0:00

In this first session on defining and measuring risk,

Â we're going to focus our attention on what we refer to as stand-alone risk.

Â That is the risk that an investor faces when investing in a single

Â asset on it's own.

Â Now, before proceeding, it's important that we acknowledge that in the day-to-day

Â world the term is risk bantered about to mean many different things.

Â Common perceptions of risk include the chance of losing money, or the possibility

Â that something will go wrong, or the likelihood that a project will fail.

Â As you can see, risk is most often talked about with very negative connotations.

Â But in finance, we take a broader view of risk, and begin by defining it as simply

Â the chance that things might turn out other than expected.

Â For better or worse.

Â 0:46

Now to illustrate this interpretation of risk.

Â Let's work with an example.

Â You are now the CFO of a very large listed company.

Â Three of your division heads come to you and request funding for

Â three alternative projects.

Â You send them away and as your prerogative,

Â you ask them to come back after collecting data relating to the past performance of

Â similar projects that have previously been undertaken by the firm.

Â 1:25

So, working first with Project One, you see that on 20% of previous iterations in

Â the project the project generated a rate of return of exactly 0% per annum.

Â On 60% of occasions, the project generated a rate of 10% per annum.

Â And on another 20% of occasions it generated a return of 20% per annum.

Â 1:47

Looking at Project Two, we see a greater variability in returns as compared with

Â Project One, on both the upside, and the downside outcomes.

Â With a 10% chance of the project generating a negative return of minus 10%,

Â but on the upside, providing a 10% chance of a return of 30%.

Â 2:05

When we consider Project Three.

Â We see that the variability of the returns have increased once again.

Â With now the downside extending to a 2% chance of generating a return of -40%.

Â Yet on the upside a 2% of a return of positive 60%.

Â So, assuming that past return histories, or

Â distributions, are a fair indication of what future distributions might look like,

Â we can now estimate two very important measures from the previous data.

Â 2:38

Firstly, the expected return of each project is a measure of what

Â we expect to get out of the project where that expectation

Â is measured before the project begins.

Â The second important measure is the Standard Deviation of Returns.

Â Where we refer to these by the Greek letter sigma.

Â 2:58

Now this is a measure of the variability of the returns of the project,

Â relative to the expected return of the project.

Â Now, we're going to spend a fair bit of time working with these two measures in

Â the next couple of modules, so

Â it's important that we know exactly how to compute them.

Â So firstly, let's draw up each of the three projects and, specifically, let's

Â graph the returns that could occur for each project, which is on the horizontal

Â axis of each graph, against the frequency with which each return occurred.

Â Which is on the vertical axis of each graph.

Â 3:36

So, we can see from these that Project One has a range of outcomes centered much more

Â closely on the return of 10% per annum.

Â Whereas Project Three, while still centered on a return of 10% per annum,

Â exhibits a greater number of occasions where the returns greatly exceeded or

Â were far less than the 10% return.

Â 3:56

Now given our earlier definition of risk, referred to risk as suggesting that it

Â involved the chances that things might turn out other than expected.

Â Intuitively, it makes sense to think of Project Two as being riskier than Project One,

Â and Project Three as being riskier than Project Two.

Â So, let's calculate the expected return of Project One.

Â To do so, we simply multiply each return that could occur

Â by the likelihood of frequency of it occurring in the past.

Â We then add up all those numbers we have just calculated.

Â So there's a 20% chance that a return of zero occurs.

Â 20% times zero equals zero.

Â 4:37

Then there's a 60% chance that a return of 10% occurs.

Â 60% times 10% equals 6%.

Â Finally, there's a 20% chance of a return of 20%.

Â So 20% times 20% equals 4%.

Â All of the other returns have a zero probability of occurring,

Â and so they can be ignored.

Â We then add each of the numbers we have calculated, 0%, 6% and 4%,

Â and we end up with an expected return of 10% per annum for the project.

Â We go through the same process for Projects Two and Three.

Â And end up with expected returns for

Â each of these projects, of 10% per annum as well.

Â 5:18

Now let me pause for a second, and take the opportunity to suggest to you that,

Â even if you think you know what's going on,

Â it probably makes sense at times like this, to pause the video and

Â carefully reconstruct the numbers in the example yourself, so

Â that you can assure yourself that you actually do understand what's going on.

Â 5:37

So all three assets have the same expected return,

Â which isn't that surprising when we look at these three distributions.

Â But what about risk?

Â We definitely believe that the risk profile of the three projects is quite

Â different.

Â Let's see. The measure of risk that we will estimate here is what's referred

Â to as the standard deviation.

Â Which once again is denoted by the Greek letter sigma.

Â 6:49

Let's take Project One once again.

Â Starting with the return of 0%,

Â the distance from the expected return of 10% is minus 10%.

Â Step 2, we square that number and get 1%.

Â Step 3, we multiply that number, 1%,

Â by the likelihood that the initial return would occur,

Â which is 20% and we get 0.2%.

Â Doing this for each of the three possible outcomes of Project One yields a total

Â sum of square differences of 0.4%,

Â which is what we refer to as the project's variance, as denoted by sigma squared.

Â The square root of this number is 6.32%, which is the project's standard deviation.

Â So we go on and we repeat this for Projects Two and Three.

Â And as our intuition told us earlier,

Â we find that Project Two is riskier than Project One.

Â And Project Three is riskier than Project Two.

Â Project One has a standard deviation of returns of 6.32% per annum.

Â Project Two a standard deviation of returns of 10.95% per annum,

Â and Project Three 19.9% per annum standard deviation.

Â Well that's well in good if you're the CEO of a large listed company,

Â who can go order his or her minions, to go off and

Â collect the intricate data required to build the histograms needed to

Â then estimate project risk and expected return.

Â But what if your out on your own?

Â Lets say you're trying to get a hand on the risk of the shares

Â of different companies.

Â Well the good news is that's relatively straight forward.

Â 8:40

Thirdly we utilize a spreadsheet program,

Â like Excel, to calculate the standard deviation of returns.

Â And finally, by convention, we scale up our daily standard deviation

Â to a standard deviation as measured on an annual or per annum basis.

Â 9:04

Step one is to download the price file for this stock.

Â Now I use the Yahoo Finance website to download Kellogg's prices,

Â but there are other free databases around.

Â One good thing about the Yahoo website is that it provides adjusted closed prices,

Â which are useful, as they account for dividends.

Â Otherwise, you will need to make sure you add dividends back in on the ex-dividend

Â date to allow for the fact that shareholders have received

Â part of their return on that day in the form of cash.

Â 9:34

Step two is to convert daily prices into daily returns.

Â We do this by simply calculating the return for today by subtracting

Â the closing price of yesterday from the closing price of today and

Â then dividing that difference by the closing price yesterday.

Â So when the price for Kellogg's fell from $58.14 on the 2nd

Â of January to $57.92 on the 3rd of January 2014,

Â we recorded daily return of -0.378%.

Â So we'll repeat this using all of the daily closing prices for 2014.

Â And observe the frequencies with which different returns occur.

Â 10:28

As you can see from these histograms, for the well known social media company

Â Facebook, and the highly popular travel portal Trip Advisor,

Â return distributions do vary remarkably between companies.

Â With both of these companies exhibiting a greater spread in realized daily return

Â than as experienced by Kellogg's.

Â Interestingly, the S&P 500 index, which is a stock index that

Â consists of 500 of the largest most frequently traded stocks in the US.

Â That index exhibited a much tighter spread in returns,

Â as compared with the individual companies documented here.

Â 11:32

in 2014 is 1.0816%.

Â The final step is to convert that Daily Standard Deviation,

Â into a Yearly Standard Deviation.

Â By simply multiplying the Daily Standard Deviation figure

Â by the square root of the number of daily returns calculated over the full year.

Â So in this case, by the square root of 251.

Â This yields an annual standard deviation measure of 17.14% per annum.

Â Now of course,

Â if I had have used 12 months of monthly returns to estimate a monthly standard

Â deviation, I would have multiplied this figure by the square root of 12.

Â And if I had have calculated the weekly standard deviation by using

Â 52 weekly returns, I would have scaled that figure by the square root of 52.

Â Pretty straightforward, right?

Â When I do this for each of the other return series.

Â I end up with Facebook having a standard deviation of returns of 35.69% per annum.

Â TripAdvisor's standard deviation of 40.8% per annum, and the stock market index,

Â the S&P 500, a standard deviation of 11.33% per annum.

Â Which gels neatly with our intuition that told us that Facebook

Â looked riskier than Kellogg's, and TripAdvisor looked riskier than Facebook.

Â 13:07

In summary, in this session we've defined the concepts of expected return and

Â standard deviation of return, which is a measure of risk

Â that looks at the variability of returns, relative to an asset's expected return.

Â 13:20

We've also demonstrated how to measure standard deviation of returns,

Â using either historical returns and probabilities or

Â frequencies, and then historical returns on their own.

Â Next up, we're going to consider how different investors might regard

Â the trade-off between risk and return differently.

Â And that might help explain why different investors hold different portfolios of

Â assets with different risk profiles.

Â