# Volatility Calculation Methodology

Daily fluctuations in stock/ETF prices can cause changes in the value of an investment portfolio. To assist users in anticipating the level of fluctuation that may occur with their smallcase investment, each smallcase is classified into one of the three volatility categories: High, Medium, and Low Volatility. This classification is based on a** comparison of the smallcase's volatility with that of the Nifty 100 Index.**

The process of identification of volatility label can be divided into three steps. Let's understand this with the help of an example.

## Standard deviation

smallcase FAME was created on 22nd Mar 2021. The smallcase has an index value of 100 as of 22nd Mar 2021 (to understand how Index value of a smallcase is calculated, please refer to return calculation methodology here). We will also require the value of Nifty 100 from 22nd Mar 2021 onwards for the calculation. Let's rebase Nifty 100 value to 100 on 22nd Mar for the purpose of illustration. The snippet of data on 22nd Mar 2021 is as below:

Value | Daily Return | |||
---|---|---|---|---|

Date | FAME Index | Nifty | FAME Index | Nifty |

31-Mar-21 | 99.60 | 99.65 | 0.92% | -0.86% |

30-Mar-21 | 98.70 | 100.51 | -0.14% | 2.07% |

26-Mar-21 | 98.84 | 98.48 | 0.96% | 1.27% |

25-Mar-21 | 97.90 | 97.25% | -1.89% | -1.63% |

24-Mar-21 | 99.78 | 98.86 | -1.16% | -1.75% |

23-Mar-21 | 100.96 | 100.62 | 0.96% | 0.62% |

22-Mar-21 | 100.00 | 100.00 | - | - |

On 10th Apr 2022, if we calculate the smallcase’s volatility ratio, we need to first calculate the rolling standard deviation of daily returns with a window of the last 1 year for both smallcase index and nifty. As per our data, we get the first set of 250 data points on 28th Mar 2022. To calculate the standard deviation on this date, we consider the daily returns from 23rd Mar 2022 to 28th Mar 2022 (both inclusive) and use the following formula:

σ = √(Σ(X - μ)^{2}/N)

X - The Value in the data distribution

μ - The population mean

N - Total number of observations

The snippet of data after performing mentioned calculation on 28th Mar 2022 is as below:

Value | Daily Return | Standard deviation | ||||
---|---|---|---|---|---|---|

Date | Index | Nifty | Index | Nifty | Index | Nifty |

28-Mar-22 | 159.34 | 117.24 | -0.58% | -0.30% | 1.65% | 1.01% |

25-Mar-22 | 160.27 | 116.90 | 0.95% | -0.34% | ||

24-Mar-22 | 158.77 | 117.30 | 0.37% | -0.09% | ||

23-Mar-22 | 158.18 | 117.41 | -0.83% | -0.30% | ||

22-Mar-22 | 159.50 | 117.76 | -0.24% | 1.01% | ||

21-Mar-22 | 159.89 | 116.58 | 1.32% | -1.04% | ||

17-Mar-22 | 157.81 | 117.80 | 0.42% | 1.79% | ||

16-Mar-22 | 157.15 | 115.74 | 4.16% | 1.92% | ||

15-Mar-22 | 150.88 | 113.55 | -0.55% | -1.19% | ||

14-Mar-22 | 151.70 | 114.92 | 0.99% | 1.18% |

Next, the same step is repeated for 29th Mar 2022 with the window of daily returns from 24th Mar 2022 to 29th Mar 2022.In the same manner, standard deviation value is calculated for the rest of the dates.

## Volatility Ratio

With the previous set of calculations, we have the data for final computation of volatility ratio. The formula for calculating Volatility Ratio is below

**Volatility Ratio (VR) = a/b** where

a = [0.7 *Average(Rolling 1y sd of smallcases daily return for last 1Y) + 0.3*Average (Rolling 1y sd of smallcases daily return, except last 1Y, and going back to a maximum of 5Y)]

b = [0.7 *Average (Rolling 1y sd of nifty’s daily return for last 1Y) + 0.3*Average (Rolling 1y sd of nifty’s daily return, except last 1Y, and going back to a maximum of 5Y) ]

On 10th Apr 2023, value of a is computed as follows:

Weight | 70% | 30% |
---|---|---|

Time Period | 05-04-2022 : 10-04-2023 | T-5Y or smallcase launch, whichever is later : 04-04-2022 |

Procedure | Average of Standard deviation of FAME index | Average of Standard deviation of FAME index |

Value | 1.56% | 1.65% |

**a** = 70% * 1.56% + 30% * 1.65% = **1.59%**

In the same way, value of b is computed as follows:

Weight | 70% | 30% |
---|---|---|

Time Period | 05-04-2022 : 10-04-2023 | T-5Y or smallcase launch, whichever is later : 04-04-2022 |

Procedure | Average of Standard deviation of FAME index | Average of Standard deviation of FAME index |

Value | 1.06% | 1.00% |

**b** = 70% * 1.06% + 30% * 1.00% = **1.05%**

Once we have values of a and b, we can divide these to get the value of volatility ratio.

**Volatility Ratio (VR)** = a/b = 1.59%/ 1.05% = **1.52**

## Volatility Label

Based on the value of the volatility ratio (VR), volatility labels are assigned as per the following cutoffs:

Volatility Ratio (VR) | Label |
---|---|

VR >= 1.2 | High Volatility |

0.8 <= VR < 1.2 | Medium Volatility |

VR < 0.8 | Low Volatility |

Now, in our current case, as the value of VR is 1.52 so the current portfolio will be getting a “High Volatility” label.

However, there can be cases where the history of smallcase is less than one year. In such cases, the above procedure cannot be applied and the volatility label is assigned based on the following logic:

If the weight of equities in the portfolio is

- less than 40%, the smallcase is assigned the Low Volatility label
- between 40% to 70%, the smallcase is assigned the Medium Volatility label

If the weight of equities in the portfolio is greater than 70%, then the weight of large-cap stocks within the equities portion is taken into consideration. In this case, if the weight of large-cap stocks within the equity portion is

- more than 85%, the smallcase is assigned the Medium Volatility label
- less than 85%, the smallcase is assigned the High Volatility label

For smallcases where the manager has not prescribed any weights, equal weights are assumed for calculations.

If the historical data of the smallcase exceeds 5 years, then the determination of the volatility label is made using only the information collected within the latest five-year timeframe.

Now, the same concept can be extended to Mutual Funds (MF) and individual stocks. Let’s go through MF and stock examples to illustrate this.

### MF Example:

Consider a mutual fund named 'MF FAME'. To understand its volatility, we will apply the same methodology used for smallcase portfolios.

The snippet of data after performing mentioned calculation on 22nd Mar 2021 is as below:

Value | Daily Return | |||
---|---|---|---|---|

Date | MF FAME Index | Nifty | MF FAME Index | Nifty |

31-Mar-21 | 98.76 | 99.65 | -0.52% | -0.86% |

30-Mar-21 | 99.28 | 100.51 | -0.26% | 2.07% |

26-Mar-21 | 99.53 | 98.48 | -0.72% | 1.27% |

25-Mar-21 | 100.26 | 97.25 | 0.84% | -1.63% |

24-Mar-21 | 99.42 | 98.86 | 0.02% | -1.75% |

23-Mar-21 | 99.9 | 100.62 | -0.61% | 0.62% |

22-Mar-21 | 100.00 | 100.00 | - | - |

After going through same set of calculations as mentioned in case of smallcase, the Volatility Ratio (VR) and Volatility Label on 10th Apr 2023 is :

Value of **a**:

Weight | 70% | 30% |
---|---|---|

Time Period | 05-04-2022 : 10-04-2023 | T-5Y or MF launch, whichever is later : 04-04-2022 |

Procedure | Average of Standard deviation of MF FAME index | |

Value | 0.97% | 0.99% |

**a** = 70% * 0.97% + 30% * 0.99% = **0.99%**

Value of **b**:

Weight | 70% | 30% |
---|---|---|

Time Period | 05-04-2022 : 10-04-2023 | T-5Y or MF launch, whichever is later : 04-04-2022 |

Procedure | Average of Standard deviation of nifty | |

Value | 1.06% | 1.00% |

**b** = 70% * 1.06% + 30% * 1.00% = **1.05%**

**Volatility Ratio (VR)** = a/b = 0.97%/ 1.05% = **0.93**

**Volatility Label** = Medium

However, there can be cases where the history of a mutual fund is less than one year. In such cases, Risk Category as assigned by the AMC is used to calculate the volatility label based on the following logic:

- Low Volatility label is assigned if the risk category is either Low or Low to Moderate
- Medium Volatility label is assigned if the risk category is either Moderate or Moderately High
- High Volatility label is assigned if the risk category is either High Risk or Very High Risk

### Stock Example:

Consider a stock named 'FAME'. To understand its volatility, we will apply the same methodology used for smallcase portfolios.

The snippet of data after performing mentioned calculation on 22nd Mar 2021 is as below:

Value | Daily Return | |||
---|---|---|---|---|

Date | Stock FAME | Nifty | Stock FAME | Nifty |

31-Mar-21 | 92.15 | 99.65 | 0.23% | -0.86% |

30-Mar-21 | 91.93 | 100.51 | -0.96% | 2.07% |

26-Mar-21 | 92.83 | 98.48 | 1.20% | 1.27% |

25-Mar-21 | 91.72 | 97.25 | -3.74% | -1.63% |

24-Mar-21 | 95.29 | 98.86 | -4.49% | -1.75% |

23-Mar-21 | 99.77 | 100.62 | -0.23% | 0.62% |

22-Mar-21 | 100.00 | 100.00 | - | - |

After going through same set of calculations as mentioned in case of smallcase, the Volatility Ratio (VR) and Volatility Label on 10th Apr 2023 is :

Value of **a**:

Weight | 70% | 30% |
---|---|---|

Time Period | 05-04-2022 : 10-04-2023 | T-5Y or stock launch, whichever is later : 04-04-2022 |

Procedure | Average of Standard deviation of Stock FAME index | |

Value | 3.44% | 3.36% |

**a** = 70% * 3.44% + 30% * 3.36% = **3.41%**

Value of **b**:

Weight | 70% | 30% |
---|---|---|

Time Period | 05-04-2022 : 10-04-2023 | T-5Y or stock launch, whichever is later : 04-04-2022 |

Procedure | Average of Standard deviation of nifty | |

Value | 1.06% | 1.00% |

**b** = 70% * 1.06% + 30% * 1.00% = **1.05%**

**Volatility Ratio (VR)** = a/b = 3.41%/ 1.05% = **3.26**

**Volatility Label** = High

In case, the price history of the stock is less than one year, the stock is assigned the High Volatility label.