[MUSIC] In this video we're going to look at the impact of correlation on portfolio risk and portfolio return. So, we are going to study the impact of correlation through an example. While typically when you construct a portfolio you have access to thousands of financial securities, we are going to illustrate what's going on in the risk of a portfolio through an example with simply three stocks, okay? And let's see how we're going to describe how the different characteristic of these stocks are going to affect the portfolio. So, in this graph I'm locating three financial securities in blue, A, B and C. These are the assets that you can use to construct your portfolio. You see that they're placed on a graph where on the x axis I measure standard deviation, measure of risk. And on the y axis I measure the expected return. So for example, stock A has an expected return of 3% and a standard deviation of 12%. Stock B, risk of 10%, expected return of 5%. And stock C risk of 20%, expected return of 8%. So typically when we invest our wealth in financial securities, we don't focus everything on a single security. We wouldn't buy 100% of stock C, or 100% of stock C. Rather, we would combine the different financial security to diversify our portfolio. So, what does it mean to actually diversify a portfolio? Well, let's look at what happens when we construct a portfolio, which here is invested at 20% in stock A, 20% in stock B and the remaining 60% in stock C. This portfolio is depicted on the graph here with the red cross and the label P, this is our portfolio. If we were to measure precisely the location of this portfolio, we will see that the return of the portfolio, which is 6.6%, is exactly the weighted average of the return of the individual securities. So far, so good. So we have a portfolio which has 20% in one stock, 20% in another, 60% in the last and its expected return is simply a weighted average, 20% of the return of Stock A, 20% of the return of Stock B, 60%, sorry, of the return of Stock C. The diversification effect, however, is displayed here by the location on the x axis. The stock A, B, and C are located here on the graph. And we see the level of risk and the level of return. What we don't see is their level of correlations. And actually, the correlations between A, B, and C is not perfect. So their level of correlation are below one. More precisely, the correlation between A and B is negative. Here it's -0.1 in this example. The correlation between A and C is positive. But it's not perfect. It's 0.4. And finally, the correlation between B and C is also not perfect. It is 0.3. So how does this level of correlation impact the risk of the portfolio? First of all, the portfolio p, as a risk level, if you measure really precisely you would see that the risk is 13.78%, so a little bit below 14%. However, if we take an average of the individual risk of the portfolio, so 20% of the risk of asset A, 20% of the risk of asset B and 60% of the risk of asset C, we wouldn't actually get the 14%. What we would get is something slightly to the right. We would actually obtain 16.4%. This effect of diversification, this reduction of risk is really at the heart of the portfolio construction. All this idea of diversification is the notion that some returns are going to compensate each other. It won't be at the detriment of the expected return. The general direction is not going to be affected by these compensation of return. However, we're going to observe a reduction in risk. The simplest way to see that is to look at the following very simplified graph of what diversification actually means. Here I've drawn two trajectory of prices. The thick line is Stock A and the dotted line is Stock B. And you see that they tend to move in opposite direction. They compensate each other if they are put in a portfolio. And the straight line that you see crossing in the middle would be the evolution of portfolio invested 50 50 in the two securities. What you see is that the average return, the general tendency of the portfolio is similar to the tendency of stock A and B. However, because the variation in B tend to go in opposite direction to the variation in A, they compensate each other and the risk of the portfolio is much lower than the risk of the individual securities. So this is the first lesson of this impact of correlation. It's summarized in a very simple sentence. The risk of the portfolio is inferior to the average of the risk of its constituents. This is the effect of diversification. [MUSIC]