Most investors are aware of the paramount benefits of diversification. Allocating funds across investments that are little or negatively correlated with each other can effectively reduce portfolio risk without sacrificing expected returns.

This is why estimating cross-asset correlations is an important step in portfolio construction. Furthermore, investors are usually rightly concerned about potential changes in correlation structures over time.

While it is fairly simple to derive a correlation matrix from a given set of investment returns, it usually involves various restrictive assumptions that can influence results. We, therefore, set up a small tool on the quantamental platform allowing us to easily calculate cross-asset correlations for flexible subsets of assets under different assumptions and throughout different periods.

Have a look at the gif below to see how cross-asset correlation structures have evolved over time. This illustration also shows why stress-testing and scenario analysis are so critical. Calm bull markets can easily lead to an overestimation of diversification benefits. The animation also emphasizes again how outstanding the year 2020 was.

It also matters at which frequency returns are measured, especially when different geographies are concerned. Due to time-shift, the same news can be priced into different markets on different days, distorting correlation matrixes estimates based on relatively high-frequency data.

Last but not least, investors need to pay attention to the currency in which returns are measured. Investors who hedge foreign currency exposure will be more interested in local currency returns. However, the correlation between currencies translated into the portfolio's base currency may be more relevant for unhedged investments.

It's important to remember that this rather illustrative approach is suitable for investors interested in developing a basic feeling for correlation structures. For quantitative portfolio optimization and risk management, it has been shown that sample covariance matrices usually perform poorly, calling for advanced approaches such as fundamental multi-factor models, Principle Component Analysis, resampling or covariance shrinkage.

For more reflections on the role of non-synchronous trading and adjustment methods using lagged or rolling returns, please also refer to our attached paper, first published in March 2020.