We argue that on electronic markets, limit and market orders should have equal effective costs on average. This symmetry implies a linear relation between the bid-ask spread and the average impact of market orders. Our empirical observations on different markets are consistent with this hypothesis. We then use this relation to justify a simple, and hitherto unnoticed, proportionality relation between the spread and the volatility per trade. We provide convincing empirical evidence for this relation. This suggests that the main determinant of the bid-ask spread is adverse selection, if one considers that the volatility per trade is a measure of the amount of ‘information’ included in prices at each transaction. Symmetry between market and limit orders stems from the self-organisation of liquidity in electronic markets. Our results appear to hold approximately on liquid specialist markets as well, although the spread is significantly larger.