In this paper we determine the extent of predictability of India’s major spot exchange rates by using the Lyapunov exponent. We first determine whether the series is fractal (self-similar) in nature. If it is indeed so, then next we determine whether the underlying dynamics of the system is deterministic or stochastic. If the dynamics is found to be deterministic then we calculate the Largest Lyapunov Exponent (LLE) to determine whether the series has deterministic chaos. Finally we use the inverse of the Lyapunov exponent to estimate the time period for which out of sample predictions for the series make sense. We find that India’s major spot exchange rates are: a) fractal in nature, b) chaotic with a high embedding dimension and c) The inverse of the LLE gives us a time frame in which any meaningful predictions can be made. These results are interpreted in two ways. First, exploiting the efficient market interpretation of randomness we conclude that since available information is fairly rapidly internalized, chaotic behaviour is mainly due to the unforeseen nature of the pool of new information affecting the systems at such short intervals of time. Second, anti-cyclical central bank interventions are conjectured to be the source of determinism in otherwise almost random movements.