1. Quoting Volatility
When comparing the volatility of different securities, it's really important
to compare like for like. This means if daily returns have been used
to get the daily standard deviation, we can't make a good comparison to
another security if weekly returns have been used to get a weekly standard
deviation. To make it easier to compare, volatility is almost always quoted
on an annual basis. There are about 260 trading days in a year,
to analyze daily standard deviations, which in turn, capped by squaring
data, the daily standard deviation is multiplied by the square root of 260
for it to be annualized. Weekly standard deviations will be multiplied by
the square root of 52 for the 52 weeks in a year,
and monthly data will be multiplied by the square of 12.
Let's use some weekly stop data in Excel to see this in action.
So let's go back to our workbook and open up the term called
quoting volatility. So here I am again, and my statistics for finance template
workbook, and I've scrolled down to the session called quoting volatility.
I'm also, in the next couple of lessons, going to be looking at
comparing securities, so I'm just going to leave the screen as it is
here by a focus on the top section, quoting volatility. Now,
I can use the shortcut Ctrl+Page down to go to the quoting volatility
sheet, and what I've got here is the weekly closing price for Apple
over a one year period. Well, I want to care at what the
weekly return is, I want to use continuously compounded return, so I'm going
to use my natural log function, and I'm just going to take the
closing price, 173.07 divided by the opening price,
close bracket. I can see that in the first week of 2022,
Apple had a 0.52% return. So I can do that all the way
down for the 52 weeks of the year. Ctrl+D to fill down and
I've worked out the weekly returns for Apple over 2022. So let's just
go back to my demo sheet. I want to work out what the
weekly standard deviation of returns are for Apple, so I'm going to use
the standard deviation of the for... Of a sample formula, and I'm going
to go back to the closing volatility sheet, and I'm just going to
select those weekly returns. Shift+Ctrl, arrow down to slick the whole column,
close bracket and hit Enter to come back to the demo workshop.
And we can see that Apple had a weekly standard deviation,
using the deviation of a sample former or 4.40%. Now, I want to
annualize this, so I have to think about my scaling factor.
Wow, I've got weekly returns. So to annualize this
weekly standard deviation, I'm going to take the square root of 52 because
it's 52 weeks in the year. So now the annualized standard deviation is
my weekly standard deviation multiplied by my scaling factor. So I can see
here that well Apple had a weekly standard deviation of a 4.40%, if I'm
gonna analyze that... And when we're quoting standard deviations, we usually
use the annualized number, Apple had an annualized standard deviation of
52.33%.
2. Let's practice!