7 – M4 L4 08 Factor Exposure And Position Constraints V3

Another common type of constraint limits the extent to which you are exposed to any individual factor. This is where you might impose specific limitations on your exposure to common risk model factors. Individual sectors, momentum, value, or company size. Remember that the factor exposure matrix has dimensions of assets and factors. When you multiply the transposed factor exposure matrix by the weight vector, which has dimensions of assets, you get a vector that has dimensions of factors. Thus, this product is still a vector. When we impose a constraint like this, where this is a single scalar, it means that the constraint applies to each element of the vector. That is, we apply the same constraint for every factor. Again, where do we get these constraint numbers from? They come from business and risk mandates. Finally, it’s common to place some ultimate constraints on the individual weights themselves just to ensure that you don’t end up in very extreme positions in individual assets. Again, remember that the weight vector is a vector with dimensions of assets, so placing a constraint like this applies to each asset weight in the vector. You can think of this constraint as a kind of insurance. In theory, the risk model should help limit portfolio risk. But in case there’s a problem with a risk model, setting limits on how much weight to put on any single stock also helps to protect the portfolio from concentrated risk exposure. This constraint is often impose so that the hedge fund can clearly communicate to investors that there is an absolute limit on the extent to which the portfolio is invested in any one asset. This value could be quoted in fund prospectus documentation.

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