The results in
Fig. 2 are obtained using the following process.
First, we generate 100 random thematic return time series. In other words, for each monthly observation in the review period, we use the historic return of a randomly-selected thematic equity strategy from the Pictet AM range. This process assumes no skill in strategy selection. The strategies included in the study were Water, Security, Health, Biotech, Premium Brands, Clean Energy, Digital, Timber, Nutrition, Robotics, SmartCity, Global Environmental Opportunities and Global Thematic Opportunities.
The thematic strategy returns used are in US dollar terms, are net of fees and are I-share classes. They were sourced from fund data published on Bloomberg. We use historical data covering the period 31.12.2008- 31.08.2019. We then take historical returns for the MSCI ACWI Index and the BofAML Global Government Bond Index, and then construct a covariance matrix for each of the 100 simulation runs.
For 5-year return estimates for global equities and global government bonds, we use PictetAM's strategy unit’s proprietary forecast model, whose methodology is described below.
The random covariance matrices and return estimates are then used to generate 100 efficient frontiers detailing the optimal allocation among the three asset classes. The thematic equity allocations quoted and shown in Fig. 2 represent the 33rd percentile of the allocation to thematic equities for each return target; in two thirds of the simulations, the suggested allocation is higher than the figure shown in the chart.
For a more detailed description of mean-variance portfolio optimisation see:
http://www.columbia.edu/~mh2078/FoundationsFE/MeanVariance-CAPM.pdf
The results in Fig. 3 are based on simulation in which we again use historical data covering the period 31.12.2008- 31.08.2019. We compute the ex-post risk and return behaviour of balanced equity-bond portfolio a: 60 per cent of which is allocated to equities represented in the MSCI ACWI Index and 40 per cent to bonds represented in the BofA Merrill Lynch Global Government Bond Index. Returns are based in US dollars. To compute the historic returns and volatility of the thematic stock universe, we use the same process we followed in the portfolio optimisation exercise above.
We then ran 500 simulations under which a 50/50 bond equity portfolio is complemented with a thematic satellite to obtain the same average risk as the 60/40 portfolio. The thematic equity allocation, which, averaged out over the 500 runs, generates the same volatility as the 60/40 portfolio is 18 per cent, with a higher return.
The results shown in Fig. 5 is a portfolio optimisation using our proprietary 5-year asset class return forecasts and a co-variance matrix derived from historical returns for the MSCI ACWI Index and the BofA Merrill Lynch Global Government Bond Index. The methodology is identical to the one followed above.