When it comes to modelling the potential risks and returns of alternatives, trustees continue to rely on mean-variance approaches (such as expected average returns and annual return volatility), but acknowledge it is not the best solution as correlations are non-stationary (that is, can vary over time), and illiquidity and leverage create tail risk. In short, mean-variance optimisation does not adequately capture the non-normality of risk involved in alternative investments and therefore does not capture tail risk – the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution.

Furthermore, we know from the literature on financial economics and conversations with trustees, that investors’ marginal utility from an extra amount of wealth tends to decrease – people hate losing $1 more than they like making $1. In Mercer’s research paperThe tail that wags the dog – modelling alternatives in four dimensions using a downside frameworkwe suggest looking further into a downside framework as a practical supplement to the use of the mean-variance approach. Mean-variance analysis, despite all of its shortcomings, does offer a few strong points – it is the workhorse of the industry, it offers a tractable outcome and is easy to implement.

We sought to examine the shortfalls in current practice and produced an adjusted mean-variance framework. Firstly, we found there is some agency risk in smoothing patterns by managers and independent valuers, and Sharpe Ratios (a measure of risk adjusted performance) may in many cases be an illusion created by smoothing and biases. Another interesting fact is that it is actually quite hard to detect skill in the alternatives world, yet this is an environment where high levels of manager skill is sought after and high levels of active risk taking is arguably encouraged because of the high watermark in performance fee arrangements. Our simulations revealed that while a Sharpe Ratio of a typical hedge fund may give the appearance that a manager has extraordinary skill, this type of performance measurement is not at all reliable in measuring manager skill.

Thus, there may be some incentive to smooth returns using valuations and ‘double or nothing’ money management which distort traditional performance measures. In normal markets, returns should be distributed independently over time with low serial correlations. However our analysis of smoothed and de-smoothed volatility and correlations revealed that this is certainly not the case for the alternative markets – private equity and real estate showed a two to three times increase of volatility on an unsmoothed basis. Our adjusted mean-variance framework addresses the impact of higher underlying volatility, higher correlation and lower return expectations. The voluntary reporting in alternatives creates selection, backfill and survivorship bias, the total of which can easily be a return impact of 2 to 4 per cent per year.

Not only are past returns likely to be overstated, but future returns may come down going forward, given the amount of money going into alternatives – thereby potentially reducing the efficiency of alternatives, and unravelling much of their perceived benefits. However, we have still not captured tail risk. The examination of current practices shows us that while trustees are familiar with mean-variance they are not happy with mean-variance in the non-normal world of alternatives. If modelled without constraints and de-smoothing, mean-variance optimisation will allocate a large part into hedge funds for high Sharpe Ratios and low correlation. Furthermore, the tail risk in alternatives does not necessarily disappear, it might just get redistributed, and hence Sharpe Ratios alone cannot be trusted. As per our earlier simulations and observations, illiquidity, money management behaviour and leverage create tail risk and skew. Finally, a downside framework is needed to capture utility asymmetry.

What‘s required is a move from a two moment to a four moment approach. While in theory the number of moments is infinite, in practice, the following four moments might be sufficient to model alternative investments: • Mean – measures location or expected return outcome (first moment) • Variance – traditional risk measure capturing the volatility – or dispersion of returns around the mean (second moment) • Skew – measures lopsidedness (third moment), and describes a distribution’s asymmetry. A positive skew describes a distribution favouring the right tail, whereas a negative skew describes a distribution favouring the left tail. • Kurtosis – measures “fat tails” – the frequency and magnitude of extreme return outcomes (fourth moment), describing the shape of the distribution of observed data around the mean.

A high kurtosis portrays a chart with fat tails and a low even, distribution whereas a low kurtosis portrays a chart with skinny tails and a distribution concentrated towards the mean. This proposed method can account for the non-normality and tail risk in alternatives investing by incorporating modified value at risk, expected shortfall, stress testing (forward) and factor analysis (forward). Our simulation modelling based on a case study (contained in the research paper) demonstrates in more detail how the method works. However to summarise, we derived the following conclusions. From a strategic asset allocation perspective, alternatives come to life as useful diversifiers in a downside framework – even after taking into account de-smoothing practices by managers, and the embedded tail risk due to leverage and illiquidity.

Our case study also showed that both mean-modified value at risk and mean-expected shortfall favour an increased allocation to alternatives from a downside perspective, at the expense of traditional asset classes. Hence the alternatives especially come to the fore when capital preservations become a major consideration. However, we also acknowledge that there may be times, such as during extreme falls in liquid markets, that the illiquidity premium becomes extreme from a tactical viewpoint. Nevertheless, this premium expansion precisely reflects some of its defensive nature. In some of the more exotic strategies, no long term data may be available to model, in which case proxy or simulated distributions will be required to be generated, all of which have their inherent limitations. Risk analytics may try to model an event which has never happened before, and human judgement will remain an important part of the equation. Explicitly modelling tail risk in a non-normal world is an important evolutionary step in the right direction for future research into capital markets.

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