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Risk & Portfolio Construction: Don’t let the tails wag the dog

Vincent Berard and Daniel Dimitrov explore ways to introduce tactical allocation tilts into a strategic portfolio using tail risk and alternative betas

Strategic asset allocation accounts for the largest fraction of the factors that  affect a portfolio’s realised return and  volatility over the long run. However, in this article we show that a proper exercise of tactical decisions based on short-term risk views will also have a large impact on portfolio performance.

There are various approaches to specifying tactical asset allocation deviations. In the following case study we focus on how portfolio performance can be improved and portfolio drawdown mitigated by employing a set of techniques aimed at portfolio tail-risk management. In combination with that, we examine the effect of granting the portfolio access to highly liquid risk premium strategies – carry, momentum, value and volatility – and applying asset selection based on contribution to the tail risk within the strategic portfolio.

We propose a quantitative, systematic approach to complement the traditional qualitative and discretionary portfolio construction methods usually employed by pension funds. This specific approach takes into account asset class ‘tail-fatness’ (the risk above what the normal or ‘bell-shaped’ curve would predict) and tail-dependency between asset classes (the propensity of extreme losses to occur simultaneously).

We show that portfolio performance is a function of several key factors:
• The relevant universe of potential asset investments;
• A viable method of identifying potential favorable and avoiding hazardous trades;
• Realistic assumptions on asset return behaviour.

As simple a concept as it first appears, there has been a lot of discussion about what measure will properly quantify the perception of financial risk. The most well-known way of defining portfolio risk dates back to Harry Markowitz and modern portfolio theory, which utilises the asset returns standard deviation (volatility) and their correlations to develop the theory of risk-efficient portfolios.

Even back then, however, the challenge that the standard deviation posed was obvious. It factors in both the upside and downside dispersion around the expected return. Moreover, it does not give a proper indication of the propensity for large losses to occur. As a result, asset-allocation models based on volatility or, for that matter, based on the normal or Gaussian-distribution model coupled with any risk measure, have failed to give investors a proper clue about the potential losses that can materialise behind their investments.

Quantitative approach
Alternatives to volatility do exist. Value at risk (VaR) was the first one to be widely recognised, as it measures, with a degree of confidence, the minimum loss that an asset or portfolio is estimated to realise over a certain period. An enhanced metric that has been getting more attention recently is expected tail loss (ETL), which measures the average loss that would be realised once the VaR threshold has been exceeded.

ETL offers a very practical look at risk by focusing purely on downside – that is, on the left tail of the estimated returns distribution. The word ‘estimated’ is key. It reminds us that risk is an ex-ante concept in that it tries to evaluate and assign probabilities to the possible future scenarios – in essence, by utilising only the information that is available before actions are taken.

In that sense, an educated market participant needs to make sure that market information is used in the most efficient way – ETL works only as far as it rests upon a comprehensive system that can model the tails of the asset returns distributions accurately. It must be dynamic and work consistently in different market regimes – self-adjusting in calm periods to avoid unnecessarily conservative risk expectations and detecting increased tail risk before extreme events hit the market.

This kind of model is able to reliably identify portfolio tail-risk contributors and diversifiers by recognising the differences in excess tail risk between assets classes and between markets. In our illustration, we deploy FinAnalytica’s patented proprietary methodology for modelling ETL.

To manage short-term risk on a position-by-position basis, we use ‘marginal contribution to risk’, which quantifies the sensitivity of portfolio risk to small variations in the weight allocation of a given position. As we define risk as ETL, the rule that we will follow is simple: portfolio tail risk is reduced by overweighting positions with low marginal contribution to ETL and underweighting positions with high marginal contribution to ETL.

On an intuitive level, several components go into marginal contribution to tail risk:
• Standalone risk – all else constant, within a long-only portfolio, positions with high standalone risk will contribute to the portfolio’s overall ETL, as long as they exhibit positive correlation with the rest of the portfolio.
• Tail dependency with the rest of the portfolio – positions that tend to react favourably when the rest of the portfolio is doing poorly will appear as diversifiers of risk and candidates for overweighting, even if their standalone risk is high.
•  Current position allocation – if the weight of the asset in the portfolio is already higher than what would be expected in a minimum risk portfolio, the position will appear as a contributor.

For our illustration, we construct an portfolio with the following pension fund structure: the duration of liabilities is 17 years, the duration of assets is eight years, the duration gap is 60% hedged and the cover ratio is 99%. The assets are well diversified and have the following strategic structure: 30% European government bonds; 25% equities; 20% European credit; 19% alternatives (7% real estate, 3% infrastucture, 2.5% commodities, 2.5% hedge funds, 2% emerging market debt, 2% high-yield bonds); 5% inflation-linked bonds; and 1% cash.

Tilted
The performance of €100 invested in the strategic portfolio is shown as the grey line in figure 1. Note that, throughout, the portfolio allocations are held fixed over time to the strategic targets. Despite the strong diversification within the portfolio, it suffers significant drawdown throughout 2008, which by the end of 2012 almost reduces the value of the portfolio below investment amount.

First, we apply a rebalancing strategy based on marginal contribution to ETL. In other words, each quarter starting in January 2007, we estimate the marginal contribution to risk of each position in the portfolio, rank the positions and reduce by 1% each of the top 10 tail-risk contributors, and increase by 1% the allocation to each of the top 10 risk diversifiers.

This tactically ‘tilted’ portfolio is then held for the next quarter, at the end of which new deviations from the strategic base are estimated and implemented. As a result we arrive at the quarterly rebalanced portfolio ‘10% tactical allocation’. It can be seen that this dynamic
reallocation strategy improves the annual average return by one percentage point, while
reducing portfolio drawdown from 12.89% to 6.01%.

As a next step, we introduce an additional alternative asset class to the initial investment universe available to the portfolio manager – the ability to invest in liquid risk premium overlays covering several quantitative strategies – carry, momentum, value and volatility.
We introduce 10 overlay strategies in total and use the marginal contribution to ETL framework each quarter to select the three strategies that will have the highest tail-risk reduction effect over the strategic portfolio. We can then lay the selected three instruments over either the tactical portfolio or the strategic portfolio itself. In the example shown in figure 2, we allocate a 5% overlay to each of the three strategies within both the strategic portfolio and the tactical allocations portfolio.

We can conclude that the combination of tactical tilt aimed at reducing the tail exposure of the portfolio, combined with an overlay of three quantitative strategies selected within the context of the portfolio leads to the highest risk-adjusted performance among the considered scenarios.

Vincent Berard is head of rates, FX and quantitative structuring for Europe at BNP Paribas and Daniel Dimitrov is client services manager for global accounts at FinAnalytica

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