More often than not meritocracy of investments is often decided by the returns. Quite simply then a fund generating more returns than the other is considered better than the other. But this is just half the story.

What most of us would appreciate is the level of risk that a fund has taken to generate this return? So what is really relevant is not just performance or returns. What matters therefore are Risk Adjusted Returns.

The only caveat whilst using any risk-adjusted performance is the fact that their clairvoyance is decided by the past. Each of these measures uses past performance data and to that extent are not accurate indicators of the future.

As an investor you just have to hope that the fund continues to be managed by the same set of principles in the future too.

The most basic of all measures- Standard Deviation allows you to evaluate the volatility of the fund. Put differently it allows you to measure the consistency of the returns.

Volatility is often a direct indicator of the risks taken by the fund. The standard deviation of a fund measures this risk by measuring the degree to which the fund fluctuates in relation to its mean return, the average return of a fund over a period of time.

A security that is volatile is also considered higher risk because its performance may change quickly in either direction at any moment.

A fund that has a consistent four-year return of 3%, for example, would have a mean, or average, of 3%. The standard deviation for this fund would then be zero because the fund's return in any given year does not differ from its four-year mean of 3%. On the other hand, a fund that in each of the last four years returned -5%, 17%, 2% and 30% will have a mean return of 11%. The fund will also exhibit a high standard deviation because each year the return of the fund differs from the mean return. This fund is therefore more risky because it fluctuates widely between negative and positive returns within a short period.

Beta is a fairly commonly used measure of risk. It basically indicates the level of volatility associated with the fund as compared to the benchmark.

So quite naturally the success of Beta is heavily dependent on the correlation between a fund and its benchmark. Thus if the fund's portfolio doesn't have a relevant benchmark index then a beta would be grossly inadequate.

A beta that is greater than one means that the fund is more volatile than the benchmark, while a beta of less than one means that the fund is less volatile than the index. A fund with a beta very close to 1 means the fund's performance closely matches the index or benchmark.

If, for example, a fund has a beta of 1.03 in relation to the BSE Sensex, the fund has been moving 3% more than the index. Therefore, if the BSE Sensex increased 10%, the fund would be expected to increase 10.30%.

Investors expecting the market to be bullish may choose funds exhibiting high betas, which increase investors' chances of beating the market. If an investor expects the market to be bearish in the near future, the funds that have betas less than 1 are a good choice because they would be expected to decline less in value than the index.

The success of Beta is dependent on the correlation of a fund to its benchmark or its index. Thus whilst considering the beta of any security, you should also consider another statistic- R squared that measures the Correlation.

The R-squared of a fund advises investors if the beta of a mutual fund is measured against an appropriate benchmark. Measuring the correlation of a fund's movements to that of an index, R-squared describes the level of association between the fund's volatility and market risk, or more specifically, the degree to which a fund's volatility is a result of the day-to-day fluctuations experienced by the overall market.

R-squared values range between 0 and 1, where 0 represents no correlation and 1 represents full correlation. If a fund's beta has an R-squared value that is close to 1, the beta of the fund should be trusted. On the other hand, an R-squared value that is less than 0.5 indicates that the beta is not particularly useful because the fund is being compared against an inappropriate benchmark.

Alpha = (Fund return-Risk free return) - Funds beta *(Benchmark return- risk free return).

Alpha is the difference between the returns one would expect from a fund, given its beta, and the return it actually produces. An alpha of -1.0 means the fund produced a return 1% higher than its beta would predict. An alpha of 1.0 means the fund produced a return 1% lower. If a fund returns more than its beta then it has a positive alpha and if it returns less then it has a negative alpha. Once the beta of a fund is known, alpha compares the fund's performance to that of the benchmark's risk-adjusted returns. It allows you to ascertain if the fund's returns outperformed the market's, given the same amount of risk.

The higher a funds risk level, the greater the returns it must generate in order to produce a high alpha.

Normally one would like to see a positive alpha for all of the funds you own. But a high alpha does not mean a fund is doing a bad job nor is the vice versa true. Because alpha measures the out performance relative to beta. So the limitations that apply to beta would also apply to alpha.

Alpha can be used to directly measure the value added or subtracted by a fund's manager.

The accuracy of an alpha rating depends on two factors: 1) the assumption that market risk, as measured by beta, is the only risk measure necessary; 2) the strength of fund's correlation to a chosen benchmark such as the BSE Sensex or the NIFTY.

Sharpe Ratio= Fund return in excess of risk free return/ Standard deviation of Fund

So what does one do for funds that have low correlation with indices or benchmarks? Use the Sharpe ratio. Since it uses only the Standard Deviation, which measures the volatility of the returns there is no problem of benchmark correlation.

The higher the Sharpe ratio, the better a funds returns relative to the amount of risk taken.

Sharpe ratios are ideal for comparing funds that have a mixed asset classes. That is balanced funds that have a component of fixed income offerings.