BIS Review 139/2009  15  Chart 5: Bank of England’s balance sheet as % of GDP 20  (a)  (c)  (b)  (f)  (e)  (d)  (g)  (h)  (i)  (k)  (j)  18 16 14 12 10 8 6 4 2  (a) Famine / End of railroad boom (1847) (b) Overextension of credit from 1855-1866 (c) Failure of Overend Gurney (1866) (d) Failure of City of Glasgow Bank (1878)  (e) Support for Barings (1890) (f) W W I (1914) (g) Currency and Bank Note Act (1928) (h) W orld W ar II (1941)  2004  1998  1992  1986  1980  1974  1968  1962  1956  1950  1944  1938  1932  1926  1920  1914  1908  1902  1896  1890  1884  1878  1872  1866  1860  1854  1848  1842  1836  1830  0  (i) Secondary Banking Crisis (1973) (j) Small Banks Crisis (1991) (k) Current Crisis (2007)  Source: Bank of England.
Since the 1970s, capital injections to the banking system have averaged around 8% of GDP at crisis time. 12 Taken together, this evidence paints a consistent picture: a progressive rise in banking risk and an accompanying widening and deepening of the state safety net. There is a ratchet. This ratchet is evidence of a policy time-consistency problem. 3. Time-consistency and the banking safety net  What explains this time-inconsistency? A simple framework is developed to explain the existence of, and ratchet in, the safety net. It focuses on the incentive structures facing owners of banks and the risk strategies they pursue. The run-up to the present crisis provides several examples of those incentives and strategies at work. Take the payoff profile facing a bank shareholder. Assume that the sensitivity of the bank’s assets to aggregate risk – in the language of finance, its beta – equals 0.1. So for every 10% movement in the market as a whole, the bank’s assets move by 1%. Assume too that the beta of the bank’s deposits is zero and that the bank has an equity capital ratio of 10%. While arbitrary, these numbers are broadly plausible. Conveniently, under those assumptions the  10  Laeven and Valencia (2009). 11  Logan (2000). 12  Laeven and Valencia (op.cit.). 4  BIS Review 139/2009  beta of the bank’s equity equals one. Figure 1 shows the payoff profile facing owners of the bank. The return on a bank’s equity lies on a 45 degree line when market returns are positive.