability is far from guaranteed.

A fund's high alpha may owe to actual managerial talent, but it could also be the result of a series of lucky stock picks or sector bets. If it was simply luck, that positive alpha figure could become negative as soon as the hot streak ends.

And just as a high-alpha doesn't provide airtight evidence of a fund's merit, don't be too quick to cross negative-alpha funds off your list. Morningstar recalculates alpha and all MPT statistics on a monthly basis, so a fund's alpha can swing quickly from positive to negative.

Additionally, keep in mind that expenses can affect alphas, even when expenses are very low.

*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**

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

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