Probability of informed trading and volatility for an ETF

We use the new procedure developed by Easley et al. (2010b) to estimate the Probability of Informed Trading (PIN), based on the volume imbalance: Volume-Synchronized Probability of Informed Trading (VPIN).  Instead of applying a maximum likelihood procedure to estimate unknown parameters they use the volumes as a proxy for the arrive of new information. The idea is that more relevant is a piece of information, more volume it will attract. Moreover, the VPIN can be seen also as a proxy of volatility since large price movements are associated with large volumes, thus sampling by volume is a proxy to sampling by volatility. We also relate the VPIN metric to volatility measures which consider the number of jumps.

We use data on the exchange traded fund tracking the S& P 500 index, the SPY, for a period of ten years. The choice of the data is due to the increasing importance of ETFs in the investment horizon. Our results are comparable to those in Easley et al. (2010b). We find that the historical distribution of Probability of informed trading follows also in our case a log-normal distribution and also the trend of our VPIN is comparable to the one for the futures. We also investigate whether VPIN metric Granger-cause volatility of whether the reverse is true. We find support that the casual link goes from VPIN metric to volatility, i.e. VPIN improves the forecast of volatility. 

We further investigate the relation between VPIN and volatility using a Heterogenous Autoregressive model of Realized Volatility with jumps like in Corsi and Renò (2010) and adding the VPIN. We compare different models with and without jumps and VPIN and we find that the model that includes both jumps and VPIN is better than the others. As a further investigation we plan to analyse the possible links between VPIN and liquidity measures.