June 2016

EDHEC RESEARCH: Minding the risk budget

The emergence of smart beta indices is directly linked to the new investment idea of ‘risk allocation’, as Felix Goltz of Edhec-Risk Institute explains.

Cap-weighted indices have been widely criticised in passive investment, but in actual fact, they would be truly optimal if the Capital Asset Pricing Model (CAPM) were true and the indices reflected the true market portfolio. Neither of these conditions is borne out in practice. Such criticism is the starting point for smart beta strategies. There are two angles that can be taken and both correspond to sides of the same coin – the inefficiency of cap-weighted indices:

  • They ignore other priced risk factors. The optimal portfolio should tilt to multiple risk factors based on the investor’s preferences.
  • They are ill-diversified portfolios, highly concentrated and trend following. The optimal portfolio should allocate weights based on (estimates of) stocks’ risk and return parameters rather than by market cap.

The first angle has led to the development of factor strategies. The second has led to the development of diversification-based weighting schemes.

Factor indices fall into two major categories. The first involves selecting stocks that are most exposed to the desired risk factor and the application of a cap-weighting scheme to this selection. While this approach responds to one limitation of cap-weighted indices, namely the choice of exposure to a good factor, the problem of poor diversification arising from high concentration in a small number of stocks remains unanswered.

The second method involves maximising the exposure to a factor, either by weighting the whole of the universe on the basis of the exposure to this factor, or by selecting and weighting by the exposure score of the stock to that factor. Here again, the maximisation of the factor exposure does not guarantee that the indices are well diversified.

Index providers have recognised that the traditional factor indices they previously offered are not good investable proxies of the relevant risk factors due to their poor diversification, and that the smart beta indices aiming at improved diversification have implicit risk exposures. As a result, providers are proposing to select and combine indices according to their implicit factor exposures.

For example, one could seek exposure to the value factor through a fundamental-weighted index. This, however, will not produce a well-diversified index, simply because the integration of the attributes characterising the value exposure into the weighting does not take the correlations between these stocks into account.

Moreover, the value tilt is an implicit result of the weighting methodology and it is questionable whether an investor seeking a value tilt would wish to hold any weight in growth stocks which will be present in a fundamentally weighted index.

An important challenge in factor index construction is to design well-diversified factor indices that capture rewarded risks while avoiding unrewarded risks. We draw on a second generation of smart beta strategies that allow investors to explore different smart beta index construction methods in order to construct a benchmark that corresponds to their own choice of factor tilt and diversification method. It allows investors to manage the exposure to systematic risk factors and diminish the exposure to unrewarded strategy-specific risks.

Stock selection, the first step in index construction, allows investors to choose the right (rewarded) risk factors to which they want to be exposed. When it is performed upon a particular stock-based characteristic linked to stocks’ specific exposure to a common factor, such as size, stock selection allows this specific factor exposure to be shifted, regardless of the weights that will be applied to individual portfolio components.

A well-diversified weighting scheme allows unrewarded or specific risks to be reduced. Stock-specific risk (such as management decisions, product success etc) is reduced through the use of a suitable diversification strategy.

However, due to imperfections in the model, there remain residual exposures to unrewarded strategy-specific risks. For example, minimum volatility portfolios are often exposed to significant sector biases.

Similarly, in spite of all the attention paid to the quality of model selection and the implementation methods for these models, the specific operational risk remains present to a certain extent. For example, robustness of the maximum Sharpe ratio scheme depends on a good estimation of the covariance matrix and expected returns. Researchers have found that the parameter estimation errors of optimised portfolio strategies are not perfectly correlated and therefore have potential to be diversified away. A diversified multi-strategy approach, which combines five different weighting schemes in equal proportions, enables the non-rewarded risks associated with each of the weighting schemes to be diversified away.

The flexible index construction process used in second-generation smart beta indices thus allows the full benefits of smart beta to be harnessed, where the stock selection defines exposure to the right (rewarded) risk factors and the smart weighting scheme allows unrewarded risks to be reduced.

Risk allocation has gained increasing popularity among sophisticated investors. What the concept exactly means, however, arguably deserves some clarification.

Asset pricing theory suggests that individual securities earn their risk premium through their exposures to rewarded factors. 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.

The word ‘diversification’ is used with two different meanings. When the focus is on the diversification of specific risks, it means reduction of specific, unrewarded risk exposures. On the other hand, when the focus is on the diversification of systematic risks, ‘diversification’ means efficient allocation to factors that bear a positive long-term reward, with Modern Portfolio Theory suggesting that efficient allocation is in fact maximum risk-reward allocation (maximum Sharpe ratio in a mean-variance context).

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 it 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 be hidden behind a seemingly well-diversified 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’.

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 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 impacting the return on various asset classes so as to equalise the risk contribution to the policy portfolio variance.

Overall, it appears that risk allocation can be thought of both 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. Indeed, one can use any set of well-diversified portfolios, as opposed to factor-replicating portfolios, as constituents, leaving to the asset allocation stage the hurdle to reach target factor exposures.

It is in a framework of this kind that the research conducted by Edhec Risk Institute to define the concept of smart factor risk allocation is situated. It involves offering both 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 of 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.

Felix Goltz is head of applied research at the Edhec-Risk Institute

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