Equity Valuation and Portfolio Management

MARGINAL CONTRIBUTION TO TRACKING ERROR

Since tracking error arises from various bets (some intentional and some unintentional) placed by the manager through overweights and underweights relative to the benchmark index, it would be useful to understand how sensitive the tracking error is to small changes in each of these bets.

Suppose, for example, a portfolio initially has an overweight of 3% in the semiconductor industry relative to its benchmark index, and that the tracking error is 6%. Suppose that the tracking error subsequently increases to 6.1% due to the semiconductor industry weight in the portfolio increasing by 1% (and hence the overweight goes to 4%). Then, it can be said that this industry adds 0.1% to tracking error for every 1% increase in its weight. That is, its marginal contribution to tracking error is 0.1%. This would hold only at the margin, that is, for a small change, and not for large changes.

Marginal contributions can be also calculated for individual stocks. If the risk analysis employs a multifactor risk model, then similar marginal contribution estimates can be obtained for the risk factors also.

Generally, marginal contributions would be positive for overweighted industries (or stocks) and negative for underweighted ones. The reason is as follows. If a portfolio already holds an excess weight in an industry, then increasing this weight would cause the portfolio to diverge further from the benchmark index. This increased divergence adds to tracking ...