[MUSIC] Hi everyone. In this video, we're going to have a look at some common mistakes, which are made when talking about strategic asset allocation and risk and diversification. So these are the main outcomes of this video, some common mistakes you will no longer make after this video. Let's start with mistake number one. Mistake number one says, is the risk of the average equal to the average of the risks? Ooh, that sounds a bit mind boggling. Let's take one example, do you remember if you've done, which I hope, course number one? And when we talked about and a long short strategy, I gave you this illustration of a man working just outside a train station here in Geneva. And he was selling ice creams and so I thought maybe what he could do is the days when the weather is nice, he sells ice cream. And when it rains, he sells umbrellas. [LAUGH] And so, this inspired me the following simulations which I show here. Let's imagine we have two firms, one which sells ice creams, and the other one which sales umbrellas. And you are an investor and we are at the beginning of the summer and you need to make some weather forecasts to find out whether it's going to be the one who sells ice creams wins, or the ones who sells umbrellas. And so, this is how the two evolve and you can see that there's a negative correlation. When one goes up, clearly the other one goes down. It's rare that you see people eating ice creams under an umbrella. So here you have the returns of these two firms, and these two strategies. So if you're long ice creams, you will be generating a total return over summer of some 23%. If you're long, so if you're buying the umbrella firm, you actually lose 26%. So ice cream firm, umbrella firm. Here are the results. Performance, you see IC for ice cream, For umbrella. Plus 23, -26. And then, the second line underneath this, I've put downside volatility. This is a measure on which we will return. I will give you more details as to how we compute this. But with downside deviation or downside volatility, what we focus on is the left, the part of the distribution of returns which is to the left of the mean, i.e., subpar returns, for that is more interesting when you're an investor. So question to you, and that's a quiz, let's assume, you don't know whether it's going to be a hot summer or a rainy one. So you don't know whether it's going to be the ice creams or the umbrella who wins. So you decide to put half of your eggs in the ice cream firm and in the baskets and the other half in the umbrella perhaps, and this gives you the 50/50 portfolio. So the average performance as we may expect is 50% of 23 plus 50% -26 and that's -1.5, pretty straightforward. Now, now about the risk? How about the downside deviation? Is it the average, i.e., between 17.2 and 8.4, i.e., 12.8? In other words, if we present this graphically, would you say that the, we have the ice creams far on the right, we have the umbrellas down on the left. Would you say that the 50:50 portfolio lies exactly in the middle or straight line that goes between these 2 assets? We can think of ice creams are being equities and umbrellas as being bonds? Will the 50:50 portfolio be exactly there? Quiz for you. Think about this. The risk of an average portfolio, say 50 umbrellas and 50 ice creams is not equal to the average of the risks of these 2 firms or two assets. And you see from this table here. We have performance. We have downside volatility and you see the 50:50 portfolio. That's very interesting actually. Look at this, we have 50:50, -1.5 for the return and 5.2 for the downside risk, i.e., the 50:50 portfolio is actually less risky than the least risky of these firms, which are umbrellas, which is umbrellas, the umbrella firm. So it's interesting. If you think of this is being equities versus bonds, we could have that. When you diversify, you end up with a portfolio which is less risky than the least risky asset which is bonds. So this is the magic impact of diversification on which we will return. So graphically, this is what we have. Ice cream, umbrellas, the 50:50 portfolio does not lie in the middle but lies to see that far to the left and this is due to the impacts of decorralation or lack of correlation. Basically when ice creams go up, umbrellas go down and conversely so here in this particular instance we have a negative correlation between the two, i.e., you may reduce risk for a same level of return. [MUSIC]