in tier 1 capital. ( d ) assumes that 50 % of dividends are paid as cocos and retained. chart 12 : cumulative amount of tier 1 capital for major uk banks £ bn including dividends paid as cocos including bonuses paid as cocos actual tier 1 capital 2000 2001 2002 2003 2004 2005 2006 2007 sources : annual accounts and bank calculations footnotes as per chart 11 bis central bankers ’ speeches table 1 : type i and type ii errors for basel regulatory ratios and market - based capital measures type i type ii basel regulatory ratios 50 % 43 % market capitalisation to book - value of total assets 21 % 5 % market capitalisation to book - value of debt 20 % 11 % market capitalisation to book - value of equity 10 % 11 % sources : capital iq and bank calculations ( a ) a type i error occurs when a bank ’ s ratio falls below the trigger level ( calculated according to a loss function as described in charts 5 – 8 ) and capital is not required ( defined as that bank not suffering a “ crisis ” over the next 365 days ). the number in this column is the proportion of days when a type i error occurs. ( b ) timely conversion is defined as a bank ’ s ratio falling below the trigger level no less than one month and no more than one year before a “ crisis ”. the number in this column is the proportion of “ crisis ” banks for which timely conversion does not occur ( i, e, there is a type ii error ) at this trigger level. ( c ) for each metric, the threshold for a signal of impending distress is as given in charts 5 to 8. bis central bankers ’ speeches

research on complex systems has confirmed hayek ’ s hunch. policy predicated on over - precision risks catastrophic error. complexity in risk models may have perpetuated hayek ’ s pretence in the minds of risk managers and regulators. ( c ) timeliness one of the purported benefits of model - based calibration is that it increases the sensitivity of capital requirements to changes in risk. reported regulatory capital ratios should better reflect risk and thus should in principle offer timely advance warnings of impending bank stress. the data tell a somewhat different story. to see that, consider the experience of a panel of 33 large international banks during the crisis. this panel conveniently partitions itself into banks subject to government intervention in the form of capital or guarantees ( “ crisis banks ” ) and those free from such intervention ( “ no crisis banks ” ). chart 5 plots the reported tier 1 capital ratio of these two sets of banks in the run - up to the lehman brothers crisis in september 2008. two observations are striking. first, the reported capital ratios of the two sets of banks are largely indistinguishable. if anything, the crisis banks looked slightly stronger pre - crisis on regulatory solvency measures. second, regulatory capital ratios offer, on average, little if any advance warning of impending problems. these conclusions are essentially unchanged using the basel iii definitions of capital. this visual evidence can be formalised by constructing some type i ( false positive ) and type ii ( missed crisis ) error estimates for the same 33 - bank panel. assume, by way of illustration only, that if a bank ’ s tier 1 capital ratio dips below 8 %, this is deemed to signal distress ( table 1 ). the probability of a type i error using regulatory capital ratios is 50 %, while the probability of a type ii error is around 43 %. on those assumptions, this suggests regulatory capital ratios do about as well in predicting crises as a coin toss. they are essentially uninformative about future bank stress. taken together, this does not paint an altogether encouraging picture. a critic might argue that regulatory capital ratios have become too complex to verify, too error - prone to be reliably hayek ( 1974 ). bis central bankers ’ speeches robust and too leaden - footed to enable prompt corrective action. from a first principles perspective, they score poorly as an optimal control device over a complex system such as finance. resurrecting the third pillar what could be done to strengthen the