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So before we finish this session let's do two more things.

First, let me highlight once again that of these two ways of measuring risks,

both of them are what we call modern portfolio They come from the beginning

of modern portfolio theory but there are many other ways of measuring risk.

And, and that is important that you keep that in mind, because we're not going to

see more ways of measuring risk in this course, but if you ever take a course on

portfolio management, if you ever take a course on investment, that you will see

that there're many other ways of assessing the risk of, of different assets.

Now, all that being said in terms of risk, it's also important that, that you keep

in mind that the ways that we calculate risk actually may get very complicated.

But sometimes people think in very simple ways.

Sometimes people think in terms of the money that they can lose, or

sometimes people tend to think on how frequently they can lose money, or

how much money they can lose.

And so risk is a little bit sometimes we say in finance,

in the eyes of the beholder.

We might try to quantify many of these things.

We may try to get very sophisticated in terms of many of these things, but

at the end of the day, individual and

sometimes institutional investors think of risk in very different and sometimes in

more simple ways than we actually, people working in finance, attempt to do.

So to wrap up this session let's go back for

a minute, and let's try to highlight what are the main concepts that we discussed.

Concept number one was the concept of periodic returns.

Or simply the returns on any given period.

That is basically the combination of the capital gain or loss.

And that is basically given by the change of price between the beginning at the end

of any given period, and the cashflow, if any, that you actually put in your pocket.

When you put together the changing price and the cash flow that you might have put

in your pocket, and you standardize everything by the value that

you paid at the beginning of the period, that's what we call the periodic return.

And typically we're not happy enough with finance with one periodic return,

we want to have actually many periodic returns.

Many monthly returns, many annual returns.

So we can say something about the return and

the risk characteristic of these assets.

Now, once we have many of those periodic returns,

then we need to aggregate information.

And the way that we aggregate that information,

is by calculating some numbers that tell us something about the return of an asset,

and something that tell us some, some information about the risk of the asset.

There's three ways of calculating mean returns, of which we have explored two.

We explored the arithmetic mean return and the geometric mean return.

The arithmetic mean return is simply an average.

There's been high returns, low returns, positive returns, negative returns.

And in the typical period, this has been a particular return.

That number does not, and I stress that number does not give you

the mean on your rate at which your capital evolved over time.

That is the geometric mean return, which is the other definition that we've seen.

Geometric mean return is precisely what you get in any given period,

compounded over time on average.

So basically that's 7.7% if you remember that we've seen for

the world market, gives you the mean annual rate,

at which a capital investor in the world equity market evolved over time.

And that is the same number that you would get if you actually expose your

capital to all the returns of the ten years that, that we explore.

Second thing to, important to keep in mind about this mean returns.

Remember the relationship between the two.

The arithmetic mean return is always larger than or

equal to the geometric mean return.

But remember for all interesting assets in finance, which have some volatility all of

them, then the arithmetic mean return is higher than the geometric mean return.

Second important thing is that this difference is increasing in the volatility

of the asset, it's increasing in the variability of the asset.

And the reason that that is important is, remember the case of the Russian market.

I could actually be telling you about a very volatile market that has a very

high arithmetic mean return, but

the geometric mean return may be far lower or may even be a negative.

Particularly when we talked about volatile assets,

you shouldn't be happy enough we're talking about mean returns.

You want to know what type of mean returns you're reading about, or

you're talking about, or you're discussing about.

You want to know whether they're arithmetic or

geometric mean returns, because only the latter will tell you the rate at

which your capital invested in this particular asset evolved over time.

And finally we talked a little bit about risk.

And remember, there are many ways of actually thinking about the risk of

an asset, but there are two that come from more than portfolio theory.

Those two are what we call,

volatility, or the standard deviation of returns, and beta.

And these two are actually different ways of assessing risk.

One, is what we call an absolute measure of risk.

And it's absolute because we focus, we look at one specific asset.

That's the standard deviation of returns.

It basically gives you an idea of uncertainty,

the degree of fluctuations and the degree of variability in the returns of an asset.

And remember, we use it in relative terms, basically,

because the higher this number is, the more volubility we

observe in these returns over time, and the more uncertainty we're going to have,

in terms of the returns that we might get in the future for these particular assets.

So the higher this number, the higher the fluctuations have been, and

the higher is the uncertainty that, that we get.

The other measure of risk is what we call Beta.

And beta remember, is a measure of risk relative to the market.

Here the question is whether an asset magnifies or

mitigates the volatility of the market.

So an asset can actually magnify the volatility of the market,

it may go up by more and fall by more than the market, or

it can actually mitigate the volatility of the market.

It can go up by less and down by less than the market does.

And when that goes pretty much just like the market, that is a beta of one.

In the first case, is a beta higher than one.

And in the other case, it's a beta lower than one.

Final thing, and with this we finish this session.

This final thing sort of gives us the link to what's coming in the next session.

How do we go from beta to from standard deviation to beta?

Well, there, there's one way of thinking about this.

And the one way of thinking about this, very simply, is, if I put all my money in

one asset and I believe that the standard deviation is a proper measure of risk,

then that's the way that I'm going to perceive the risk of that asset.

Uncertainty about the returns that I'm going to get.

The higher this number, the more uncertainty I'm going to have.

So, that's basically one way of thinking about risk.

Now, what happens if instead of putting all my money in this particular asset

in isolation, I actually start building a portfolio with different assets.

Well, what happens is that part of the risk of

each individual asset diversifies away.

What does it mean diversify away?

Well, that if I have many assets in my portfolio, on any given day, week, or

month some assets will go up and some assets will go down.

I'll have some good news and some bad news on

the different companies in my portfolio, and a lot of those things will cancel out.

Well, many of things will cancel out, but many things will remain exposed too.

And that is what we call sometimes, the risk that we cannot diversify away.

And that is precisely what Beta measures.

So the way we go from volatility into beta,

is thinking if I have all my money invested in this one individual asset,

I assess risk with the volatility of the asset.

If I have this asset within a diversified portfolio, a lot of this risk diversifies

away and only the risk that I cannot diversify away, which is measured by beta,

is the risk I get to bear when I have this asset built into a diversified portfolio.

So, we'll discuss some of these issues in the second session.

This is the end of session one.

See you soon.

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