23. January 2023
10 minutes

Latest Scientific Innovations for our Investment Products

As an innovative and scientifically driven asset manager, we always strive to offer our clients the best possible investment solutions. After extensive research, we are happy to present further developments of the OLZ investment solutions based on the latest methods from empirical finance research. We have improved the OLZ minimum-variance products to reduce portfolio risks even more efficiently and to achieve greater added value for our investors. This involves three major innovations:

The first innovation, called «Nonlinear Shrinkage», is a new state-of-the-art covariance matrix estimator, which allows us to further improve our minimum-variance optimization and thus offer our clients an added value compared to our competitors' products. This scientifically based method provides smoothed estimates of volatilities and correlations to make the portfolio more stable and balanced1.

The second further development is an exclusion procedure based on risk filters designed to identify and avoid particularly risky companies. This systematic preselection thus enables a more comprehensive reduction of the portfolio risk and ensures that only «high-quality» companies are considered.

The third model development is to use individual and adaptive maximum weights at the single stock level, thereby increasing the degrees of freedom of portfolio optimization. The improved estimation of risk parameters allows us to increase the absolute maximum weights – where it makes sense – and to capture the long-term low-volatility premium in a more targeted way.

Example OLZ Developed Markets

The systematic combination of these three innovations has a positive impact on the quality and risk-adjusted performance of the OLZ minimum-variance solutions. To visualize the benefits of the model enhancements, we have plotted the performance of the backtests of the previous and the new OLZ Developed Markets minimum-variance solution for the past year 2022 in Figure 1 and present their most important metrics in Table 12. Due to various turbulent events – interest rate hikes, inflation and war – risk-optimized strategies have performed quite well this year. In particular, they were able to significantly reduce risk relative to the benchmark and almost halved volatility. Especially during these periods, the positive impact of our new risk estimate becomes apparent, lowering the maximum loss by almost 5 percentage points in 2022 and generating an outperformance of 10%. The return and risk metrics are consistently better for the model going forward compared to the previous model. Particularly noteworthy is the stability of the new risk estimation, which translates into an impressive reduction in turnover of about 80%.

Figure 1: Performance of the previous and the new OLZ Developed Markets minimum-variance portfolio (including costs) and the MSCI World benchmark from 3.1.2022 to 30.12.2022.
Table 1: Return and risk metrics for the previous and the new OLZ Developed Markets minimum-variance portfolios (including costs) and the MSCI World benchmark from 3.1.2022 to 30.12.2022.

The next few short sections will take a closer look at the intuition behind the three innovations.

1. Nonlinear Shrinkage

In the computation of a minimum-variance portfolio, the estimation of the covariance matrix is the central element. Within the framework of academic research, our research analysts have worked together with renowned research partners (including Nobel Prize winner Robert F. Engle and the «inventors» of shrinkage Olivier Ledoit and Michael Wolf) on exactly this estimation of covariance matrices3. The models were then further developed internally and integrated into the OLZ portfolio optimization technology. To further improve the OLZ minimum-variance investment solutions, we now apply one of the latest methods from science: analytical «nonlinear shrinkage»4. The proprietary shrinkage estimator is a fast and reliable method for robustly estimating a high-dimensional minimum-variance portfolio. It not only further reduces the volatility of the portfolio, but also computes a more stable and better-balanced portfolio with less extreme allocations and a cost-optimized implementation because of the significant reduction of the turnover5.

2. Risk Filters

To achieve an even more reliable risk reduction and quality enhancement of OLZ's investment solutions, we introduce our risk filters in addition to shrinkage. In an optimized portfolio, risky companies can be included in the portfolio because they make an attractive risk-reduction contribution to the overall portfolio risk due to their low correlation with the other stocks. Often, however, such low correlation is simply a consequence of the company being in trouble and moving in the opposite direction to the market. However, a company that is in a clear downtrend and has a low correlation to the market is not a meaningful component of a risk-optimized investment strategy. De facto, such stocks even increase portfolio risk, even if they can mathematically help to reduce ex ante portfolio volatility. The introduction of OLZ's proprietary «High-Risk» and «Low-Quality» risk filters significantly mitigates the so-called «Fooled by Correlation» problem by identifying and excluding problematic companies through prescreening.

3. Adaptive Upper Bounds

By improving the covariance matrix estimation via shrinkage and risk filters, we further increase the quality of risk reduction of the OLZ investment solutions, which is why we can allow more degrees of freedom within the portfolio optimization. The so-called «Adaptive Upper Bounds» are a rule-based procedure for determining the maximum weights per stock depending on its tradability and size. By increasing the potential maximum weights, more from the long-term risk-adjusted low-volatility premium can be gained. Furthermore, relative maximum weights per stock are also defined, taking into account market capitalization and liquidity, in order to avoid extreme deviations for smaller stocks compared to the benchmark.


The introduction of nonlinear shrinkage and risk filters makes the OLZ investment solutions even more robust. This increased stability allows us to introduce more degrees of freedom in the optimization, among other things in the form of individual maximum weights on stocks depending on their size and liquidity. Thanks to the latest model developments, the OLZ investment solutions can

  1. skim off the long-term risk-adjusted low-volatility premium more efficiently,

  2. enable a further reduction in volatility,

  3. achieve a more stable portfolio allocation with significant reduction of turnover, and

  4. offer further design options for «customized solutions», in terms of ESG, factors, exclusions, etc.

1 Ledoit, O. and Wolf, M. (2022). The power of (non-)linear shrinking: A review and guide to covariance matrix estimation. Journal of Financial Econometrics, 20:187-218

2 All published backtest results are in CHF and include costs.

3 See e.g., De Nard, G., Engle, R. F., Ledoit, O., and Wolf, M. (2022). Large dynamic covariance matrices: Enhancements based on intraday data. Journal of Banking and Finance, 138:106426

4 See e.g., Ledoit, O. and Wolf, M. (2020). Analytical nonlinear shrinkage of large-dimensional covariance matrices. Annals of Statistics, 48:3043-3065

5 More detailed explanations on the function and benefits of the new OLZ Nonlinear Shrinkage Estimator will be published in an OLZ Research Note.

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