[MUSIC] So, welcome to this session on the pitfalls of modern portfolio theory which we shall call MPT. 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 figure on the left was the normal symmetric around the mean. Here on the right side you have two graphs where we show a negatively skewed and positively skewed distribution. The negatively skewed means that there's a higher probability of having negative returns. And that's precisely what you have when you invest in the stock market. So to conclude, we have a violation of this normality assumption for stocks, it's also true for bonds, it's also true for derivative securities. So, then the next problem is that MPT is a one period model, a single period model, but it's used for strategic asset location over long horizons. So, in order to do this, again you have to make one of two assumptions. Either you say investors have myopic utility functions, that means they are short-sighted, and today they don't care about what happens to their returns the next month or in one year or in ten years. So, it would be like if i take my glasses off, and I don't see anything. Okay so, clearly this is not the case. So, what could you do then? Well, you could see I apply the MPT optimization period by period and I repeat it, but this is only valid or a correct way of doing the optimization if returns are intertemporally independent. And in fact, there's been hundreds of studies that have shown over short horizons, daily, weekly, ssset returns, in particular stock returns, tend to be serially positively correlated. So that means that if the return is high today, there is a likelihood it's going to be high the next day. And over long horizons, well, here the idea would be the following. Suppose I have a horizon here of one, two, three, up to ten years. And I ask myself, suppose I want to forecast the five year ahead horizon, by looking at the five preceding years behind me returns. In principle, if returns are independent, there's no information in the past previous five years returns, to predict the five years ahead returns. And, regressing, that means, running a relationship where you look at the return of the next five years, as a function of the return over the preceding five years should give you a coefficient, a slope coefficient, which is equal to 0. If you look at the column 5 return horizon years for 5 years, you see that in fact you get coefficients for an equally weighted portfolio of -0.47. And the decile rows are for the market cap of the portfolio. And you see that these coefficients are not equal to zero and the star means they're significantly different from zero, which means, and since they're negative, that returns tend to be negatively, serially correlated or, in other words, display mean reversion in the long horizon perspective. Now let's look again at utility. We said you can use MPT if you assume quadratic utility, but the Nobel Prize winners Kahneman and Tversky have actually looked at people in the laboratory, and shown that the utility function is actually not symmetric for most investors. In other words, it hurts more for me to lose $10 than it makes me happy to gain $10, so it means I'm a loss averse investor. So to summarize, the joint normality assumption or the quadratic utility assumptions are violated, but so is the intertemporal optimization, which relies on the single period mean variance optimization model. And that may question why this model is still alive. So we'll stop here for the theoretical assumptions, and let's see in the next video whether people follow the [INAUDIBLE]. [MUSIC]