Historically speaking

Quantitative Finance Level 1

How is historical trading-day volatility measured?

Step 1:
A) Calculate the absolute change in closing prices as the data set.
B) Calculate the percentage change in closing prices as the data set.

Step 2:
C) Calculate the standard deviation of the data set.
D) Calculate the variance of the data set.

Step 3:
E) Multiply it by $\sqrt{ 252}$ .
F) Multiply it by $\sqrt{365}$ .

Image credit: Google Finance

A, D, E A, C, F B, C, F A, D, F B, D, E B, C, E B, D, F A, C, E

1 solution

Chew-Seong Cheong
Feb 15, 2015

In finance, volatility is a measure for variation of price of a financial instrument over time. Mathematically, volatility is defined as the standard deviation of price of a financial instrument. If the daily standard deviation of closing prices of a financial instrument is $\sigma_{SD}$ and the time period of returns is $P$ then the annualized volatility is given by:

$\sigma = \dfrac {\sigma_{SD}}{\sqrt{P}}$

There are $\approx 252$ trading days per year, we have $P = \dfrac {1}{252}$ , therefore,

$\sigma_{annual} = \dfrac {\sigma_{SD}}{\sqrt{\frac{1}{252}}} = \sigma_{SD} \sqrt {252}$

Thanks!

It has been pointed that I did not explicitly say that we're calculating the trading-day volatility. Those who previously answered "B, C, F" have been marked correct. I've updated the problem accordingly, and "B, C, E" is the correct answer.

Calvin Lin Staff - 6 years, 3 months ago

The standard convention is 252 trading-days/year.

George Tavlarios - 1 year, 4 months ago

That's true. I've updated the problem accordingly.

Calvin Lin Staff - 1 year, 4 months ago

Historically speaking

Image credit: Google Finance

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