5 – M4 L4 06 Standard Constraints V4

But we’re not quite done. As you know, we can impose lots of different constraints on the problem. These usually have to do with real-world constraints on the way we want our portfolio to behave. Sometimes they just make sure our results aren’t really wacky. Let’s discuss some common constraints. First off, we need to think about whether our portfolio is long only or whether we are allowed to take short positions. We’d usually know this from limitations in our trading environment. If we needed to enforce the constraint that our portfolio be long only, we’d require that each of our portfolio weights to be positive. If we can take long or short positions, we’d place no such constraint. It’s very common to require that our portfolio be market neutral. What do we mean by that? In effect, it means that across the board, we short as much capital as we long. This means that we lose as much as we gain from movements that affect the entire market. In other words, when a portfolio is designed to be market neutral, the portfolio’s returns are hopefully less affected by movement in the entire market. We mentioned making the portfolio market neutral when we discussed alpha factors. The difference here is that we place this as a constraint on the portfolio weights themselves, so that the constraint will be enforced by the optimization. Hedge funds usually require that the sum of the weights be zero. However, an alternative is to control the balance of long to short positions by requiring that the sum of the weights remain in some range.

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