  We show that the cost of market orders and the profit of infinitesimal
market-making or -taking strategies can be expressed in terms of directly
observable quantities, namely the spread and the lag-dependent impact function.
Imposing that any market taking or liquidity providing strategies is at best
marginally profitable, we obtain a linear relation between the bid-ask spread
and the instantaneous impact of market orders, in good agreement with our
empirical observations on electronic markets. We then use this relation to
justify a strong, and hitherto unnoticed, empirical correlation between the
spread and the volatility_per trade_, with R^2s exceeding 0.9. This correlation
suggests both that the main determinant of the bid-ask spread is adverse
selection, and that most of the volatilitycomes from trade impact. We argue
that the role of the time-horizon appearing in the definition of costs is
crucial and that long-range correlations in the order flow, overlooked in
previous studies, must be carefully factored in. We find that the spread is
significantly larger on the nyse, a liquid market with specialists, where
monopoly rents appear to be present.
