The London Stock Exchange (LSE) has been the most-valued stock exchange in Europe since 2003, except for ten days in the autumn of 2022 when Paris took the lead. But it has no influence. To see how that’s possible, let’s draw a parallel. Warren Buffet is currently the world’s fifth-wealthiest person. Others closely watch his investment choices as they try to emulate his success. At the same time, Elon Musk is the second-richest, but most have stopped listening to him. Pedo guy, accusations of market manipulation, and the chaos surrounding the Twitter takeover have tired the audience. Being big is not the same as being influential. Nor is being loud. This article finds that the London Stock Exchange is more Elon than Warren.
London’s place
Influence is the ability to cause others to change their behaviour, beliefs, or opinion. It’s not straightforward to measure, but Network Theory offers several suggestions. We averaged four definitions to calculate the importance of each stock market in the US$ 1 Trillion Club for every year from 2012 to 2022. We then lifted out London and compared the pattern of influence with its European clubmates (Fig 1). The picture looks tangled, but we see matching trends when we zoom in.
From 2012 to 2016, London shared a pattern with Nasdaq Nordic, albeit at a lower level. That’s alright; we later see that Nasdaq Nordic is a global top-ranker. Then, from 2016 to 2019, London diverged, and its pattern resembles the Swiss Market Index. Again, that’s alright. Being similar to a strong and independent European market in the wake of the Brexit referendum is encouraging. In 2019 the pattern switched to match Germany’s Deutsche Boerse. The two markets swapped positions regularly until 2019, but London has remained firmly at the bottom since.
London was never influential in the past decade – and over the last four years, it has lost more of what little it had. That’s not the end of the world – it simply means that London’s performance does not influence other markets, and vice versa. We saw in this article that being an outsider has upsides, too: isolated markets are worth a gamble during downturns but are less sure to deliver when times are good. London needs to know its place. And use that to its advantage – embracing its inner Elon, however uncool that may be.
In what follows, we briefly describe the analysis. A Jupyter notebook with the code (preview) and the data is available here on GitHub for anyone interested in the detail.
Data and networks
Our analysis starts with the 18 markets in the US$ 1 Trillion Club. We exclude Tehran Stock Exchange because we cannot find data. Euronext is out, too, as its first full year was only in 2015. Johannesburg and Brazil stock exchanges are just short of US$ 1 Trillion and serve as substitutes. We collected values for the period January 1, 2012, to December 31, 2022, from Yahoo Finance, with one exception: Saudi Stock Exchange (Tadawul) numbers were unavailable and downloaded from Investing.com instead. Fig 2 shows the evolution of market values in local currency over time.
The yellow-green line represents London, and the graph already provides some intuition that its trends are different from other major markets. London didn’t experience the hump in 2014-16, saw a sharper increase in 2019, and dropped back to pre-COVID levels in early 2021. But we go beyond visual inspection.
First, we find the global network of relationships between stock exchanges for each year. We calculate daily log returns correlations between each market and every other market and then convert the coefficients into distances. Then, we use the distances to generate networks and maintain only the significant connections. Fig 3 displays the results.
They look like star constellations. The networks are undirected, meaning that influence can flow in either direction, but markets on the intersections are more important. We coloured London orange to make it easy to spot, its European peers are blue, and the rest of the world is grey. The shapes vary from year to year, but a few features are consistent. We generally see a European cluster with Nasdaq Nordic, Swiss, Deutsche and London, an American group with New York, Nasdaq, Toronto and Brazil, and an Asian collection with Shanghai, Hongkong, Shenzhen, Taiwan, Japan and Korea. Even though clustering is reasonably stable for these markets, positions within groups change. Australia, India, Johannesburg, and Saudi change alliances more often.
The four definitions
With networks in hand, we now apply the four Network Theory definitions to measure importance: degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality. They all measure influence, but each has a different emphasis. Let’s see what that is.
Degree centrality
The degree is simply the number of connections a node has. For example, on Twitter, Elon Musk has a degree of 130.1 million because that’s how many followers he has.
Degree centrality is the number of connections expressed as a fraction of the total possible connections. A node with a high degree centrality can influence the behaviour of many others. In Fig 4, the purple node is more influential than the orange node.
Fig 5 shows the degree centrality over time for all markets in our analysis in the top panel and Europe separately at the bottom. Globally, New York, Nasdaq Nordic, and Korea tend to be best connected and are most central to their clusters. The Swiss Market Index also does well in Europe, while London trails near the bottom.
Betweenness centrality
Betweenness centrality measures a node’s influence over the flow of information in the network. It’s the number of shortest paths that pass through it. The shortest path is the minimum number of hops from one node to another. Fig 6 shows an example.
The shortest path from the purple to the orange node is one hop on the diagonal line (B). Another route is possible (C), but with two jumps, that’s not the shortest path.
It’s tempting to think that the node with the most connections also has the most shortest paths. It can be, but it often isn’t. Fig 7 illustrates the point.
A and B each have seven nodes and six edges, but the networks have different structures. Network A has a star shape. The purple node in the middle has the highest degree centrality with six connections and the highest betweenness centrality because it is on the shortest path between any other two nodes.
In network B, however, the roles fall on separate nodes. The blue nodes have the highest degree centrality, with three connections each. But the orange node has the highest betweenness centrality: every shortest path from the left to the right side, and vice versa, has to pass through it. It’s a bridge between the two larger components of the network. Shapes like network B are more common in the real world, so the highest degree and betweenness centrality are often different nodes.
Fig 8 displays the betweenness centrality over time, again with all markets in the top panel and Europe separately at the bottom. Nasdaq Nordic and Korea have the highest averages globally, followed at a small distance by Swiss, India, New York, and Taiwan. London scored zero in 2019 and every year after because it has only one connection – Deutsche Boerse.
Closeness centrality
Closeness centrality expresses how close a node is to all other nodes. It measures the lengths of the shortest paths between a node and all other nodes that can be reached from it. We calculate it as the reciprocal of the sum of the shortest paths, and Fig 9 helps us see how that works.
Let’s compute closeness centrality for the purple node. There are four other nodes in the network, and they can all be reached. The numbers indicate the shortest path length from the purple node to that node. Then, the closeness centrality for the purple node is 4 / (1 + 1 + 2 + 2) = 4 / 6 = 2 / 3.
In Fig 10, we see closeness centrality over time for the markets in our analysis in the same format as before. Nasdaq Nordic, Korea, Swiss, India, Taiwan and New York are at the top, with average scores not far apart. London is, again, in the bottom half of the pack and lowest in Europe from 2019.
Eigenvector centrality
Eigenvector centrality indicates a node’s importance based on its connections. It’s a more sophisticated measure that takes into account indirect influence. A node is more important if it is linked to another with many connections. Fig 11 illustrates the idea: the importance of the purple node depends on the orange one it is connected to.
Finally, Fig 12 shows eigenvector centrality over time for our analysis. Nasdaq Nordic has the highest average, followed by New York, Korea and the Swiss Market Index, which have similar scores. London, on average, ranks 15th in a field of 18 – performing worse on eigenvector centrality than any other measure. London was on the network’s edge for the past four years, connected only to Germany’s Deutsche Boerse. Deutsche Boerse, in turn, connects to either the influential Nasdaq Nordic or Swiss Market Index and, for that reason, is placed in the top 10.
The four definitions of importance each measure different aspects of influence. In the final step, we take the average of the four statistics to reduce the error caused by any single method.