Of course, the next piece in evaluating performance is measuring risk, right?
provides an appropriate compensation for the risk involved in the investment.
So in this lecture, we're going to revisit how we measure risk.
If you've taken the previous courses, this should be a refresher for you.
If not, it should help you get up to speed.
All right. So what creates risk?
There are several different sources of risk or risk factors.
Right? What we call risk factors.
fluctuations in the overall economy.
Others only apply to some asset classes more than others.
that can be identified when investing.
exchange rate risk, political risk and so on.
Now, this list is by no means a completely exhaustive list for every asset class.
And not every asset class is exposed to each type of risk.
But you can see that there's a wide range of risks that might be encountered.
that cause asset prices to change as the factors change.
every type of these risks.
assets can be exposed to.
With that brief introduction to sources of risk, how do we measure risk?
we define risk as the variability or the dispersion in returns.
therefore, the most common measure of risk is the volatility of returns.
Which is measured as the standard deviation of the return distribution.
So, given a sample of N returns.
How do we estimate the standard deviation, sigma, from a sample of N returns?
by going from 1 to N.
All under the square root.
the return for observation i.
And is the number of observations we have.
Why is this N minus one?
This is the sample standard deviation.
the bias since r bar is an estimate itself.
If you replace N by N minus one with N.
In other words, with one over N then you would get the population.
So remember, what is the standard deviation.
Well, it's the square root of the average squared deviations from the mean.
Then the standard deviation has various useful statistical properties.
minus one standard deviation around the mean.
minus three standard deviations from the mean.
how often good or bad events are expected to occur.
measure of risk for distribution of asset returns.
March 2003 to December 2005.
which, by the way, is pretty high by historical standards.
And the sample standard deviation was 16.13%.
minus one standard deviation from this mean.
So, in the second column, I computed the deviation from the mean for you.
within this plus or minus one standard deviation.
about 8 out of these 12 observations to fall within this range.
9 quarters out of this 12 quarter period.
We're indeed within the range.
we usually convert them to a standardized measure such as annualized returns.
one holding period to a annualized measure.
So say you have a monthly volatility measure.
How do we annualize this volatility?
volatility measure by the square root of the number of holding periods in a year.
multiply it by the square root of 12 to get the annualized volatility.
of the Russell 3000 quarterly returns was 16.13%.
This is the quarterly volatility.
right, which is going to give us 32.26%.
by multiplying it by the square root of the number of days, weeks etc.
in this lecture we revisited how we measure risk.
Volatility is the most common measure of risk that we use.
And we measure volatility by the standard deviation of returns.
We also have the normal distribution.
depending on how widely distributed, how far away from the mean, they are.