0:00

In this first session on defining and measuring risk,

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

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

asset on it's own.

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

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

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

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

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

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

the chance that things might turn out other than expected.

For better or worse.

0:46

Now to illustrate this interpretation of risk.

Let's work with an example.

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

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

three alternative projects.

You send them away and as your prerogative,

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

similar projects that have previously been undertaken by the firm.

1:25

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

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

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

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

1:47

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

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

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

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

2:05

When we consider Project Three.

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

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

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

So, assuming that past return histories, or

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

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

2:38

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

we expect to get out of the project where that expectation

is measured before the project begins.

The second important measure is the Standard Deviation of Returns.

Where we refer to these by the Greek letter sigma.

2:58

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

relative to the expected return of the project.

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

the next couple of modules, so

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

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

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

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

Which is on the vertical axis of each graph.

3:36

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

closely on the return of 10% per annum.

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

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

were far less than the 10% return.

3:56

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

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

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

and Project Three as being riskier than Project Two.

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

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

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

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

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

20% times zero equals zero.

4:37

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

60% times 10% equals 6%.

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

So 20% times 20% equals 4%.

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

and so they can be ignored.

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

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

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

And end up with expected returns for

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

5:18

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

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

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

carefully reconstruct the numbers in the example yourself, so

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

5:37

So all three assets have the same expected return,

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

But what about risk?

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

different.

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

to as the standard deviation.

Which once again is denoted by the Greek letter sigma.

6:49

Let's take Project One once again.

Starting with the return of 0%,

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

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

Step 3, we multiply that number, 1%,

by the likelihood that the initial return would occur,

which is 20% and we get 0.2%.

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

sum of square differences of 0.4%,

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

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

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

And as our intuition told us earlier,

we find that Project Two is riskier than Project One.

And Project Three is riskier than Project Two.

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

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

and Project Three 19.9% per annum standard deviation.

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

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

collect the intricate data required to build the histograms needed to

then estimate project risk and expected return.

But what if your out on your own?

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

of different companies.

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

8:40

Thirdly we utilize a spreadsheet program,

like Excel, to calculate the standard deviation of returns.

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

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

9:04

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

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

but there are other free databases around.

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

which are useful, as they account for dividends.

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

date to allow for the fact that shareholders have received

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

9:34

Step two is to convert daily prices into daily returns.

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

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

then dividing that difference by the closing price yesterday.

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

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

we recorded daily return of -0.378%.

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

And observe the frequencies with which different returns occur.

10:28

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

Facebook, and the highly popular travel portal Trip Advisor,

return distributions do vary remarkably between companies.

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

than as experienced by Kellogg's.

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

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

That index exhibited a much tighter spread in returns,

as compared with the individual companies documented here.

11:32

in 2014 is 1.0816%.

The final step is to convert that Daily Standard Deviation,

into a Yearly Standard Deviation.

By simply multiplying the Daily Standard Deviation figure

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

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

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

Now of course,

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

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

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

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

Pretty straightforward, right?

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

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

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

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

Which gels neatly with our intuition that told us that Facebook

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

13:07

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

standard deviation of return, which is a measure of risk

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

13:20

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

using either historical returns and probabilities or

frequencies, and then historical returns on their own.

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

the trade-off between risk and return differently.

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

assets with different risk profiles.