[MUSIC] Hello, this is Ines and today we are going to talk about the information ratio. You ask your fund manager to beat a certain benchmark. So the fund manager is going to try to deviate from the benchmark by changing the composition of the portfolio, investing in new stocks or removing some stocks. Changing the sector of the portfolio by putting let's say more weight on the IT compared to the benchmark or also invest more in small stocks and so on. So the return of the portfolio of the fund manager is going to be different from the benchmark and the difference in the return is what we call the active return. If we take the expected value of this active return which is just, actually an excess return relative to the benchmark, we obtain what we call the expected excess return relative to the benchmark. But your front manager by doing that is taking risk compared to the risk of the benchmark. How do we capture that? By taking the volatility of the active return. So the volatility of the active return is what we call the tracking error or also the active risk. So let's take a poll, what is the tracking error of an ETF that tries to stay very close to a benchmark? Yeah, sure you got it right. But the tracking error of this ETF is very close to zero as the case for its active return, by the way. Now, if we take the ratio of the expected excess return to the tracking error volatility, we obtain our information ratio. So it's something of ratio of these two things. The average active return or that we also call the expected excess return relative to the benchmark and in the denominator, the tracking error. So the information ratio is a risk adjusted performance measure of active manager relative to the passive index. A higher ratio, the higher the ratio the better. And in industry what is considered as a good information ratio something of 0.5 or higher of course. Now let's take another poll, the tracking error volatility is 4% and information ratio is 0.5. Can you please tell me what is the expected excess return of the fund, relative to the benchmark? Is it A, 2% or is it B, 12.5%? If you answered A, you got it right. Remember the information ratio, is that ratio between the expected accessory turn and the tracking error, here am giving you the tracking error and the information ratio. So just multiply this two and you will get the 2%. Well you probably saw something that looks similar, but watch this is completely different from the sharpe ratio. The sharpe ratio is also a ratio of excess return to volatility, but the excess return is measured relative to the risk free rate. And the volatility in the denominator is a total volatility risk, which is actually also the same as volatility of the excess return relative to the risk free rate. Now the information ratio is the ratio of the excess return to the tracking error, and the accessory return measured relative to the benchmark. And the tracking error is the volatility of the difference in the return between the portfolio of the fund manager and the benchmark. Let's now take an example. Here are ten observations of the realized returns on the portfolio of your fund manager. And I'm also providing you with the returns on the benchmark portfolio. If you take the difference between these two, you get the active return, that's the third column. As you see for example, the first row is just 4% minus 4%, that's the 0%. The last row's telling us that your fund manager had a return of -7% while the benchmark had -6% only. So your fund manager underperformed for that period by -1%. Now, if we take the average active return we get an average of 0.7%, that's just the average of these ten observations. If we take the standard deviation of this difference between the fund return and the benchmark return that we call the active return. You obtain a volatility of 2.5% and just take the ratio of these 2 you obtain an information ratio of 0.3. So what does this information ratio tells us? The information ratio tells us how much reward your fund manager was able to generate in relation to the risk she took by deviating from the benchmark. And we can use this information ratio either ex ante by putting constraint on our fund manager on how much tracking error he can take. And how much information ratio we want him to achieve or expose to measure the performance of the fund manager. So this is also a measure of the outperformance if it's positive, the outperformance on a risk adjusted basis. Compared to the risk that the manager took relative to the benchmark. Now this information ratio depends on the time period under measurement and on the choice of the benchmark. So let's go back to our example, and he realize that the fund manager missed to include two other observations. And these two other observations have an active return negative of 2%. So if we add these two observations and compute again the average active return, we obtain only 0.3%. We still have the similar tracking error of 2.5%. If we take the ratio of 2, we obtain an information ratio only 0.1. So you see that measurement period is very important to measuring this ex-post information ratio. Now, how about the choice of the benchmark? Let's assume that our fund manager actually was benchmarked against, this is what I call the benchmark two, which you see here in blue. And now we are computing, we are doing the same computation as before, we are computing the active return, taking the return of the fund minus the return on the benchmark. But now it's the benchmark 2 and that's what you read here in the last column of this table. And we're computing the average active return which is here -0.8%. A tracking error which is similar 2.6% what we had before and if you take the ratio of these 2, we obtain a negative information ratio of -0.3. Is it really true that the information ratio tells it all? Well, the information ratio does not tell us how this out performance was achieved. Was it really by the high skills of our fund manager or is it pure luck? Is it based on persistent small gains or just one extreme positive event? Does our fund manager really predicted this outcome based on his strategy? Is he going to be able to persistently beat the benchmark? So all these important questions that we cannot read from the information ratio. So what did we learn after this video, you'll be able to compute the active return tracking error and information ratio. Understand that the information ratio computed ex-post depends on the measurement period and on the choice of the benchmark. And understand where the information ratio tells us and what it does not tell us.