When you’re waiting for the next round of earnings announcements to come out, there’s a lot of emphasis put on the consensus view – the average (or occasionally median) of all the major analysts covering the stock. That’s a straightforward measure, which has its own advantages, but it assumes analysts from different firms aren’t influencing each other, which probably isn’t true. Even without talking to each other information can flow in other ways – both directly as analysts keep an eye on the competition and indirectly simply by being aware of the current consensus and subconsciously moving toward it.

“We propose a novel approach for extracting incremental information from analyst forecasts. Instead of taking the more common methodology of using a linear regression of analyst characteristics to forecast an analyst’s accuracy we employ graph theory to extract interactions between analysts,” write Citi analysts Chris Montagu and Matthew Burgess in their paper *Searching for Alpha: Networking with Analysts*.

### Analyst forecasts converge at the end of the year

While it seems reasonable that analysts would influence each other over time, there’s also some evidence that what Montagu and Burgess call the ‘smart thesis’ disseminates through the analyst community. As you get closer and closer to full-year reports, the error and the dispersion both fall off, implying that even when analysts start off being either too bullish or too bearish, they recognize the better thesis and tend toward it. You could interpret the information other ways, for instance that the analyst with the best thesis is likely to have the highest conviction and influence the consensus instead of having an anchoring bias. Regardless, this motivates the idea that giving everyone equal weight might not be the best approach.

To construct their weights, Montagu and Burgess first construct a fully connected adjacency matrix using the difference in EPS forecasts as their notion of distance. That may sound complicated, but it really just means that if one analyst forecasts $1.10 EPS for a stock and a second analyst forecasts $1.20, they are considered to be $0.10 away from each other, and then repeat for every other pair of analysts. You can visualize the information as a graph like the one above.

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Next, you can calculate an analysts ‘closeness,’ a measure of centrality, by adding up all the numbers in each column and taking the inverse. They also calculate something called Bonacich Power Centrality and point out that graph theory has a number of other alternate measures for centrality that could be used, but closeness turns out to be a better predictor anyways, at least in Europe. The end result are a different set of weights to use when averaging analyst forecasts.

### Every forecast is unlikely to be accurate, says Citi

The obvious question is what you get for the extra work, and it’s probably not as much as you’d like, but that’s because analyst forecasts in general are of limited use.

“As a crude example, a flood in a mine will affect the earnings of a company, however none of the analysts following that company are likely to have predicted it. Every forecast, and therefore any measure of consensus, is unlikely to be accurate,” write Montagu and Burgess.

Closeness gives a better signal than either median forecasts or Bonacich power centrality (all three do better than taking an average, but with P-values above 40%), and when used to inform investments it only had two down years out of fourteen when covering European stock, outperforming the other two measures over the same time frame.

Closeness has a higher correlation with other investing styles (and a stronger negative correlation with value investing), as well as extremely high turnover rates. Montagu and Burgess argue that because there is a long alpha decay, persisting up to a year, you can slow down turnover to rein in transaction costs and still benefit from the signal.

### Closeness seems to work in Asia, but not the US

Montagu and Burgess test this idea in two out of sample stock markets, Asia ex-Japan and the US, and the results are mixed. In both cases the median forecast has the worst performance over the full fourteen-year period (though not over some subsections, but closeness and Bonacich power centrality are a lot less impressive in the US.

“One potential explanation for the poor performance of the US strategy is that many consider it to be a more efficient market than some of its global counterparts,” they write, speculating that quarterly reporting requirements, versus semi-annual reporting in Europe and Asia, could play a role.

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