CONSTRAINING SHORTFALL
The standard active management, mean-variance optimization problem trades off risk against return. To limit the portfolio's exposure to extreme losses, we may constrain the shortfall beta of the portfolio. This is done by adding a single constraint, giving us what we will call the shortfall-constrained optimization problem:
where h are the portfolio weights, α is the vector of alphas, Σ is the covariance matrix, and λ is the risk aversion parameter. The term βS is the vector of asset-level shortfall betas (βS,i) with respect to the benchmark portfolio and S is the maximum portfolio shortfall beta permitted.6
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