# 17 – M4 L3a 151 The Fundamental Law Of Active Management Part 1 V4

A metric that is a special application of the Sharpe ratio is the information ratio. Recall that we are separating known factors as risk factors, which drive the variants of stocks and Alpha factors which drive portfolio returns after neutralizing to those risk factors. The return driven by risk factors is the systematic return, whereas the return driven by the Alpha factors after taking out the effect of risk factors, well, this is the specific return. The specific return is also referred to as the residual return because it is the residual amount of return that remains after taking out the systematic return. The information ratio is the Sharpe ratio applied to the specific return. So, it’s the average specific return divided by its standard deviation annualized. The information ratio can be interpreted as the Sharpe ratio that measures the performance that the fund manager contributes to the portfolio. Note that in the context of what we’re doing in this lesson, that is Alpha modeling, we are creating a market and common factor neutral portfolio. Note that in this case, the Sharpe ratio equals the information ratio. We simply introduced the term information ratio here because you will see it often in academic literature. As I stated previously, the most important metric in evaluating an Alpha factor and ultimately a trading strategy or fund is the Sharpe ratio. So, some good advice might be, okay, just create Alpha strategies with high Sharpe ratios. That advice though is pretty useless because it’s descriptive not proscriptive. In other words, it tells us what we want to achieve, but it says nothing about how to get there. So, how do we actually create high Sharpe Ratio strategies? Well, the fundamental law of active management gives us some insight. From a philosophical standpoint, perhaps the most important thing you will learn in this program is the following relationship; IR equals IC times the square root of B. This comes from the seminal work a Richard Grinold, which is aptly titled, the Fundamental Law of Active Management. This is further detailed in the subsequent book by both Richard Grinold and Ronald Khan titled, Active Portfolio Management. By the way, this formula IR equals IC times the square root of B sometimes referred to as the E equals MC squared of finance. I just want to make a point about this formula. This result is based on some simplifying assumptions and should be thought of as a guide. It would be more correct to say that IR is proportional to IC times the square root of B as opposed to equal. This is not a formula we will use directly. Meaning, we don’t actually use it to make calculations. Rather, we use this identity to direct how we structure our investment process. Also, don’t worry if the relationship between IR, IC, and B doesn’t look obvious to you as it’s not supposed to be. If you’re interested in the derivation, you can check out the original paper or the book by Grinold and Kahn. I haven’t defined what IR, IC, and B mean in the context of this relationship. But stay tuned, it’s coming up.