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So, what are the learning objectives of this presentation?

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

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

Â Then we will actually ask ourself the question,

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

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

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

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

Â Is he dead?

Â And what is the way, future.

Â So, just to remind you quickly,

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

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

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

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

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

Â a given level of risk.

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

Â standard deviation namely,

Â you would have a lower portfolio return in expectation terms.

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

Â inefficient portfolios or inefficient positions in single assets.

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

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

Â and so achieve an expected return at the lower cost,

Â meaning at the lower risk level for your portfolio.

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

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

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

Â either investor's utility is quadratic in their wealth or

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

Â minus the risk aversion coefficient B times the wealth squared.

Â Or you have to assume that asset returns,

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

Â Well, if we assume that investors have quadratic utility,

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

Â they would invest less in the risky assets and

Â that certainly contradicts rational behavior.

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

Â way to describe investors, risk tolerance or risk appetite.

Â Okay then let's leave side the quadratic utility,

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

Â stock returns are jointly, normally distributed.

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

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

Â The blue curve is a distribution which has thinner extremities,

Â it's called platykurtic.

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

Â which is so called leptokurtic.

Â It means it has fatter left and right tails.

Â Clearly a violation of the normality assumption.

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

Â 4:09

figure on the left was the normal symmetric around the mean.

Â Here on the right side you have two graphs where we show a negatively skewed and

Â positively skewed distribution.

Â The negatively skewed means that there's a higher probability of having

Â negative returns.

Â And that's precisely what you have when you invest in the stock market.

Â So to conclude, we have a violation of this normality assumption for

Â stocks, it's also true for bonds, it's also true for derivative securities.

Â So, then the next problem is that MPT is a one period model, a single period model,

Â but it's used for strategic asset location over long horizons.

Â So, in order to do this, again you have to make one of two assumptions.

Â Either you say investors have myopic utility functions,

Â that means they are short-sighted, and today they don't care about

Â what happens to their returns the next month or in one year or in ten years.

Â So, it would be like if i take my glasses off, and I don't see anything.

Â Okay so, clearly this is not the case.

Â So, what could you do then?

Â Well, you could see I apply the MPT optimization period by period and

Â I repeat it, but this is only valid or a correct way of doing

Â the optimization if returns are intertemporally independent.

Â And in fact, there's been hundreds of studies that have shown over short

Â horizons, daily, weekly, ssset returns,

Â in particular stock returns, tend to be serially positively correlated.

Â So that means that if the return is high today,

Â there is a likelihood it's going to be high the next day.

Â And over long horizons, well, here the idea would be the following.

Â Suppose I have a horizon here of one, two, three, up to ten years.

Â And I ask myself, suppose I want to forecast the five year ahead horizon,

Â by looking at the five preceding years behind me returns.

Â 6:27

In principle, if returns are independent, there's no information in the past

Â previous five years returns, to predict the five years ahead returns.

Â And, regressing, that means, running a relationship

Â where you look at the return of the next five years,

Â as a function of the return over the preceding five years should give you

Â a coefficient, a slope coefficient, which is equal to 0.

Â If you look at the column 5 return horizon years for

Â 5 years, you see that in fact you get coefficients for

Â an equally weighted portfolio of -0.47.

Â And the decile rows are for the market cap of the portfolio.

Â And you see that these coefficients are not equal to zero and

Â the star means they're significantly different from zero, which means, and

Â since they're negative, that returns tend to be negatively, serially correlated or,

Â in other words, display mean reversion in the long horizon perspective.

Â 7:36

Now let's look again at utility.

Â We said you can use MPT if you assume quadratic utility,

Â but the Nobel Prize winners Kahneman and

Â Tversky have actually looked at people in the laboratory, and

Â shown that the utility function is actually not symmetric for most investors.

Â In other words, it hurts more for me to lose $10 than it makes me happy to

Â gain $10, so it means I'm a loss averse investor.

Â So to summarize, the joint normality assumption or

Â the quadratic utility assumptions are violated, but

Â so is the intertemporal optimization,

Â which relies on the single period mean variance optimization model.

Â And that may question why this model is still alive.

Â So we'll stop here for the theoretical assumptions, and

Â let's see in the next video whether people follow the [INAUDIBLE].

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