Evaluation methods for portfolio management

We distinguish the evaluation methods for two main kinds of investment strategies, namely, passive and active portfolio management. Passive portfolio management aims at tracking an underlying index as close as possible with the most important measure being the tracking error. To claim the tracking error not exceeding a certain threshold, we apply the concept of noninferiority test as opposed to the common malpractice of one-sided test, which tries to accept the null hypothesis when there is insufficient evidence to reject it. In contrast, the normal one-sided test should be adopted in active portfolio management, which requires another crucial statistic, the information ratio, of an active portfolio to exceed the underlying benchmark in a risk adjusted sense. The asymptotic variances of the tracking error and the difference between two information ratios are derived, which allow proper evaluation and comparison of strategies within the passive and active portfolio management frameworks.