Professional investors care about the expected returns of assets and the variance (risk), and the covariances of those assets (which determines the benefits of diversification). Those parameters are the key elements of portfolio selection models. In practical applications of the classic mean-variance approach to mixed-asset portfolio selections, the risk and covariance parameters are typically estimated using historical data – calculating mean returns, standard deviations of those returns and correlations of returns across asset classes and use these as inputs to optimise asset allocation.
In practice, investors do not know the exact distribution of asset returns. Therefore, estimation of the return distribution using historical data contains estimation errors. It is more realistic to assume that investors form prior beliefs about all possible distributions of asset returns and are averse to the ‘uncertainty’ inherent in the actual future distribution. Thus, by considering estimation error and aversion to uncertainty, this study examines how the portfolio allocations in the listed real estate sector differ under the uncertainty aversion framework when compared to the classic mean-variance framework.
By comparison to the standard mean-variance approach, optimal allocations to listed real estate show much greater stability under the uncertainty aversion approach. This is illustrated in Figure One below, which shows the proportion of listed real estate in mixed-asset portfolios and how this varies over time using the classical MV approach (the blue line) and the uncertainty aversion approach (with three different degrees of uncertainty) to estimate optimal investment mix.
Our study uses four asset classes (European listed real estate, European stocks, European government bonds and commodities) to form portfolios over time. Figure 1. shows the optimal allocations to European listed real estate over time using anchored windows (where the expected return, correlations and risk is based on the full available performance history to that point from 2002 – adding new information as it would have become available to investors). The blue line indicates the traditional ‘optimal’ allocations to listed real estate under the classic mean-variance approach. The orange, green, and red lines indicate the optimal allocations to listed real estate under the uncertainty aversion approach with various degrees of uncertainty. The red line has the highest degree of uncertainty and shows the greatest stability in optimal allocations to listed real estate.
An important implication of the more stable asset allocations over time is the major reduction in the need for portfolio rebalancing with an implied reduction in transaction costs. Although the optimal allocation to listed real estate under the uncertainty aversion approach is still higher than the observed allocation of institutional investors (suggesting that they should perhaps increase their real estate holdings), the allocation conforms more to professional practice and produces more feasible allocations than the simplistic mean-variance approach.
Investors should be cautious to avoid over-allocation to the sector relying on historical information alone. A transition from a period of strong returns in the listed real estate market to a period of weak returns would lead to a significant reduction in the target allocation to listed real estate if uncertainty aversion had not been considered, forcing investors to bear substantial rebalancing costs and to sell into a falling market. Uncertainty aversion portfolios are more stable over time and deliver a higher return/risk ratio.
Given the heterogeneity in the performance of listed real estate among different European countries over different periods, an investor could form a portfolio including listed real estate from many countries. Since the uncertainty aversion approach gives us relatively stable allocations over time (even with many assets), the model will give us modest shifts in allocations in listed real estate from one country to another over time.
The results of our multiple country analysis (UK, France and Germany) show a modest shift in listed real estate allocation from France to Germany after 2016. Thus, another implication of the uncertainty aversion model is that it permits dynamic allocation of funds into the listed real estate sector with superior performance without generating extreme allocations and avoiding significant rebalancing costs.
 A high level confidence interval indicates a higher degree of uncertainty.