Smart beta multi-factor portfolio construction: The tracking error factor

Felix Goltz

Felix Goltz

Felix Goltz explores how dynamic risk allocation can deliver the benefits of factor investing without the crippling tracking error risk

M any investors are seeking to improve the performance of their equity portfolios by capturing exposure to rewarded factors. However, factor-tilted portfolios may expose investors to substantial relative risk – deviations from cap-weighted reference indices which might result in underperformance over any given short time horizon, despite the long-term potential for outperformance provided by the factor tilts. 

It is often the case that investors maintain the cap-weighted index as a benchmark, which has the merit of macro-consistency and is well-understood by all stakeholders. In this context, a multi-smart-beta solution can be regarded as a reliable cost-efficient substitute for expensive active managers, and the most relevant perspective is not an absolute-return perspective but a relative perspective with respect to the cap-weighted index. 

In this article, we present two risk-allocation approaches that may be suitable for enhancing performance with limited relative risk: 

• Equal (relative) risk budgets. A relative equal risk allocation (R-ERC) portfolio, which focuses on equalising the contribution of the smart factor-tilted indices to the portfolio tracking error.

• Minimum (relative) risk approach. a relative global minimum variance portfolio (R-GMV), also known as minimum tracking error portfolio, which focuses on minimising the variance of the portfolio relative returns with respect to the cap-weighted index. Note that we implement this approach under long-only constraints.

We refer to the 2014 paper ‘Risk Allocation, Factor Investing and Smart Beta: Reconciling Innovations in Equity Portfolio Construction’ from the EDHEC-Risk Institute with the support of Amundi ETF & Indexing, for a detailed discussion of these allocation procedures. In this article, we discuss the composition and performance statistics of applying this approach to an equity universe of large and mid-cap stocks from developed markets. 

The Developed dataset extends over the 10-year period from 31 December 2003 to 31 December 2013 and uses five non-overlapping regions from the global developed universe: US, UK, Developed Europe ex-UK, Japan and Asia Pacific ex-Japan. Using four smart multi-strategy indices as proxies for the value, size, momentum, and volatility-rewarded tilts in each sub-region, we obtain a total of 5x4=20 constituents. Tests of these approaches over long-term US data (over 40 years) have led to qualitatively similar results and are reported in the full EDHEC-Risk Institute paper.

In figure 1, we show the allocations of the relative GMV and relative ERC portfolios. First of all, we find that the relative ERC allocation is more stable over time, which is due to the higher sensitivity of the relative GMV allocation to the parameter estimates, confirming a higher degree of robustness with the ERC approach. Even though both allocation strategies rely on risk parameter estimates, the risk minimisation approach tends to over-use input information compared with the more agnostic risk-budgeting diversification, which makes more parsimonious use of input estimates.

1 Weight distribution - relative ERC

2 Weight distribution - relative GMV

3 In-sample relative risk contribution by asset - relative ERC

4 In-sample risk contrbution by asset - relative GMV

Secondly, by construction, we observe that relative ERC leads to identical constituent contributions to the tracking error. However, the relative GMV portfolio involves non-equal time-varying contributions from various constituents to the tracking error of the portfolio. This observation is in line with the relative GMV objective – that is, the components that have high tracking error are under-weighted relative to ones that have lower tracking error.

Figure 2 displays the risk and return characteristics of the relative ERC and GMV allocation strategies. We note that the focus on relative return leads to low tracking error levels. For example, the ex-post tracking error is around 2.50% for these portfolios. Relative GMV, as per its objective, results in lower tracking error (2.43%) compared with relative ERC (2.56%). However, relative ERC exhibits greater outperformance (+3.12%) compared with relative GMV (+2.15%).

Relative ERC and relative GMV allocation to the CW index across smart factor indices

The table compares the performance and risk of Scientific Beta Diversified Multi-Strategy indices converted into US dollars. We look at relative ERC and relative GMV allocations invested in the 20 Diversified Multi-Strategy indices with stock selection based on mid-cap, momentum, low volatility, and value in the five US, UK, Developed Europe ex-UK, Japan and Asia Pacific ex-Japan sub-regions. Outperformance Probability is the probability of obtaining positive excess returns over CW if one invests in the strategy at any point in time for a period of three years. It is computed as the frequency of positive values in the series of excess returns assessed over a rolling window of three years and step size of one week covering the entire investment horizon. The quarters with positive market returns are considered bullish and the quarters with negative returns are considered bearish. The period is from 31 December 2003 to 31 December 2013

2. Relative ERC and Relative GMV allocation to the CW index across smart factor indices (developed universe)

Such low tracking error levels, associated with substantial outperformance, eventually lead to exceedingly high information ratios. In particular, the relative ERC has an information ratio of 1.22, which is the highest level among all portfolio strategies tested so far, with an outperformance probability of 100% over any given three-year investment horizon during the same period. We also find that the focus on relative risk leads to lower tracking errors in bull and bear market regimes compared with their absolute risk counterparts.

The benefit of exposure to multiple factors can be seen from conditional performance analysis. Both allocations are able to outperform the cap-weighted (CW) benchmark in both bull and bear market conditions. For example, the relative allocation beats the CW benchmark by 2.30% in bull markets and by 3.92% in bear markets.

When considering the risk and return properties of our risk allocation strategies applied to smart factor indices, we find that substantial value can be added. In particular, using the relative ERC or relative GMV approach at the allocation stage, improves outcomes for investors with a tracking-error budget. As a result, extremely substantial levels of risk-adjusted outperformance (information ratios) can be achieved even in the absence of views on factor returns. 

The portfolio strategies we have presented in this article can be regarded as robust attempts at generating an efficient strategic factor allocation process in the equity space in the context of benchmarked investment management. While possibilities for adding value through smart beta allocation are manifold, the robust performance improvements obtained through relative ERC and relative GMV allocations to the four main consensual factors displayed in this article, provide evidence that the benefits of multi-factor allocations exist in a context of strong relative risk constraints and are sizeable.

Felix Goltz is head of applied research at the EDHEC-Risk Institute and research director at ERI Scientific Beta

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