The Geometry of the World of Currency Volatilities

Using empirical data and the properties they reveal, we develop a factor that captures changes of both currency implied correlation and volatilities. For this purpose, we apply the Guldin–Pappus theorem in Euclidean space for rotating triangles to construct a specific factor, which we define as gravity radius. This approach allows the construction of a portfolio index aggregating all currency pairwise trades. Our factor, which is a weighted sum of all gravity radius factors in a portfolio, exhibits characteristics that are similar to the well-known turbulence metric defined in the literature and has moderate correlation to the CBOE VIX index. This factor therefore can serve as a risk indicator. We argue that the changes in volatilities impact the gravity radius factor value considerably more than changes in correlations. Portfolio managers and risk managers can use the new metric to identify correlation and volatility changes that dynamically react to new information.