Portfolio Resampling: Review and Critique

A well-understood fact of asset allocation is that the traditional portfolio optimization algorithm is too powerful for the quality of the inputs. Recently, a new concept called “resampled efficiency” has been introduced into the asset management world to deal with estimation error. The objective of this article is to describe this new technology, put it into the context of established procedures, and point to some peculiarities of the approach. Even though portfolio resampling is a thoughtful heuristic, some features make it difficult to interpret by the inexperienced. "Portfolio Resampling: Review and Critique": A Comment A long-established problem of portfolio optimization is that it suffers from error maximization. The acceptability of quantitative methods in portfolio construction has suffered from this fact; eventually, these methods gave rise to risk budgeting to enforce diversification. At the heart of the problem lies the portfolio optimization algorithm, which is too powerful for the quality of the inputs. Because portfolio construction calls for decisions between marginal risks and returns of competing assets and because the inputs are measured with error, the efficient allocation of risk among investment opportunities requires a practical solution to the problem of estimation error.Recently, a method known as resampled efficiency has found increasing interest among practitioners as a way to deal with this important problem. In this article, I review the concept of portfolio resampling and resampled efficiency. One of the beauties of portfolio resampling is that it allows the user to visualize the impact of estimation errors on optimized portfolio weights, which otherwise would be virtually impossible because of the complex interactions among assets. Because resampling provides the distribution of portfolio weights, it can be used to test whether the inclusion of assets is statistically significant or whether additional information is sufficient to justify portfolio rebalancing (i.e., whether two portfolios are statistically different). Resampled efficiency allows the construction of efficient frontiers (geometric location of future investment opportunities) based on efficient sets that in most circumstances would be regarded as more diversified than traditional mean–variance-optimized portfolios. Changes in inputs or return requirements trigger only small changes in suggested allocations, so the algorithm compares favorably in the eyes of most practitioners with traditional mean–variance-based portfolio construction.As I review the portfolio-resampling method, however, I inevitably detect some weak spots. Although the lack of a decision theoretic foundation for the method might not be perceived as troublesome by many practitioners, other features are troubling in practice and deserve careful attention. First, the concept of resampled efficiency may force highly volatile and otherwise dominated assets into the solution. Samples from a highly volatile asset sometimes also exhibit very attractive mean returns, making that asset dominate all other assets at the aggressive end of the efficient frontier. Equally likely negative mean returns, however, will not yield large negative weights because the long-only constraint (which is so typical of institutional investors) does not allow negative allocations. The higher the volatility of the asset, the more pronounced this effect. Aggressive allocations derived via resampling should thus be treated with care.In addition, one of the basic properties of efficient-portfolio mathematics is that the efficient frontier does not contain upward-bending parts. Such a phenomenon would imply that one can construct portfolios superior to the frontier by linearly combining two neighboring frontier portfolios. Portfolio resampling, however, does allow upward-bending parts.A final criticism results from the special importance portfolio resampling gives to the original set of inputs. Because all resamplings are derived from the same vector and covariance matrix and the true distribution is unknown, all the resampled portfolios will suffer from deviation of the parameters from the true distribution in much the same way. Hence, it is fair to say that all portfolios inherit the same estimation error.Resampled efficiency is an interesting heuristic to deal with an important problem—error maximization. We do not have a theoretical basis for why it should be optimal, however, and it does have some characteristics that should make practitioners cautious when using it.