October 2014

EDHEC: Reconciling risk with smart factors

No 1Noël Amenc and Lionel Martellini, of Edhec Business School point out flaws in smart beta allocation and suggest how to overcome them with more efficient allocation to rewarded factors.

For a better understanding of the true meaning of “risk factor allocation”, it is useful to return to the foundations of asset pricing theory, which suggest that individual securities earn their risk premium through their exposures to rewarded factors. 

Asset pricing theory also suggests that factors are (positively) rewarded if and only if they perform poorly during bad times, and more than compensate during good times so as to generate a positive excess return on average across all possible market conditions. 

Standard examples of such rewarded factors in the equity space are the “value” factor (represented by a portfolio going long value stocks and short growth stocks) and “size” factor (represented by a portfolio going long small-cap stocks and short large-cap stocks), which can be regarded as possible proxies for a “distress” factor. On the other hand, the low-volatility factor (represented by a portfolio going long low-volatility stocks and short high-volatility stocks) is an anomaly since the less risky stocks enjoy the highest performance levels.

In this context, one can argue that the ultimate goal of portfolio construction techniques is to invest in risky assets so as to ensure efficient diversification of specific and systematic risks within the portfolio. Note that the word “diversification” is used with two different meanings. When the focus is on the diversification of specific risks, “diversification” means reduction of specific risk exposures, which are not desirable because not rewarded. On the other hand, when the focus is on the diversification of systematic risks, it means efficient allocation to factors that bear a positive long-term reward.

This recognition provides us with a first interpretation for what the “risk allocation paradigm” might mean. If the whole focus of portfolio construction is ultimately to harvest risk premia to be expected from holding an exposure to rewarded factors, it seems natural to express the allocation decision in terms of such risk factors. In this context, the term “factor allocation” is a new paradigm advocating that investment decisions should usefully be cast in terms of risk factor allocation decisions, as opposed to asset class allocation decisions, which are based on somewhat arbitrary classifications. 

The second interpretation is to precisely define the paradigm as a portfolio construction technique that can be used to estimate what an efficient allocation to underlying components (which could be asset classes or underlying risk factors), should be. The starting point for this novel approach to portfolio construction is the recognition that a heavily concentrated set of risk exposures can actually be hidden behind a seemingly well-diversified allocation. 

In this context, the risk allocation approach, also known as risk budgeting approach, to portfolio construction, consists advocating a focus on risk, as opposed to dollar, allocation. In a nutshell, the goal of the risk allocation methodology is to ensure that the contribution of each constituent to the overall risk of the portfolio is equal to a target risk budget. In the specific case when the allocated risk budget is identical for all constituents of the portfolio, the strategy is known as “risk parity”, which stands in contrast to an equally weighted strategy that would recommend an equal contribution in terms of dollar budgets. 

To better understand the connection between this portfolio construction technique and standard recommendations from modern portfolio selection techniques, it is useful to recognise that, when applied to uncorrelated factors, risk budgeting is consistent with mean-variance portfolio optimisation under the assumption that Sharpe ratios are proportional to risk budgets. Thus, risk parity is a specific case of risk budgeting, a natural neutral starting point that is consistent for uncorrelated factors with Sharpe ratio optimisation assuming constant Sharpe ratios at the factor level. 

Such risk allocation techniques, defined as portfolio construction techniques focusing on allocating wealth proportionally to risk budgets, can be used in two different contexts: across asset classes (for the design of a policy portfolio) or within asset classes (for the design of an asset class benchmark). In an asset allocation context, the focus of risk parity
is to allocate to a variety of rewarded risk factors affecting the return on various asset classes so as to equalise (in the case of a specific focus on risk parity) the risk contribution to the policy portfolio variance. 

Overall, it appears that risk allocation can be thought of as a new investment paradigm advocating a focus on allocating to uncorrelated rewarded risk factors, as opposed to correlated asset classes, and a portfolio construction technique stipulating how to optimally allocate to these risk factors. 

It should be noted in closing that the existence of uncorrelated long-short factor replicating portfolios is not a necessary condition to perform risk budgeting, which is fortunate since such uncorrelated pure factors are hardly investable in practice. An investor could use any set of well-diversified portfolios, as opposed to factor-replicating portfolios, as constituents, leaving the hurdle to reach target factor exposures to the asset allocation stage. 

It is in such a framework that the research conducted by Edhec-Risk Institute to define the concept of smart factor risk allocation is situated. It involves offering the ingredients and the allocation methods that allow one to benefit, on the one hand, from the diversification offered by smart beta weighting schemes, which reduce the unrewarded or specific risks, and on the other, to make an efficient allocation to systematic or rewarded risk factors. 

This dual perspective is an effective response to the traditional criticism levied at
cap-weighted indices, which are both poorly diversified, because they are highly concentrated in a small number of large-cap stocks, and exposed to poorly rewarded risk factors, such as large and growth stocks. 

This risk allocation to smart beta has translated into smart factor index offerings proposed by Edhec-Risk Institute’s venture that is dedicated to the design and production of smart beta indices: ERI Scientific Beta.

This smart factor index offering is innovative compared to the traditional approaches to factor index construction in the long-only universe. Factor indices are often constructed using a selection of stocks that are exposed to the right factor, but their weighting is not the most efficient. One can have traditional cap-weighted factor indices or indices weighted according to the stocks’ exposure to the factor. In both cases, even though the goal of the choice of alternative benchmark was to respond not only to the poor factor exposure but also to the poor diversification of cap-weighted indices, the latter problem is not really addressed by traditional factor indices.

Being aware of this problem, index providers have recently tried to reconcile factor investing and smart beta’s promise of diversification by offering a multi-smart-beta index allocation. 

This involves measuring the factor biases of different weighting schemes and offering to combine them to map an allocation to risk factors. 

Unfortunately, this approach is not optimal. Using an equal-weighted index for a broad large-cap/mid-cap universe as a proxy for size will not give the best and most stable exposure to the size factor, since the index will include a considerable share of large stocks, and, therefore, a short exposure to the positively rewarded small-cap factor. 

In the same way, choosing a minimum volatility index to approximate the low volatility factor means forgetting that a minimum volatility index, since it is often “deconcentrated” by constraints relative to cap-weighting, is not the most exposed to low volatility stocks. 

It is in this spirit, as part of the Smart Beta 2.0 approach that ERI Scientific Beta offers smart factor indices that are constructed using a dual approach. Conscious that whatever the precautions for ensuring the robustness of their implementation, all diversification strategies contain risks of their own (strategy-specific or model risk), ERI Scientific Beta also proposes to diversify these risks using the concept of the multi-strategy index has led to the offer of a diversification method based on equal weighting of the diversification strategies available on the Scientific Beta platform. 

These multi-strategy smart factor indices are, in our view, the ideal ingredients for the implementation of a risk allocation strategy that is also called “multi-smart-beta,” whether defined in absolute or relative terms. 

Noël Amenc is professor of finance, Edhec Business School, director, Edhec-Risk Institute, CEO, ERI Scientific Beta. Lionel Martellini is professor of finance, Edhec Business School, scientific director Edhec-Risk Institute, senior scientific advisor, ERI Scientific Beta

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