The persistence phenomenon is studied in a financial context by using a novel mapping of the time evolution of the values of shares in a portfolio onto Ising spins. The method is applied to historical data from the London Financial Times Stock Exchange 100 index (FTSE 100) over an arbitrarily chosen period. By following the time dependence of the spins, we find evidence for a power law decay of the proportion of shares that remain either above or below their ‘starting’ values. As a result, we estimate a persistence exponent for the underlying financial market to be . Preliminary results from computer simulations on persistence in the economic dynamics of a toy model appear to reproduce the behaviour observed in real markets.