# How to implement industry neutralization?

How do you implement industry neutralization in S&P top 3000/top200? Market neutralization is straightforward but how do you assigns weights to the industries and then to stocks in it?

For classifying companies into industries, a common approach is to use a benchmark classification like the Industry Classification Benchmark or Thomson Reuters Business Classification.

These are generally multi-level classifications, from less granular to more granular. For example, the first level of the ICB (the "Industry" level) has categories Oil and Gas, Basic Materials, Consumer Goods etc. The fourth level ("Subsector") has Oil Equipment and Services, Pipelines, Renewable Energy Equipment, Alternative Fuels etc.

These classifications are generally binary, but for some large companies it may make sense to classify them across multiple industries or sectors.

To implement industry neutrality, one way is to consider your $n\times 1$ vector of positions $x$ (where $n$ is the number of stocks) and a $m\times n$ matrix $A$ (where $m$ is the number of industries) where

$$A_{ij} = \begin{cases} 1 & \textrm{stock j is a member of industry i} \\ 0 & \textrm{otherwise} \end{cases}$$

You have industry neutrality if

$$Ax = 0$$

which you can use a constraint in your portfolio optimizer, or otherwise implement with heuristics.

• Actually I'm asking how do you neutralize (equals Long and short) within the industry if particular weights are given to the stock. For example in market neutralization the weight of a stock w(new) = (w/Mean of all weights)-1. This is how we can market neutralize. But how to carry out industry neutralization? Jan 23, 2017 at 10:45
• You can do the same thing, but instead of "mean of all weights" you use "mean of all weights within each industry". I must point out that this is a very odd way to do market-neutralization, though! Jan 23, 2017 at 11:55
• But how do you allocate money to different industries? and in the end it should make BookSize/2 Long and Booksize/2 short. Jan 23, 2017 at 12:32
• Your allocation to each industry is up to you! A simple approach would be to assign equal risk to each industry portfolio. Or you could assign the risk to each industry portfolio in proportion to the market cap of stocks in that industry. Or assign weight to each portfolio in proportion to how much edge you think you have in the industry. There is not a single, canonical 'best' way to do it. The advantage of using a portfolio optimizer is that it is 'declarative' - you declare your objective function and constraints, and it makes the allocation decision for you. Jan 23, 2017 at 12:50