Despite the recent interest from institutional investors into alternative investments, investors have had difficulty deciding on the appropriate level of alternative assets within their portfolios. In many cases, allocation is based on simple rules of thumb, for example, “5% to15%, because that’s what everybody else does” is one we hear quite frequently. The other variation is the US endowment model, e.g. Yale invests 25% in real estate, 25% in hedge funds and 20% in private equity.

Investment in alternatives is usually for return stability, not return magnitude, and preservation of capital. Indeed, from a strategic asset allocation, alternatives come to life as useful diversifiers in a downside framework. In terms of asset allocation, has long been acknowledged that mean variance optimisation does not adequately capture the non-normality of the risk involved. Furthermore, from the utility curves, and conversations with trustees, we know that people do not value risk symmetrically.

For some alternatives, returns are overstated due to various biases and risk is understated due to return smoothing by fund managers. We have researched various methods to adjust the input parameters to mean-variance models to more properly reflect the characteristics of alternative investments. However, as LTCM¹ or the recent credit crisis demonstrate, risk does not always disappear. There is a high probability that it gets re-distributed into tail risk in the case of alternatives. Mean-variance, assuming a symmetrical distribution, cannot capture tail risk under these circumstances.

However, mean-variance does offer a few strong points.

• It is the workhorse of the industry

• The parametric approach involved assumes a normal distribution which has 2 major advantages: it offers a tractable outcome and is easy to implement.

Taking into account our findings, we have shown in figure 1 the conceptual impact on mean-variance optimization of adjusting for higher volatility, higher correlation and lower return expectations for alternatives². 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 from e.g. Sovereign Wealth Funds. The efficient frontier is likely to shift back to the lower right hand corner, thereby undoing much of the perceived benefit of alternatives.

Figure 1. Adjusted mean-variance framework after de-smoothing and return and correlation adjustment.

However, we still have not captured tail risk. It is clear that investors value losses much more than gains, especially in alternatives. Specifically, they invest in alternatives because:

• They seek return stability, preservation of capital, returns uncorrelated with traditional markets.

• Risk is not symmetrical – people hate losing $1 more than they like making $1. Which is why a fair bet is not “fair”³. 

To capture the behaviour of tail risk, we suggest in our paper that a down-side framework approach is appropriate, as a tractable and understandable supplement to the mean variance approach⁴. Our research addresses the following areas.

1. The de-smoothing of returns reported by managers/valuers in illiquid markets.
    
2. The capture of the illiquidity/leverage premium through the modelling of tail risk. We use a 4 moment downside framework using Value at Risk (VaR) and expected shortfall as the risk measure. VaR shows us where the tail starts, expected shortfall shows us what we can expect to lose on average once we enter the tail.
    
3. A case study of a five asset portfolio consisting of US stocks, bonds, real estate, private equity and hedge funds to show the difference in optimal weights using a 2 moment versus a 4 moment approach. Real estate is used as a proxy for defensive alternatives, private equity for growth alternatives, and hedge funds for alpha based alternatives.
    
4. Risk measures such as projected drawdown and market sensitivity.

One limitation of our research is that we have not included liability modelling as our focus was mainly on strategic asset allocation for defined contribution funds and endowments / foundations. Furthermore, we have used broad industry indices. The smaller the sample size, the more idiosyncratic risk will be taken on, the tail event of which is notoriously difficult to model.

However, we believe that the methodologies suggested may be used to supplement standard mean-variance and analysis. Whilst we have examined various other methods for alternatives modelling from literature, and integrate various parts, we also acknowledge that no de-facto industry standard yet exists for alternatives modelling. Furthermore, no quantitative method can fully capture the idiosyncratic risk or constantly changing nature present in many alternatives. The findings we present should be seen as a step forward in modelling tail risk in alternatives to predict return outcomes, not the final answer.

Notes:

1. Long Term Capital Management was a US hedge fund which failed spectacularly in the late 1990s, leading to a massive bailout.

2. Voluntary reporting in alternatives creates Selection, Backfill and Survival bias. The total bias can easily be 2-4% of returns. See e.g. Fung, W.H., and D.A. Hsieh, (2000), “Performance characteristics of hedge funds and CTA funds: Natural versus spurious biases”, Journal of Quantitative and Financial Analysis, 35, pp. 291-307.

3. Our paper describes some of the characteristics of decreasing marginal utility with increasing wealth. Markowitz (1959) in Portfolio Selection, Yale University Press, discussed some early preference for downside risk, referring to the use of semi-variance. More recent financial literature examines the use of downside betas and correlations and their relationships to excess returns.

4. More specifically, our paper extends traditional 2-dimensional mean-variance optimisation to 4-dimensional mean-variance-skew-kurtosis optimisation and assumes a non-normal distribution.