Combining forecasts in the presence of ambiguity over correlation structures

We suggest a framework to analyse how sophisticated decision makers combine multiple sources of information to form predictions. In particular, we focus on situations in which: (i) Decision makers understand each information source in isolation but are uncertain about the correlation between the sources; (ii) Decision makers consider a range of bounded correlation scenarios to yield a set of possible predictions; (iii) Decision makers face ambiguity in relation to the set of predictions they consider. We measure the bound on correlation scenarios by using the notion of pointwise mutual information. We show that the set of predictions the decision makers considers is completely characterised by two parameters: the Naïve-Bayes interpretation of forecasts (correlation neglect), and the bound on the correlation between information sources. The analysis yields two countervailing effects on behaviour. First, when the Naïve-Bayes interpretation of information is relatively precise, it can induce risky behaviour, irrespective of what correlation scenario is chosen. Second, a higher correlation bound creates more uncertainty and therefore potentially more conservative behaviour. We show how this trade-off affects behaviour in different applications, including financial investments, group decision making and CDO ratings. For the latter, we show that when faced with complex assets, decision makers are likely to behave in ways that are consistent with complete correlation neglect.