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# Standard Deviation, Mutual Fund Beta, and Sharpe Ratio

February 5, 2022 6 minutes

As a prospective investor, there are a few important terms and concepts that you must understand in order to have a good investment journey. So, read on to know what standard deviation, Sharpe ratio and mutual fund beta mean.

## Standard Deviation

### What is meant by Standard Deviation?

Standard deviation is used to measure variation from arithmetic mean generally. But in finance, standard deviation refers to a statistical measure or tool that represents the volatility or risk in a market instrument such as stocks, mutual funds etc.

Standard deviation is an accurate measure of how much deviation occurs from the historical mean. The higher the standard deviation, the greater the fluctuation is.

### Method used to calculate Standard Deviation

It is calculated as the square root of variance. The formula for the same is as follows –

Standard Deviation = [1/n * (xi – x)2]1/2

where:

xi = each datapoint

x = mean

n = number of datapoints or time periods

### What is the use of Standard Deviation in Mutual Fund?

It is used to measure the dispersion of the actual return from the mutual fund’s expected return. It is a widely used measure due to its consistency.

### What are the Limitations of Standard Deviation?

• It does not show how well the mutual fund performs against its benchmark.
• It cannot be applied when a portfolio has multiple funds within it.
• It does not show or proof or accurately predict the future consistency of the investment.
• Usually, it assumes a bell-shaped distribution of data values indicating that the same probability exists for achieving values below or above the mean value which isn’t necessarily correct.
• The accuracy of the data rests in the size of the data set, i.e. the larger the data set, the more accurate the standard deviation is.

## Beta Ratio

### What is Beta Ratio?

• It is an instrument of the financial market used to quantify the performance of the mutual fund.
• It is a historical measure used to evaluate the investment portfolio’s returns over a period of time.
• It is used to quantify the mutual fund’s response to market volatility.
• It is a representation of the relative risk of the fund.

### Calculation of Beta

It is calculated as –

Beta ratio = Covariance/Variance of market’s returns.

Where,

Covariance = how two different stocks respond to each other in varying market conditions. A positive covariance indicates that they move in compliance with each other and a negative covariance indicates that they move in opposite directions.

Variance = is the price deviation of the fund from its average or mean.

### How to read Beta Values?

• Beta ratio starts with a baseline of 1.
• If the value is one, then the fund’s response is equivalent to the markets or the shift in the price of the mutual fund is the same as the benchmark movements.
• A beta value that exceeds one shows that the fund is more responsive than the benchmark movement.
• The converse is the case when the ratio is less than 1.

### Importance of Beta Ratio

• Beta values that show a value of one have low risk and low growth potential.
• An investor with a higher risk appetite must invest in a fund that has a beta ratio that exceeds one. The growth prospects of such a fund are high too.
• It can help the investor decide whether a specific fund must be included in the investment portfolio or not as it will help the investor identify the cause for good or poor performance of the fund.
• It overcomes the limitations posed by the standard deviation and sharpe ratio.

## Sharpe Ratio

### What is Sharpe Ratio?

The ratio is the average return that the investor gains as per the risk-free rate per unit of volatility or total risk.

It adjusts the portfolio’s past or future performance.

It is a fairly good estimation of the outperformance per unit of the portfolio’s volatility.

The higher the sharpe ratio, the better the fund is.

### How Is It Calculated?

It is calculated as –

Sharpe Ratio= Rp – Rfp

Where,

Rp =return of portfolio

Rf =risk-free rate

σp =standard deviation

### ​What is the Use of Sharpe Ratio?

It is used to keep tabs on the changes in the risk return when new assets or an asset class itself is added to the portfolio.

The Sharpe ratio calculated using past performance can be compared on a fair basis to expected future performance of the fund.

Sharpe Ratios above 1.00 are generally considered good.

A sharpe ratio of one might be considered inadequate.

### What are the Advantages of ssing the Sharpe Ratio?

• It helps find the risk adjusted returns of a particular fund.
• It can be used to evaluate past performance as well as future performance too.

### What are the limitations of using the Sharpe Ratio?

• It comes with an assumption that risk equals volatility which is a very narrow way of looking at all investments.
• Though a higher sharpe ratio implies better returns, these are only worth it if the higher returns are not a product of excess additional risk to the investor.
• A negative sharpe ratio fails to convey any useful meaning.
• It uses standard deviation as its denominator with an assumption that the returns are distributed normally, which need not necessarily be the case.
• Portfolio managers can use it to alter the risk-adjusted returns history. To do so, they have to increase the measurement interval or choose the best suited interval.

### Relationship Between Sharpe Ratio, Sortino Ratio and Treynor Ratio

• Sortino ratio is only a variation of the sharpe ratio.
• Sortino ratio removes the effects of price movements that move upwards.. Instead, it shows you the returns that are lesser than the required return.
• This ratio also replaces risk free rate with required return.
• Treynor ratio is a version of the sharpe ratio that is calculated using a portfolio’s beta (a measure of market volatility).
• The purpose of this ratio is to help find out whether investors are being rewarded for taking a risk.

Risk and reward must be properly considered when making investment choices. The aforementioned ratios help make these investment choices wisely.

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