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Given only the historic net asset value of a large-cap mutual fund, which members of some universe of stocks are held by the fund? Discovering an exact solution is combinatorially intractable because there are, for example, C(500, 30) or 1.4 × 10^48 possible portfolios of 30 stocks drawn from the S&P 500. The authors extend an existing linear clones approach and introduce a new sequential oscillating selection method to produce a computationally efficient inference. Such techniques could inform efforts to detect fund window dressing of disclosure statements or to adjust market positions in advance of major fund disclosure dates. The authors test the approach by tasking the algorithm with inferring the constituents of exchange-traded funds for which the components can be later examined. Depending on the details of the specific problem, the algorithm runs on consumer hardware in 8 to 15 seconds and identifies target portfolio constituents with an accuracy of 88.2% to 98.6%.