**Introduction**

A mutual fund’s performance and risk can be ascertained by many statistical tools.

Among the Mutual Fund tools are risk & reward ratios, which help to ascertain the level of risk and reward associated with a particular mutual fund in a given circumstance at a point in time.

Let us discuss 4 risk measurement tools and a statistical tool to measure the reward.These Mutual Fund Analysis tools are predominantly used by investors while selecting the fund

**Table of Contents:**

The Relationship between Risk & Volatility

1.)R-squared

2.)Beta

3.)Sharpe Ratio

4.)Standard Deviation

5.)ALPHA

Conclusion

**The Relationship between Risk & Volatility:**

Volatility is something all investors face, especially while investing in equities and equity mutual funds. But when we talk about risks and volatility, one should keep in mind that they are different.

Volatility is a side effect of risk. It’s what happens when potential risks like economic, price, sector…etc become a reality.Even with Mutual Fund evaluation tools, it is hard to predict accurately the risk level involved in a particular fund.

If volatility is how risk manifests itself, all the historical “risk” measurements that you see — standard deviation, beta, r-squared, and Sharpe ratio gauge how volatile, not how risky an investment has been in the past.

These measurements don’t take into account any risks that have yet to manifest themselves as volatility. Mutual Fund evaluation tools can be effective in predicting the volatility of your investments.

But does that mean one should not consider these volatility measures?

- Evaluating a scheme just on performance is not enough, one has to take the risks/volatility into measure to get a good idea about the risk-adjusted rate of return. For this, you can make use of the Mutual Fund Analysis tool.
- There is a very good chance that a scheme that has been volatile in the past will continue to be so in the future, until and unless there has been a drastic and fundamental change in the portfolio or investment approach.

The following are the 4 common measures, which are used to measure a fund’s volatility

**1. R-squared**:

What is R- squared in mutual funds?

The R-squared scale ranges from 0 to 100, with 100 indicating that a fund’s performance is highly correlated with the index it tracks.

It is the statistical measure of how closely the portfolio’s performance correlates with the performance of a benchmark index. R-squared is a proportion that ranges between 0.00 and 1.00. For example, an R-squared of 1.00 indicates a perfect correlation to the benchmark index, while an R-squared of 0.00 indicates no correlation. Therefore, a lower R-squared indicates that fund performance is significantly affected by factors other than the market.

Let’s take an example.

- A fund has an R-squared of 1(typically an index fund) with the S&P CNX 500 index. This means that when the index has gone up, so has the fund, and when it has gone down, the fund has too.
- A fund that invests in unlisted stocks or ADR/GDRs or in stocks, that are not listed in the S&P CNX 500 index, will have an R-squared less than 1. The behavior of this fund will not match the index.

So in this way R-squared in Mutual Funds can be used as an important parameter in determining your ideal funds.

*All diversified equity mutual funds have a high correlation with their respective benchmark indices, but not a perfect correlation. The reason for this is simple – the components (individual stocks) in diversified active equity mutual fund portfolios and the indices are not exactly the same and then there is the issue of trading and time also. *

**2. Beta** :

**What does Beta in Mutual Funds mean?**

Beta is also referred to as Beta co-efficient. It is a tool to measure the volatility of a specific security or a mutual fund by comparing it to the performance of a related benchmark over a period of time.

It is the statistical measure of a portfolio’s sensitivity to market movements.

Beta measures the relative risk of a mutual fund or portfolio in relation to the market portfolio. It reflects the systematic risk associated with the mutual fund. The market index has a beta of one. Where if the is beta is higher than one, it means that the mutual fund is riskier than the benchmark.

Similarly, a beta of less than one indicate lesser volatility than the benchmark. A beta of 1.1 signifies that the mutual fund has a volatility of 1.1 times the benchmark volatility.

Volatility per se is not bad. Beta suggests that if the individual stocks in an equity mutual fund are chosen in such a way that the cumulative beta stand at 1.2, then, when the market benchmark escalates by 10%, the equity mutual fund is expected to move up by 12% and the converse is also true.

Certain Mutual Fund Evaluation Tools can help in figuring out the Beta Ratio in Mutual Funds.

**What kind of returns can Beta give?**

In a bullish market, a mutual fund with higher beta will yield better returns for the investor as higher returns for taking higher risk are expected. While in a bearish market, a mutual fund with lower beta would be more appropriate as it is defensive against the market.

Based on the Beta, the Alpha formula may also be represented thus:

Alpha (?) = (Actual return of mutual fund – risk free return) – beta of mutual fund*(benchmark return – risk free return)

Let’s understand this by evaluating an example.

Working for a one-year performance period:

Illustration: Actual return of mutual fund: 30, Risk free return: 8%, Beta of mutual fund: 1.1, Benchmark return: 20%

? = (0.30-0.08)- 1.1*(0.20-0.08) = 0.088 i.e., this mutual fund has outperformed the benchmark index by 8.8%.By this formula, we can calculate the alpha of a Mutual Fund.

It is very important to note for the alpha and beta produce the correct results, the benchmark has to be properly worked out and ready.

For example, a benchmark index such as the BSE Sensex or S&P CNX 500 has a beta of 1.0. A beta of more or less than 1.0 shows that a fund’s historical returns have fluctuated more or less than the relevant benchmark.

For example, if a fund has a beta of 1.1 and the market index declines 10%, you could expect the security to decline 11%(on average). A fund with beta less than 1.0 is less volatile than the market, and could be expected to rise and fall at a slower rate.

Typically you need to use beta in conjunction with R-squared for a better understanding of the scheme’s risk-adjusted performance. The lower the R-squared (which means less correlation between the scheme and the benchmark utilized), the beta(measure of volatility) becomes less reliable

So far you have come to know what is alpha and beta in Mutual Funds.

**3. Sharpe Ratio** :

What is the Sharpe Ratio in Mutual Funds?

It is the statistical measure of a portfolio’s historic “risk-adjusted” performance and is calculated by dividing a fund’s excess return by the standard deviation of those returns. As a measure of reward per unit of total risk, the higher the ratio, the better.

The main drawback of the Sharpe ratio is that it is expressed as a raw number. Consequently, it’s difficult for one to evaluate the Sharpe ratio of an individual fund by itself. We know the higher the Sharpe ratio the better, but given no other information, we don’t know whether a Sharpe ratio of 1.5 is good or bad. Only when you compare one scheme’s Sharpe ratio with that of another fund (or group of funds) do you get a feel for its risk-adjusted return relative to other investment options? So one can say the selection of Mutual Funds through the Sharpe Ratio isn’t that straight forward.

**4. Standard Deviation**:

What is called Standard Deviation in Mutual Funds?

It is a statistical measure of the historic volatility of a portfolio. It measures the dispersion of a fund’s periodic returns (often based on 36 months of monthly returns). The wider the dispersions, the larger the standard deviation and the higher the risk.

For example let’s compare two Mutual Funds – A & B

- Fund A posts annual returns of 8%, 10%, and 12%. Over the three years, it earns an average annual return of 10%, with a standard deviation of 1.63.
- Fund B returns 1%, 9%, and 20%. It too earns an average return of 10%, but its standard deviation is 7.79.

Thus we know that Fund B has been more volatile than Fund A..

This measure also like the others cannot be used in isolation – one needs to check the standard deviations of other schemes to get a better picture of the scheme’s relative volatility. A problem with standard deviation is that it rewards consistency above all else and hence, even if a scheme loses money but does it so very consistently it can have a very low standard deviation!!

Given the investment objective of our diversified equity schemes, it is clear that the Large-cap Fund is the least volatile as it invests in large cap stocks that tend to be less volatile. Midcap Fund which invests in mid cap and turnaround stocks has high volatility given that these categories of stocks are more sensitive to market sentiments and speculation.

**Final Thoughts on Risk Measurement Tools:**

All risk measures have limitations. First, they are based on past performance. Second, no single measure paints a complete picture of risk. For example, some may exclude other measures by using only R-squared and beta (which allow evaluation of schemes against a common benchmark) which is not correct. Investors should also consider qualitative risk factors such as investment style and portfolio concentration.

One should also keep that investment is not all about numbers and it is not about “avoiding” risk but about “understanding” risk. One needs to be conscious of risk, but not push it to the last decimal point. It’s about awareness, rather than mathematics.

So these are a few key things that you should remember while using Statistical Tools.

**5. ALPHA**

**Why is Alpha and Beta In Mutual Funds important?**

**What is the Relationship between Alpha and Beta? **

Salient features of Alpha and Beta are:

Alpha and Beta are both risk & reward ratios that the investors use as tools to calculate, and compare the returns and risk and to select the mutual funds.

Both the measurements use benchmark indexes and compare them against the individual security or a mutual fund to highlight a particular tendency.

To enhance returns from the total portfolio, a desired level of risk has to be consistently maintained and hence one needs to individually select exposure to alpha and beta.This can also be considered as one of the ways how we compare two Mutual Funds.

**What Alpha means?**

Alpha is considered to be a measurement of the portfolio / mutual fund manager’s aptitude. Let us look at an example to understand what exactly Alpha connotes.

When the investments made by a portfolio/ mutual fund manager provides a return of 10% for a growth mutual fund, against the overall return of 6% in the equity markets then it is considered to be far more impressive than in a situation where the equity returns are earning 14%. In the first case, the portfolio manager would have a relatively high alpha, while it would be the opposite in the case of the second.

**What does Alpha represent?**

Alpha is the representation of the difference between the mutual fund’s actual return and the expected return. It is a measure to gauge the level of our performance, or in simpler terms how good or bad the mutual fund has performed when compared to a benchmark.

A positive alpha implies that a mutual fund has performed above its yardstick or benchmark index. As in the example above, an alpha of 4 would indicate that a mutual fund has provided 4% higher returns than the market while an alpha of -4 would indicate that the mutual fund has produced 4% lower returns than its market benchmark. A portfolio / mutual fund manager always seeks a positive alpha.

So by now, we have come to know Alpha and Beta in Mutual Funds isare regarded as a key metric in choosing a Mutual Fund Scheme.

**Alpha versus Beta**

If an investor were looking to take advantage of the bullish momentum that he expects in the market, it would be wise to ascertain the beta of various short-listed equity mutual funds, which would eventually help him to choose the right vehicle to participate in the expected market action.

If the investor believes that the market has a lot of shares, that which are not correctly priced, and there is considerable scope for market correction, then it is likely for him to look for actively managed mutual funds that can locate these “mispriced” opportunities.

Ultimately it can guide investors to choose the right and appropriate selection of Mutual Funds.

This will help to make money over what the market makes, over time. Here it is the “alpha” that the investor seeks to achieve – a return over market returns – which is primarily attributable to his superior stock picking skills.

**Conclusion**

If an investor desires alpha returns, by evaluating the past performance of a mutual fund manager and the alpha he has delivered over the incremental expenses over a long period, the investor can achieve this objective.

Though, this track record may provide a hint to the upcoming performance, it is no guarantee for high returns.An important point to be noted here is the data that you derive from statistical tools has its limitations.

If the primary concern for the investor is the near term momentum (upwards or downwards), beta is a better measure to focus on. If long-term out performance and wealth creation are the primary concerns, then the ability and track record of the mutual fund manager in delivering alpha is what you should be looked into minutely.The decision is finally yours.

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