Superkurtosis

Risk metrics users assume that the moments of asset returns exist, irrespectively of the trading frequency, hence the observed values of these moments are used to capture the potential losses from asset trading (e.g. with Value-at-Risk (VaR) or Expected Shortfall (ES) calculations). Despite the fact that the behavior of traditional risk metrics is well-examined for high frequency data (e.g. at daily intervals), very little is known on how these metrics behave under Ultra-High Frequency Trading (UHFT). We fill this void by firstly examining the existence of the daily and intraday returns moments, and subsequently by assessing the impact of their (non)existence in a risk management framework. We find that the third and fourth moments of the distribution of asset returns do not exist. We next use both real and simulated data to show that, when daily trading is implemented, VaR or ES deliver estimates in line with what the theory predicts. We show, however, that when UHFT is considered, assuming finite higher order moments, potential losses are much bigger than what the theory predicts, and they increase exponentially as the trading frequency increases. We argue that two possible explanations affect potential loses; first, the exponential increase in the sample data points at UHFT; second, the fact that the data, which are sampled from a heavy-tailed distribution, tend to have higher sample moments than the theory suggests - we call this phenomenon superkurtosis. Our findings entail that traditional risk metrics are unable to properly judge capital adequacy. Hence, the use of risk management techniques such as VaR or ES, by market participants who engage with UHFT, impose serious threats to the stability of financial markets, given that capital ratios may be severely underestimated.