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Basic measures of risk

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Basic measures of risk

In this module, we focus on the central problem of performance measurement: how do you assess the increase in your wealth over a given period and evaluate the risk that was involved? In this module, you will learn how to calculate different return and risk measures and how you use these measures to evaluate a portfolio’s performance relative to a benchmark.

Investment Strategies and Portfolio Analysis

Rice University

Course 4 of 5 in the Investment and Portfolio Management Specialization

In this course, you will learn about latest investment strategies and performance evaluation. You will start by learning portfolio performance measures and discuss best practices in portfolio performance evaluation. You will explore different evaluation techniques such as style analysis and attribution analysis and apply them to evaluate different investment strategies. Special emphasis will be given to recent financial market innovations and current investment trends. After this course, learners will be able to: • Describe performance measurement measures • Evaluate portfolio performance • Describe and contrast different investment strategies • Propose investment strategy solutions

Taught By

Arzu Ozoguz
Finance Faculty

Transcript

Hello, everyone, welcome back.

In the last few lectures, we talked about the different ways of measuring returns

to evaluate portfolio performance.

Of course, the next piece in evaluating performance is measuring risk, right?

After all, we would like to know if the return

provides an appropriate compensation for the risk involved in the investment.

So in this lecture, we're going to revisit how we measure risk.

If you've taken the previous courses, this should be a refresher for you.

If not, it should help you get up to speed.

All right. So what creates risk?

There are several different sources of risk or risk factors.

Right? What we call risk factors.

Some of them are related to economy-wide uncertainties or

fluctuations in the overall economy.

Others only apply to some asset classes more than others.

So, for example, here's a list of the different types of risks

that can be identified when investing.

You have business cycle risk, credit risk, interest rate risk,

exchange rate risk, political risk and so on.

Now, this list is by no means a completely exhaustive list for every asset class.

And not every asset class is exposed to each type of risk.

But you can see that there's a wide range of risks that might be encountered.

All of these sources of risk or risk factors

that cause asset prices to change as the factors change.

We will not have a full discussion how to measure each and

every type of these risks.

But you can think about the wide variety of risk factors that

assets can be exposed to.

Okay.

With that brief introduction to sources of risk, how do we measure risk?

As you remember from our previous courses,

we define risk as the variability or the dispersion in returns.

So the most common,

therefore, the most common measure of risk is the volatility of returns.

Right?

Which is measured as the standard deviation of the return distribution.

So, given a sample of N returns.

N observations.

How do we estimate the standard deviation, sigma, from a sample of N returns?

Well it is simply 1 over N-1,

by going from 1 to N.

All under the square root.

Where our i is basically

the return for observation i.

Our bar is the mean return

And is the number of observations we have.

Why is this N minus one?

Remember?

This is the sample standard deviation.

N-1 in the denominator is used to correct

the bias since r bar is an estimate itself.

If you replace N by N minus one with N.

In other words, with one over N then you would get the population.

Standard deviation.

So remember, what is the standard deviation.

Well, it's the square root of the average squared deviations from the mean.

Now, if we also assume that returns are, for all practical purposes,

normally distributed.

Then the standard deviation has various useful statistical properties.

For example, for a normal distribution, we would expect 68% of

all return observations to fall within the range of plus or

minus one standard deviation around the mean.

We would expect about 95% of all the observations to fall within plus or

minus two standard deviations from the mean.

And finally, we would expect 99.7% of all observations to fall within plus or

minus three standard deviations from the mean.

Right?

This is important because, this allows us to make probability statements about

how often good or bad events are expected to occur.

So for this reason standard deviations are fundamentally used for

measure of risk for distribution of asset returns.

Okay, so let me give you an example.

So here I have three years of quarterly returns for the Russell 3000 Index from

March 2003 to December 2005.

I calculated the mean, which is 12.82%,

which, by the way, is pretty high by historical standards.

And the sample standard deviation was 16.13%.

Now, under the normal distribution assumption,

you would expect 68% of the observations that we have to fall within the plus or

minus one standard deviation from this mean.

So, in the second column, I computed the deviation from the mean for you.

And in the last column, I noted whether the value falls, indeed,

within this plus or minus one standard deviation.

So understand it under normal distribution assumption, we would expect

about 8 out of these 12 observations to fall within this range.

What do we see?

Well, 1, 2, 3, 4, 5, 6, 7, 8,

9 quarters out of this 12 quarter period.

We're indeed within the range.

Okay.

So to compare returns over different periods,

we usually convert them to a standardized measure such as annualized returns.

So it's useful to know also how to convert the standard deviation for

one holding period to a annualized measure.

So say you have a monthly volatility measure.

How do we annualize this volatility?

Well, we multiply this

volatility measure by the square root of the number of holding periods in a year.

So if you have a monthly volatility we're going to

multiply it by the square root of 12 to get the annualized volatility.

So for example in the previous example, the standard deviation

of the Russell 3000 quarterly returns was 16.13%.

This is the quarterly volatility.

All right.

In order to annualize this volatility, we need to

Multiply it by the square root of four,

right, which is going to give us 32.26%.

We have the daily volatility, then we would compute the annualized volatility

by multiplying it by the square root of the number of days, weeks etc.

Same idea. All right, so

in this lecture we revisited how we measure risk.

Volatility is the most common measure of risk that we use.

And we measure volatility by the standard deviation of returns.

We also have the normal distribution.

Then we can make probabilistic assessments of how likely certain outcomes are,

depending on how widely distributed, how far away from the mean, they are.

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