0:11

So, in order to now move on a little bit, we're going to think in terms of return.

Â We're going to focus for the next few minutes in terms of risk.

Â And, and the important thing here is, first and

Â foremost, in finance, these two things go always together.

Â You cannot really separate return from risk.

Â These are like two sides of the same coin.

Â You can only interpret properly a given amount of return only if

Â you're thinking of the return that, of the risk that investors are exposed to

Â when they expect or they get those those returns.

Â So, before we start with risks let's keep one thing in mind.

Â We can measure the return of an asset in two different ways.

Â As a matter of fact, there are three different definitions of mean returns.

Â One of which we will read directly from the technical note but

Â we will not actually cover in the, in this session.

Â So, let's say there's more than one way of calculating mean returns and

Â there's more than one way of calculating risk.

Â Before we start with, with thinking about possible definitions of risk, and

Â for our purposes we're going to cover two.

Â One thing that is important and I will highlight again at the end and

Â that is that there are very many definitions of risk.

Â In finance we may think about two or three ways of summarizing mean returns.

Â And, and again those different ways of summarizing mean returns.

Â They sort of designed to answer different questions and

Â they give you obviously different answers, numerical and, in terms of interpretation.

Â And exactly the same thing, is about risk, with one difference.

Â There are many more ways to access the risk of

Â an asset than they are to access the mean return of an asset.

Â And the reason for this is, is obvious if,

Â if you, I, I ask ten people to evaluate the performance of

Â an asset over ten years all of them will actually give me the same number.

Â They will look at the value of the asset at the beginning.

Â They will look at the value of the asset at the end.

Â They will look at the cash flows that they got in between.

Â And then they would calculate either the mean return, or

Â the return between the beginning and the end of the period.

Â But there's no controversy there.

Â Ten people looking at the same data will come up with exactly the same

Â return obtained by being invested in the asset over that ten year period.

Â If I were to ask those ten people to give me an idea of the risk of

Â the asset then I might get ten completely different answers.

Â Some people might focus on variability, some people might focus on losses.

Â Some people might focus on how large those losses were.

Â Some other people would focus on how frequently those losses happen, and

Â so, you know, we open a little bit of Pandora's box.

Â We don't really know what is going to come out.

Â And that is important that you know from the beginning that when we

Â assess the risk of an asset there are multiple ways of doing so.

Â Of all those ways we're going to focus on the two that are what we

Â typically call the standard of modern corporate finance ways of assessing risk.

Â And that is, just so that you get the names, are what we call volatility,

Â sometimes also called the standard deviation of returns and beta.

Â A beta is a very widely used variable very famous quote, unquote.

Â And we're going to encounter beta later on when we explore the cost of

Â capital in the third and fourth sessions of this of this course.

Â But again, before we actually define and

Â calculate the standard deviation of returns or volatility, and

Â beta keep in mind that we could actually assess the risk of the four assets we've

Â been working on, or any other asset in many, many, many different ways.

Â Now, modern portfolio theory sort of goes back to the early 50s.

Â And in the early 50s a guy by the name of Harry Markowitz that

Â eventually won the Nobel Prize in economics precisely for this

Â contributions to the risk of individual assets and to the risk of the portfolio.

Â What Markowitz actually proposed, is that, one way we can think of

Â the risk of an individual asset is by the variability of the asset.

Â And that is, technically speaking, what we call, the standard deviation of returns.

Â So, you may or may not know about, if I give you a very long series of returns,

Â I can actually look at that, the distribution of returns.

Â I can calculate the mean of that distribution, and

Â that would be the arithmetic mean that we already talked about.

Â And I can calculate the standard deviation, which basically gives you

Â an idea of dispersion around that arithmetic mean return.

Â So, you know, I could look at some asset, like for

Â example, a one year treasury bill.

Â In which, if we look at all the historical returns, we calculate the mean return and

Â we look at the dispersion around those mean returns.

Â Well, that dispersion is not going to be very large.

Â And the reason it's not going to be very large because, is simply because,

Â you didn't get very high returns, and you didn't get very low returns.

Â You get returns that are more or less clustered closely around that mean return.

Â Now, let's suppose that I give you instead the distribution of

Â returns of an emerging market, like Russia.

Â Well, you know, you calculate the arithmetic mean return, but

Â then you get returns that are very far away on the positive side, and

Â very far away from the negative side from that mean return.

Â That means that you get a lot more dispersion,

Â you get a lot more variability.

Â Why is that important?

Â Well because, one way you're thinking about this volatility or

Â standard deviation of returns is simply as a measure of uncertainty.

Â You know, in the case of the one year treasury bill,

Â history tells me that I'm not going to make a lot of money and

Â I'm not going to lose a lot of money is that, you know,

Â I have returns that are more or less predictable within a fairly narrow range.

Â But if I look at the history of the Russian market,

Â that actually will tell me that I have a huge uncertainty.

Â Because there are periods in which I could have more than doubled my money, and

Â there are periods in which I could actually lost more than half of my money.

Â And that uncertainty is precisely what the standard deviation tends to capture.

Â That volatility, that uncertainty, that variability is something that in finance

Â we do not spend a lot of time trying to think of the actual meaning of a number.

Â And another way to put that is to say that typically we look,

Â we use volatility in relative terms.

Â What does that mean?

Â Well, let's go back to our dataset that's the calculation of the volatility numbers.

Â And let me remind you of one thing.

Â Let me remind you that the numbers that we have here are total returns.

Â The numbers that we have here are dollar returns.

Â We have the arithmetic mean returns already calculated.

Â And what these numbers basically mean, and

Â remember we're not doing any formulas here.

Â You have the formulas in the technical node that

Â compliments this particular session.

Â But, you know, if you look at the number for the US, it's 17.9%,

Â 28% for Spain, 64% for Egypt and about 20% for the world market.

Â And what I was meaning before, when I said that we usually use this variable in

Â relative terms, is that we compare the 18% for the US with the 28% with Spain.

Â And we say, well, returns in Spain tend to fluctuate more and

Â they're more uncertain than they are in the US.

Â We compare the 28% of Spain with 64% of Egypt and

Â we say, well, you know, look at, just look at the returns.

Â Returns in Egypt tend to be far more variable than they are in Spain and

Â than they are in the US.

Â In other words, we never tried and, you know,

Â as much as, for example, for the geometric mean return.

Â We gave it very clear and

Â precise definition of what they, each of those numbers meant.

Â So, for example, the 7.7% for the world market was the mean

Â annual compound rate at which a capital invested evolved time.

Â We give a very precise definition.

Â We're not going to do that for the standard deviation.

Â And more often than not, that's the way we used it.

Â The higher the number, the more uncertainty,

Â the more variability in the data.

Â And so, do not stress to, you know, in trying to interpret well,

Â but what does 28% of one mean?

Â Well, if you actually look at the formula that we use to calculate a standard

Â deviation, strictly speaking, what that is, and you hold on to your seat here,

Â this is the square root of the average quadratic deviation,

Â with respect to the arithmetic mean return.

Â Now, you can as well, forget that.

Â You're not going to use the definition in that way.

Â What matters to you, is that 28 is higher than 18,

Â 64 is higher than 28 and 17, and 20 is lower than 64.

Â And that gives you an idea of relative variability, relative volatility,

Â of the markets that we're actually discussing.

Â So, that is as far as the interpretation of the volatility or

Â standard deviation goes.

Â The higher this number, the more dispersion around the mean,

Â the more variability in the data, the more uncertainty we have

Â about the returns that we observed, but obviously, the more uncertainty we have

Â about the returns that we expect from this particular from this particular asset.

Â And again, we're not really going to go much further,

Â in terms of trying to explain what we mean by volatility.

Â We're going to stay with the fact that the higher this number is, then the more

Â uncertainty you're going to have about the expected returns that that asset

Â might actually give you, particularly from the point of view of your pocket.

Â More uncertainty means, more uncertainty in terms of what capital you're going to

Â have, at the end of any given period.

Â And how that capital, is going to be fluctuating over time.

Â Now, one more thing and then we move on to the next measure of risk which is beta.

Â And another thing with volatility is you know,

Â the reason that sometimes we use it in relative terms is because if

Â you work in finance you would have some numbers in the back of your head.

Â So, for example, historical volatility, in annual terms of the US equity market,

Â is between 17 and 20%, depending on the periods that you actually look at.

Â But if you have that number in the back of your head and

Â someone shows you an equity market with a volatility of 60%,

Â well, you know, that that market is actually very volatile.

Â You're going to have a lot of uncertainty, but if someone actually brings you

Â an asset with a volatility, annual volatility of 5%,

Â then you know that this is a very stable asset, at least compared to the US market.

Â So, the way that we typically use volatility is,

Â again, not only in relative terms, but

Â also in relative terms after having a few numbers in the back of our head.

Â So again, two numbers that you may want to put in the back of your head is

Â historical volatility of the US equity market between 17 and 20%.

Â Historical bola, volatility of the US bond market between eight and

Â 11%, again, depending on the periods that you look at.

Â [MUSIC]

Â