So, what are the learning objectives of this presentation?

First of all, to assess I would say the theoretical conceptual

limitations of MPT and of some of it's key assumptions.

Then we will actually ask ourself the question,

well do investors follow the MPT, and if not why and

what biases could explain their deviations from this optimal Asset allocations.

And then we'll say well, today, more than 60 years after it

was actually invented by Marcovitz in 1952, is MPT still alive?

Is he dead?

And what is the way, future.

So, just to remind you quickly,

we will talk about mean-variance optimization only with risky assets.

And the way to do that was shown by Markowitz to say you want

to maximize the expected return of your portfolio for a given level of risk.

And you can see that very nicely on that Hyperbola curve that you have here,

which upper part is efficient which means it maximizes the expected return for

a given level of risk.

And whose lower part is inefficient because at the same level of risk,

standard deviation namely,

you would have a lower portfolio return in expectation terms.

And all the points on the right side of the hyperbola would be called

inefficient portfolios or inefficient positions in single assets.

So the key principle that It's advocated is there is no free lunch.

The best way for you to optimize is to be well fully diversified,

and so achieve an expected return at the lower cost,

meaning at the lower risk level for your portfolio.

So, now let's look at in order to implement this MPT or

mean variance optimization, we need to rely on a certain number of assumptions.

So the first assumption is to say this model is valid if

either investor's utility is quadratic in their wealth or

U of V means the utility of wealth, which is equal to the wealth

minus the risk aversion coefficient B times the wealth squared.

Or you have to assume that asset returns,

let's say stock returns here, are jointly normally distributed.

Well, if we assume that investors have quadratic utility,

that leads to the absurd statement that as they get more wealthy,

they would invest less in the risky assets and

that certainly contradicts rational behavior.

So the quadratic utility has also been shown in the laboratory Is not a good

way to describe investors, risk tolerance or risk appetite.

Okay then let's leave side the quadratic utility,

but then in order to do MPT, I have to assume that asset returns or

stock returns are jointly, normally distributed.

So just to remind you, on the left graph the red bell curve which

is nicely shaped and symmetric around the mean, is the normal distribution.

The blue curve is a distribution which has thinner extremities,

it's called platykurtic.

And in fact stock returns would resemble the green distribution on the left,

which is so called leptokurtic.

It means it has fatter left and right tails.

Clearly a violation of the normality assumption.

Now let's look at the right Again,remember the red bell shaped