# 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. Lets understand this with the help of an example.

## Standard deviation

Portfolio FAME was created on 22nd Mar 2021. The portfolio 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. Lets 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:

DateValueDaily Return
FAME IndexNiftyFAME IndexNifty
31-Mar-2199.6099.650.92%-0.86%
30-Mar-2198.70100.51-0.14%2.07%
26-Mar-2198.8498.840.96%1.27%
25-Mar-2197.9097.25%-1.89%-1.63%
24-Mar-2199.7898.86-1.16%-1.75%
23-Mar-21100.96100.620.96%0.62%
22-Mar-21100.00100.00--

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:

ValueDaily ReturnStandard deviation
IndexNiftyIndexNiftyIndexNifty
28-Mar-22159.34117.24-0.58%-0.30%1.65%1.01%
25-Mar-22160.27116.900.95%-0.34%
24-Mar-22158.77117.300.37%-0.09%
23-Mar-22158.18117.41-0.83%-0.30%
22-Mar-22159.50117.76-0.24%1.01%
21-Mar-22159.89116.581.32%-1.04%
17-Mar-22157.81117.800.42%1.79%
16-Mar-22157.15115.744.16%1.92%
15-Mar-22150.88113.55-0.55%-1.19%
14-Mar-22151.70114.920.99%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 2022, value of a is computed as follows:

Weight70%30%
Time Period05-04-2022 : 10-04-2023T-5Y or smallcase launch, whichever is later : 04-04-2022
ProcedureAverage of Standard deviation of FAME indexAverage of Standard deviation of FAME index
Value1.56%1.65%

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

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

Weight70%30%
Time Period05-04-2022 : 10-04-2023T-5Y or smallcase launch, whichever is later : 04-04-2022
ProcedureAverage of Standard deviation of FAME indexAverage of Standard deviation of FAME index
Value1.06%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 cuttoffs:

Volatility Ratio (VR)Label
VR >= 1.2High Volatility
0.8 <= VR < 1.2Medium Volatility
VR < 0.8Low 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.