The addition of uncorrelated or negatively correlated investment strategies, regardless of robustness, would significantly reduce the likelihood that the majority of funds would underperform over the short run (the most common evaluation horizon chosen by principals); therein lies the agent’s incentive to lose sight of the principal’s long-term best interest.
1. Today, many investment options offered as smart beta strategies, quickly becoming synonymous with factor investing, are not robust sources of long-run returns. Beck et al. (2016) present a framework under which a factor is considered to be robust if it: 1) is sufficiently well explored in the academic literature, 2) is robust to perturbations in definition, and 3) provides a return advantage in different geographies. Beck et al. find that value, momentum, and low beta factors are robust sources of long-run returns, whereas several popular factors, such as size, are not. The robustness of the quality factor, now that “quality” has come to mean many different things, is largely dependent on the way quality is defined.
2. More information is available on the potential costs to investor performance arising from “shorter” evaluation horizons in West and Ko (2014) and Aram and Treussard (2016).
3. The results are qualitatively similar if the firing rule is changed to “Fire the agent if the equally weighted portfolio aggregated from the selected funds underperforms the benchmark by more than 2%.”
4. These value-added returns do not take into account transaction costs.
5. Although value alone appears to generate a higher value-add (1.7%) than the combination of value and momentum (1.4%), the performance differences of 12.0% and 11.7% are not economically meaningful and likely not statistically significant. Note that we are not suggesting value outperforms a combination of value and momentum. The reason value does better in our particular case is that two non-robust versions of momentum are included in the momentum strategies: momentum based on 2-6 month past returns, rebalanced monthly, and 2-12 month past returns, rebalanced annually. To keep the firing rules consistent across perturbations, we need to keep the number of strategies in the allocation fixed at eight, which means that to equally allocate across value and momentum strategies, we need four value and four momentum strategies that are all different in order to mimic variation across different managers. Unlike value, only a limited number of ways to reasonably measure momentum are available, so we are forced to include two that are not very good at capturing the momentum premium. Because these performance measures do not account for implementation issues such as transaction costs, we should not read too much into their relative magnitudes.
6. Under Firing Rule Two, the chances of being fired are directly related to the tracking error because the firing rule is based on an allocation’s threshold value of benchmark underperformance. Under Firing Rule One, the chances of being fired are directly related to the correlation of the strategies in the allocation. Highly correlated strategies increase the chance that, at any given time, more than half of the strategies experience underperformance. We have discussed how diversification across uncorrelated or negatively correlated strategies results in an allocation that approaches the market, which means the more diverse the allocation, the lower the tracking error. So as an allocation’s strategies become less correlated, the allocation’s tracking error declines and along with it, the changes of being fired at any given time due to the simultaneous underperformance of strategies.
7. Technically, the agent is indifferent where these lines cross if all the agent cares about is their own risk of being fired. We assume, however, that the agent also cares about their fiduciary responsibility, and in the case of indifference, will choose the allocation that gives the principal the largest value-add.
8. Mathematically, the expected outperformance grows linearly with time while the confidence bounds grow at a rate proportional to the square root of time. This means that initially the growth is much faster than linear, while over longer horizons, the growth is slower than linear.
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