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.

使用经验数据和它们揭示的属性，我们开发了一个因子来捕捉货币隐含相关性和波动性的变化。为此，我们在欧几里得空间中应用 Guldin-Pappus 定理来构建旋转三角形的特定因子，我们将其定义为重力半径。这种方法允许构建一个聚合所有货币对交易的投资组合指数。我们的因子是投资组合中所有重力半径因子的加权总和，表现出类似于文献中定义的众所周知的湍流指标的特征，并且与 CBOE VIX 指数具有中等相关性。因此，该因素可以作为风险指标。我们认为，波动率的变化比相关性的变化对重力半径因子值的影响要大得多。