In this paper, we undertake a mathematical investigation of 20 countries to answer three questions in relation to the evolution of the COVID-19 pandemic, the real economy and the financial economy. We study three multivariate time series measuring country’s daily mobility data, daily COVID-19 cases, and financial index performance. First, we analyse which countries behave similarly with respect to each of these features independently. Second, all countries’ trajectories are studied in conjunction to determine if any two candidate features exhibit more pronounced similarity. We demonstrate that mobility data and financial indices exhibit the most similarity in their trajectories. Finally, we study whether there is a difference in the time taken for COVID-19 cases data to be reflected in financial index performance and economic activity. A new optimisation method is introduced which demonstrates that mobility data tends to lag financial market performance, highlighting greater efficiency among financial market participants than governments in considering and acting upon new COVID-19 data. This finding suggests that studying mobility data as a leading indicator for financial market performance during the pandemic was, at least in the short-term, misguided.
Motivation for the study:
During the pandemic there was a surge of interest in alternative data among the investment management community. One of these data sources was Apple mobility data. The basic hypothesis here, was that mobility data may be a leading economic indicator and provide insights into the probable movement of financial indices. The initial motivation for this study, was seeking to determine whether such mobility data provided any utility to investment managers in their estimating future performance of respective financial indices. The countries included in this study are: Argentina, Australia, Brazil, Canada, Denmark, France, Germany, India, Italy, Japan, Mexico, the Netherlands, New Zealand, Norway, Russia, Singapore, Spain, Switzerland, United Kingdom and United States. For each country, we analyse three time series (COVID-19 new cases, financial index performance, mobility data). Our analysis uses data starting 1/1/2020 and finishing 30/12/2020. The data sources are Bloomberg, Apple Mobility and Our World in Data.
In this section we study the independent behaviours of COVID-19 new cases, mobility activity and financial index performance among our 20 countries of interest. In each section, we generate a distance matrix between the normalised trajectories of each country’s respective feature. We apply hierarchical clustering to each distance matrix to study the groupings and candidate similarity among countries. A summary of clustering results is below.
The COVID-19 cases trajectory dendrogram is comprised of 2 clusters, a large predominant cluster and a small cluster of outlier countries (New Zealand, Australia, and Singapore). The larger cluster is characterised by new case trajectories exhibiting multiple waves of new cases, with many countries experiencing growth in cases toward the end of 2020. The common theme among the countries in the anomalous cluster, (consisting of New Zealand, Australia and Singapore) is their low total number of cases throughout 2020, and their suppressed growth in cases toward the end of 2020.
The mobility activity trajectory dendrogram is comprised of 2 more equally-sized clusters. The first cluster includes: Mexico, Brazil, Australia, Argentina, Singapore, India, New Zealand and Japan. Mobility trajectories within this cluster are consistently increasing (or, in select instances, flat) among these countries. These trajectories are representative of countries that experienced waves of COVID-19 cases earlier in 2020, imposed restrictions to reduce case numbers, and gradually reopened their economies. The second cluster consists of the United Kingdom, Spain, the United States, Canada, the Netherlands, Italy, Switzerland, Germany, France, Denmark, Russia and Norway. All mobility trajectories for countries within this cluster possess declining trajectories in their mobility. This is almost certainly due to government restrictions in respective countries, which were in response to significant growth in COVID-19 cases and deaths. Interestingly, the two clusters exhibit geographical affinity. The first cluster consists of countries in South America and Oceania, while the second cluster comprises European and North American countries. This highlights the similarity in the timing of lockdowns among many countries in proximal geographies.
Financial index performance:
The financial trajectories dendrogram consists of 2 clusters, a primary cluster and a smaller anomalous cluster. The anomalous cluster consists of the United Kingdom, Mexico, Spain and Singapore. The outlier cluster is comprised of countries that share similar financial index trajectories. Specifically, there is a large drop in March, a subsequent drop in November and a slight to moderate recovery during the latter half of November and December. Interestingly, all of these countries’ financial indices finish 2020 at a level lower than their pre-COVID position. The dominant cluster which consists of the remaining countries, exhibits far less uniform trajectories. However, many countries in the dominant cluster experienced more substantial recoveries than the anomalous cluster. For instance, the United States and New Zealand (which possess highly similar trajectories) both post consistent gains after their precipitous drops in March.
Trajectory associations and interplay
The preceding analysis highlights several noteworthy points regarding the consistency in country cluster behaviours in reference to the above features.
- There is no consistency in cluster structure among COVID-19 cases, mobility activity and financial index performance. The size of the clusters is highly variable. However, in all dendrogram
- There is no consistency in cluster composition. In both the COVID-19 cases and financial index performance dendrograms there is a small, anomalous cluster. There is limited intersection between the countries in each anomalous cluster, highlighting a lack of consistency in the way that countries naturally group — when clusters are formed with respect to different metrics’ trajectories.
- There is clearly no relationship between countries’ financial index performance and their mobility or COVID-19 trajectories. The most obvious example of this is Singapore. Hierarchical clustering highlights that Singapore managed COVID-19 cases anomalously well, while its financial index performance was anomalously poor. By contrast, the United States leads the world in COVID-19 cases and deaths and exhibited very strong financial index performance. This is seen in Figure 4.
Next, we seek to determine collective similarity among country attributes that we have studied. To do so, we generate a 60 x 60 matrix measuring the normalised inner product between all attributes’ trajectories, and apply hierarchical clustering to the resulting distance matrix. The results can be seen in Figure 5. There is obvious structure in this dendrogram. Financial and mobility activity trajectories are highly similar, while COVID-19 case trajectories are significantly less similar. This makes sense. Both the mobility and financial index trajectories exhibit similar shapes; there is generally a sharp drop around March, followed by a subsequent recovery in activity and gains respectively. COVID-19 cases on the other hand exhibit dissimilar trajectories. First, COVID-19 case trajectories between countries are much more dissimilar — influenced by many factors such as the government’s willingness to enforce restrictions, the restriction of travel and human movement, etc. Second, COVID-19 case trajectories are prone to `wave’ behaviour, where there may be multiple peaks and troughs throughout the evolution of a country’s 2020 case numbers. Interestingly, there is no tendency for trajectories to be grouped based on country. For example, the Japan COVID-19 cases, financial index performance and mobility trajectories do not cluster similarly. Given the collective phenomenology, one would naturally wish to understand whether COVID-19 cases impact financial indices or mobility activity first — and whether this varies among countries.
Given the similarity in the behaviour of mobility activity and financial index performance, we now compare the efficiency of governments and financial market participants in their use of COVID-19 data for decision-making. To do so, we introduce a new inner product-based optimisation framework, where the objective function is to estimate an offset between any two trajectories such that their inner product is maximised. Effectively, this aligns the major peaks and troughs in any two candidate trajectories. In this model, we assume that either mobility activity or financial index performance may be the laggard. The offset results displayed in Table 1 reveal several findings.
- In general, mobility trajectories lag financial index trajectories. In fact, only 3/20 countries possess trajectories where their mobility activity reflects COVID-19 case information more quickly than the respective financial index.
- There is significant variability in the offset among countries. The range of offsets is 16 days. Spain and Switzerland have offsets of only 2 days, while Japan has an 18 day lag between its financial index and mobility activity trajectories.
- The 18 day mobility lag in Japan suggests that COVID-19 information was captured far more efficiently by financial markets than the Japanese government. This is made clear in Figure 6.
Discussion and limitations:
All studies have their limitations, and this one is no different. Out analysis could be improved in several ways. First, one could study more granular financial and mobility data. It is possible that analysing data that is aggregated at the country and financial index level respectively, we may be ignoring subtleties in the data and may fail to capture important relationships. That being said, there are several interesting findings in this work. First, we demonstrate that there is very little consistency in cluster behaviours or constituents when studying the trajectories of COVID-19 cases, mobility activity and financial index performance. This was most clearly evidenced by Singapore, who managed their COVID-19 case numbers particularly well and had particularly weak performance in its financial index. By contrast, the United States experienced huge COVID-19 case (and death) numbers, while the country index produced strong performance after the market crash in March. Next, we demonstrate that financial index and mobility trajectories are most similar, with no tendency for trajectories to be grouped around their respective countries. Having established this similarity, our new optimisation method demonstrates that mobility trajectories generally lag financial index trajectories. This suggests that throughout the pandemic, financial market participants incorporated COVID-19 case numbers into their trading decisions faster than governments were able to act on this information by way of instituting restrictions.
I have tried to keep mathematical notation to a minimum for the sake of readability. If you have any questions related to the above article, please feel free to contact me at [email protected]