[MUSIC] Learning outcomes. After finishing this video, you'll be able to understand the various factors that are to be considered when evaluating fund performance. Evaluate the performance of funds using metrics like Sharpe ratio, Information ratio, Sortino ratio and Treynor's ratio. How do you evaluate funds? [MUSIC] Managing a fund constituted of other people's money is not for the fainthearted. The reason behind the success of the fund management industry is that it is cost prohibitive for an average investor to accumulate the required information that is needed to manage a portfolio. More often than not, an average investor does not have the necessary education or the skills or the time to actively manage a portfolio. And therefore you have skilled people who offer their services for a fee to manage your money. It is assumed that they're able to efficiently allocate capital across funds so as to maximize returns. But how do you know whether they're doing it correctly or not? How do you know whether you are better off investing in a risk-free fixed income instrument, or an index fund, than handing over your money to a fund manager? Is the fund manager generating alpha? How do you rank a particular fund? In this section, we will try and explore some of these questions a little bit more. Let's start off with diversification. We've touched upon it before and we'll touch upon it again. Let's start with the basics, the free lunch available with financial markets. Diversification. The trick in putting together a portfolio is to find two uncorrelated return streams that, when combined together, offer superior returns. Combining two investments with the same expected return and the same volatility can provide the same expected return with low volatility. This is because of a lack of correlation. You can see that in this graph below. Two uncorrelated assets with identical distributions, combined together, get the same expected return, but lower volatility. So how can we see whether two return streams are correlated or not? One easy tool is a scatter plot. A scatter plot is a plot of x versus y that depicts what is going on in y while the same thing or something different is going on in x. They're two contemporaneous returns. It's a nifty tool to visualize the presence of correlation. Look at the scatter plots below. There are returns with high positive correlation, high negative correlation, and low correlation. For assets that are highly correlated, returns move in lock step with each other. If assets aren't correlated, the scatter plot has no discernible pattern. The plot on the extreme right. The correlation between returns two with the same volatility is quantified by the slope of the best fit line. If the line is flat, then the return streams are uncorrelated. Ideally, fund managers would be able to diversify. Like on the right, and generate positive expected returns at low risk with zero or no correlation. That would be the ideal investment manager. Now when evaluating [COUGH] Let's stop this, just. The ideal fund manager will diversify, like on the graph on the right, will generate positive excess return at low risk, with zero to low correlation with your existing portfolio. Here's the pickle in practice. Returns are easy to observe, correlations are not. The scale of a fund manager. Of an asset allocator, lies in picking assets that are uncorrelated. It's easy to see what is uncorrelated in the past, but even harder it is to see what will be uncorrelated in the future. Diversification can fail when you have positively correlated assets. Because that means you're repeating the same bets twice. Diversifying into negative correlated assets is also bad because the two offset each other while you're paying fees on both sides. So fees add up. My returns get cancelled out. So the ideal situation is low correlation to existing portfolio. Let's move on and try and judge the return distribution of funds. Suppose you have to choose between two funds, A and B. The return distribution of fund A is marked by the blue line, and that of fun B is marked by the orange line. Which one would you choose? The spread of the blue distribution is wider. In providing the presence of more extreme outcomes. The blue distribution has a higher standard deviation, and thus implies a higher probability of extreme events. On the right graph, the orange distribution is positively skewed, implying a bit greater chance of positive extreme events. Based on these two return distributions, we would choose fund B over fund D. [MUSIC]