So here we have histograms of the returns of the two securities, Microsoft and IBM.

You see that now instead of having a representation through time,

we have a representation of the different possible returns.

The histogram represents the frequency,

how often we observe the various level of return.

And you see on the x-axis, on the horizontal axis,

we measure the level of return going from -20% to +20%.

Here it's written in decimal form, so we see we have -0.2 up to 0.2.

And the height of each of these blue bar represent the frequency.

So there is a very large bar here a little bit to the right of 0 for

Microsoft, which represent the most frequent observation of returns.

And then you have, for example, for Microsoft on the right-hand side,

a few little bars around 0.2.

These represent vary large monthly return, 20%.

But they occurred relatively rarely,

only a few occurrence were observable during that ten year period.

The same information is represented on the other graph for IBM.

You see that the two histograms are different.

They display the same type of information,

but the two financial securities have different return distribution.

In particular, we're very interested in observing a measure of tendency.

What's the average return?

What is the return we observe more frequently?

What is the average direction of the financial security and

how dispersed the distribution is?

The standard measure of tendency is going to be the expected return.

Whereas, the standard measure of dispersion

is going to be what we call the standard deviation, okay?

So from the histogram,

we can see that Microsoft seems to have a little bit more dispersion than IBM.

So a proper representation of dispersion would indicate that the metric

we used to measure dispersion is larger for Microsoft than it is for IBM.

So I've actually computed the average and standard deviation for

these two distribution and we're going to look at the result.

The standard deviation represents a measure of dispersion,

as I was saying, and it is computed by looking at the distance

of each observation from the average.