18 – M4 L3a 152 The Fundamental Law Of Active Management Part 2 V7

The breadth is the number of independent trading opportunities annualized. The key insight on this is the word “independent.” For example, if we are long 30 oil services stocks and short 30 semiconductor stocks for a year, how many independent bets is that? The answer is one. Not 60, one. Why? Because we expect the stock holdings in each sector are diversified to such an extent that we are likely not going to get any material impact from any one stock, and we have simply one bet that the oil service sector will outperform the semiconductor sector. The key takeaway here is that in order to maximize the number of independent bets in our portfolio, we need to remove exposure to common risk factors. Again, risk factors are factors which indicate which stocks have strong commonality. If we hold positions with strong commonality, then we are not holding independent positions. At the Alpha research stage, this is precisely why we often demean by sector. One way to improve our Sharpe ratio is to increase the probability that our Alpha factor can accurately choose the correct stocks. This is measured by the information coefficient. We should always strive to do this but recognize that this is indeed very challenging. The other way to improve performance is to increase the number of independent bets we make. This is the breadth. This is the key advantage quants have over everyone else; the ability to achieve high breadth. In general, a reason why institutional investors take a cross-sectional approach of trading multiple stocks is to maximize breadth and improve their performance which can be measured as the information ratio. Additionally, institutional investors will combine many Alpha factors, again to maximize breadth.

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