The computational complexity of a naïve Monte Carlo estimator of a simple risk measure, involving a nested expectation, of a financial portfolio of P options is O (max(P ϵ^-2, ϵ^-3})) for an error ϵ. In this talk, we show that combining MLMC with an adaptive sampling strategy reduces the complexity to O(P ϵ^-2, ϵ^-2 |logϵ|^2). Moreover, by sub-sampling the options in the portfolio the cost is reduced further to O(ϵ^-2 |logϵ|^2), independently of P.