Question

5) If the weekly volatility of a stock is 2%, what is the monthly volatility?

Answer 1

Solution:

Given:

Weekly Volatility or Standard Deviation of Stock = 2 %

To Calculate:

The Monthly Volatility of the Stock.

Process: Calculations:

Note: In order to calculate the monthly volatility of the stock, first we will find the annual volatility of the stock from weekly volatility and then find the monthly volatility from the calculated annual volatility.

Step: 1 Calculation of Annual Volatility of Stock from Weekly Volatility:

Formula:

Annualized Volatility of Stock = Weekly Volatility of Stock × √ 52

Explanation of Formula:

Since there are Total 52 Weeks in a Year, so we multiply the square root of 52 in Weekly Volatility to find the Annual Volatility of Stock. It is due to the reason that Volatility is Standard Deviation and Standard Deviation is the square root of Variance.

Here:

Weekly Volatility of Stock = 2 %

On putting the values in the formula, we get,

Annualized Volatility of Stock = 2 % × √ 52

Annualized Volatility of Stock = 2 % × 7.2111025509

Annualized Volatility of Stock = 14.422205102 % ≈ 14.42 %

Annualized Volatility of Stock = 14.42 %

Step: 2 Calculation of Monthly Volatility of Stock from the Calculated Annualized Volatility with respect to Weekly Volatility:

Formula:

Monthly Volatility of Stock = Annualized Volatility of Stock / √ 12

Explanation of Formula:

Since there are Total 12 Months in a Year, so we divide the Annual Volatility by the square root of 12 to find the Monthly Volatility of Stock. It is due to the reason that Volatility is Standard Deviation and Standard Deviation is the square root of Variance.

Here:

Annualized Volatility of Stock = 14.42 %

On putting the values in the formula, we get,

Monthly Volatility of Stock = 14.42 % / √ 12

Monthly Volatility of Stock = 14.42 % / 3.4641016151

Monthly Volatility of Stock = 4.1626954409 % ≈ 4.16 %

Monthly Volatility of Stock = 4.16 %

Ans: Monthly Volatility of Stock = 4.16 % (Approximately).