Translating your objectives into financial metrics

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En provenance du cours de HEC Paris

Investment Management in an Evolving and Volatile World by HEC Paris and AXA Investment Managers

334 notes

HEC Paris

Investment Management in an Evolving and Volatile World by HEC Paris and AXA Investment Managers

334 notes

Have you ever wanted to invest in financial markets, but were always afraid that you didn’t have the proper tools or knowledge to make informed decisions? Have you ever wondered how investment management companies operate and what fund managers do? AXA Investment Managers, in partnership with HEC Paris, will introduce you to the most important ideas and concepts in investment management, to help you better understand your financial future. This course will enable you to: • Define what type of investor you are, your investment objectives, and potential constraints. • Identify the main investable assets and important players in financial markets. • Understand basic portfolio management techniques. • Apply these techniques in real case studies from the outset, through practical assessments. Finally, we will provide a comprehensive overview of today's asset management industry: the product cycles, professionals, and regulations. For those who want to identify a talented fund manager to invest for you, we offer important criteria for selecting one. For those who are interested in learning more about this fascinating industry, we lay the foundation for your ongoing financial journey. Join us now to explore the world of investment management! Course Launching Date The first session of the course will be launched on April 11th, 2016. Course Specialists The course has been developed in collaboration between HEC Paris, with Hugues Langlois managing the academic aspect, and AXA Investment Managers specialists, sharing their experiences and expertise and coordinated by Marion Le Morhedec. AXA Investment Managers participants include Maxime Alimi, Stephanie Condra, Nicholas Jeans, Elodie Laugel, Pierre-François de Mont-Serrat, Jean-Gabriel Pierre (AXA Group), Dorothée Sauloup, Irina Topa-Serry, Fiona Southall, Patrice Viot Coster, Susanna Warner, and Joachim Weitgasser. Recommended Background We expect most participants to have a basic level of knowledge in mathematics and economics. However this is not essential, and we believe that people from any background can succeed with commitment and a strong interest. Be aware that in the case study, you will have to use Excel. Course Format This course will run for 4 weeks and consists of 4 modules, each with a series of lecture videos between 5 to 8 minutes long. Each module contains a set of practice and graded quiz questions. A complete portfolio management exercise covers concepts learned in all modules Language The course is in English, with Spanish, Italian, German, French, and Chinese (Simplified) subtitles. The Project The preparation of this MOOC has been an exciting adventure for many professionals at AXA Investment Managers and HEC, both for the speakers and a wealth of contributors. Thank you to all of them. We hope you enjoy this course as much as we enjoyed creating it!

À partir de la leçon

Defining Your Objectives and Universe

As the first module of the course, we will start with helping you to identify which kind of investor you are, and what are your investment objectives. Then, we will give you an overall view of investible assets and the financial market. In addition, we will introduce the concepts of risk and returns in portfolio management which will help you to make better investment decisions.

Introduction to the Course2:22

What kind of investor are you?8:57

What do you want to achieve as an investor?7:22

Translating your objectives into financial metrics10:02

Rencontrer les enseignants

Hugues Langlois
Assistant Professor of Finance
Finance department
Marion Le Morhedec
Senior Fund manager
AXA IM

We discussed in the last video that investors can choose

investments by considering and optimising the following

trade-off: investment reward minus risk aversion, times

investment risk. Today, we see how to precisely measure

our preference metric.

The first part about investment reward is simple enough:

in almost all cases we will measure investment reward by

the expected rate of return E(r).

The expected return of a financial asset return r is the

probability-weighted average of its possible values.

For example if there are n possible values of returns so

r1 with probability p1, r2 with probability p2,

up to rn with probability pn; then the expected return

is given by the following equation.

So you have, expected return is equal to the

product of the probability and the return

value,

summed over all n possible values.

The expected return is a probability concept.

Expected returns are unknown; for example we do not know

what is the expected return on a stock like Amazon or Microsoft.

In reality we therefore use a statistical estimator to

estimate these expected returns.

The most often used statistical estimator of the expected

return is the sample average return.

If you have a sample of T returns, then the

sample average return is computed as the sum over all T

returns divided by T.

Here the hat symbol over E(r) indicates that we obtain an

estimator of E(r), not the true unknown value.

For example you can compute the average monthly return of

Amazon stock since it was issued, to estimate the

expected return over the next month.

Note that the sample average return is not the only

statistical estimator of the expected return.

You may think for example, that recent returns are more

representative of future returns, and consequently use

the average return on the most recent 5 years, instead of

using all historical returns.

But what about investment risk?

We start with the simplest measure of risk - the variance.

While it is not a perfect measure of risk, we begin with

variance because it happens to be the most widely used measure.

The variance is a measure of dispersion of returns around expected return.

As risk-averse investors, we prefer investments with

lower variance, because we are more certain of the return

we will realise on our investment.

The variance is also a probability-weighted average, like

the expected return.

However,

in this case, it is not a

probability-weighted average of all returns, but rather

we take the average of squared deviations of returns from

their expected value.

As we can use a sample average return to estimate the

expected return, we can use a sample variance of returns

to estimate the true unknown variance.

Here we divide by T-1, in order to obtain the

unbiased estimator.

We also often refer to this type of risk as the

volatility, which is the square root of variance.

The volatility of annual returns usually is a number such

as 5-10% for bonds, and 15-25%

for stocks in developed markets.

Now that we have a precise measure of investment reward

and risk, we can express our basic preference metric as

the expected return minus half of our risk aversion,

times the variance of returns.

As will become clear in module 2, we scale here risk

aversion by a factor of 1/2, just for mathematical convenience.

Note that we have not discussed how to measure risk aversion.

From experiments in psychology, we know that typical

values range from 2 to 10.

There are consultancy firms that specialise in measuring your risk aversion.

A simpler approach is to look at portfolios obtained with

different levels of risk aversion, and determine with

which you are more comfortable. So let's come back to our stock vs.

bond example from the last video.

This table contains the average return and volatility

computed over the whole sample, for both investments.

Stocks have outperformed bonds over the 1971 to 2015

period, but they also experienced higher volatility.

How can we then determine which one is preferable on a standalone basis?

This new row shows the preference metric computed with a risk aversion of 5.

An investment in the S&P 500, corresponds to a preference

equivalent return of 5.29%,

whereas bonds correspond to a preference

equivalent return of 5.94%.

By "preference equivalent

return", I mean that that the preference metric would be

the same for the stock investment than for an investment

with no risk that pays a return of 5.29%

We can use a preference equivalent

return in order to compare investments that have

different average return and volatility.

Naturally, we prefer investments with the highest

preference equivalent return.

Therefore, an investor with a risk aversion of 5, would

have been better off leaving all his savings in bonds during this period.

Because bonds'preference equivalent return at 5.94%

is higher than the one for stocks.

But hold on! There are no one-size-fits-all solution.

Consider an investor who is willing to take on more risk,

in order to potentially reap higher returns.

The last row here, shows a preference equivalent return

when you have a risk aversion of 2.

In this case it is 8.77%

for stocks, and only 6.59%

for bonds, which indicates this less risk-averse

investor would have been better off choosing stocks as an investment.

But even if the preference metric is harder for one

versus the other, is it still good enough?

We usually compute returns in excess of the risk-free

rate Rf, which is obtained by investing in a safe asset,

for example a short-term bond from a developed country's government.

We consider it as the ultimate benchmark, because we can

always park our money in the safe asset and achieve this

rate of return with no risk.

Clearly, an asset that has a preference metric of 5%, is

not as attractive when the risk-free rate is 8%, than when it is 2%.

So note that the preference metric of the risk-free

security is its rate of return Rf.

Over the 1971 to 2015 period, the average risk-free rate

of return was 5.21%, meaning that both our risk aversion

of 2 and risk aversion of 5 investors would have

preferred to invest either in the stock market or their

long-term bond, instead of the risk-free asset.

So let's wrap up with one question.

If your risk aversion is 2, do you prefer an investment

that has an expected return of 8% and a volatility of

15%, or an investment with an expected return of 9%

and a volatility of 20%?

Here, be careful not to use these numbers in percentage,

but rather in their decimal form.

The possible answers are:

a) I prefer the first investment

b) I prefer the second investment, or

c) I am indifferent between the 2 investments.

The answer is a. You prefer the first investment, which

has a preference equivalent return of 0.8

minus your risk aversion of 2, divided by 2,

times the volatility of 0.15,

squared in order to get the variance.

Which is equal to 5.75%,

hereas the preference equivalent

return of the second investment is only equal to 5%.

So we've discussed in this module the different types of

investors and what kind of preference they have.

We have also examined how to choose between different investments.

In the next lesson we dive deeper into financial markets

in which thousands of investments are available.

The choice will then become selecting the appropriate mix

of these investments.

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