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So I want to give a little more intuition about standard deviation as a measure of
risk. So I want you to think about two types of investments. So we're going to
invest in two stocks. Let's say, asset A is Amazon, asset B is Boeing, alright? And
we'll say we'll have monthly investments. So Ra is the monthly return of asset A.
That's a random variable. Rb is the monthly return of asset B. And let's just
assume that the normal distribution describes these distributions. So, the
monthly return on Amazon is normally distributed with mean mu A and variant
sigma A squared. The monthly return on Boeing is normally distributed with mean
mu B and variant sigma B squared. So, how do you interpret the parameters? Well, mu
A is the mean of the distribution for the return on asset A. That's the expected
monthly return. So if you invest in Amazon, you know what is the return that
you expect over the month? Well, it's the most, it's the middle of the distribution.
So that's so that's what mu A is. It's your expected return. And then sigma A is
the spread about the expected return. So this in sense measures the uncertainty
associated with the investment. So if sigma A is big there is lot of uncertainty
associated with your investment. If sigma A is small there is not much uncertainty
associated it. Now and the same is true for the parameters for mu B and sigma B.
Now one of the things that we typically find, so we actually look at real data on
investments in different kinds of stocks. Suppose that the average return, the
return that we expect on Amazon is bigger than the return that we expect on Boeing.
So in average we expect to get more money by investing in Amazon, than we expect to
get by investing in Boeing. We typically find that the standard deviation of the
return on Amazon is also bigger than the standard deviation on Boeing. So that when
one asset has a higher average return, it also tends to have higher standard
deviation, or higher risk. And so this is I like to call this kind of like the no
free lunch principle abo ut investing. You know, if one asset has a higher expect in
return. Well you don't get something for nothing. In order to get a higher average
return you typically have to take on more risk, right? Now this isn't always the
case but it's generally true. So what we'll often find in, in data is something
that looks like this. So if let's say the Boeing distribution is the blue line. So
on average we get a one% monthly return, and a standard deviation of five%. So the
dotted blue line represents my normal distribution for Boeing, okay? Now Amazon,
you get a higher average return, but you also have a higher standard deviation. And
so, that's this black line here. So on average we get a higher return, but
there's a bigger spread about the average which means we could have a, there's more
likely to get a bigger negative return, but it's also more likely we can get a big
positive return, okay? So you know, again there's risks on the upside and there's
risks on the downside, okay? When people talk about risk, they really I think most
people are concerned with the risk of loss so it's kind of downside risk. Standard
deviation and normal distribution is symmetric, right? So the risk on the
downside is the same as the risk on the upside. So, and some people view risk as
opportunity, right? So if you really care about making money, then you prefer the
black distribution because, you know, there's a higher likelihood that you can
get a big killing. But your results are higher likely that you can get a loss. If
you're willing to take the possibility of loss and you really like the upside gain,
then you might prefer the black distribution over the blue distribution.
On the other hand, if you're extremely risk adverse, if you don't like
uncertainty, then you would prefer the blue distribution so you might tolerate a
lower average return and, and it's because there's lower risk associated with that.