Measures of kurtosis – the fatness of the tails – of UK house price inflation are 6 times larger over the full sample than over the Golden Decade; for UK bond yields 10 times larger; and for UK equity returns 16 times larger. To bring these stylised facts to life, consider the distribution of equity returns in Chart 7. If we assumed the Golden Era distribution was the true one, the three worst monthly returns in history – the bursting of the South Sea bubble in September and October 1720, and Black Monday in October 1987 – would have been respectively 12.7, 6.9 and 6.5-sigma events. All three would have appeared to be once in a lifetime – of the universe – events. Underestimation of risk, whether variances or tail outcomes, has consequences for the risks facing both individual firms and for the system as a whole. As an example of the former, Chart 9 plots some unconditional 90th percentile VaRs for a selection of UK banks, based on their equity returns up until end-July 2007 and then extended to include the present crisis. 3 These unconditional VaRs for UK banks increase, on average, by almost 60% once the sample is extended; and for some banks these risk measures more than double. For the system as a whole, one way of illustrating the consequences of underestimating risk is to translate it into “fair value” insurance premia. For example, consider a financial firm offering insurance against moves in future equity prices by writing put options in mid-2007.

Annex:  Chart 1: Probability density estimates  Chart 2: Probability density estimates  for UK GDP Growth  for UK RPI Whole sample (1857-2007) Golden Decade' (1998-2007)  Density 0.60  Whole sample (1857-2007) Golden Decade' (1998-2007)  Density 0.60  0.50  0.50  0.40  0.40  0.30  0.30  0.20  0.20  0.10  0.10  0.00 -15  -10  -5  0 5 10 Annual GDP Growth (%)  15  0.00 -40  -20  0 20 Annual RPI (%)  40  Chart 3: Probability density estimates  Chart 4: Probability density estimates  for UK Unemployment  for Annual Earnings Growth  Whole sample (1857-2007) Golden Decade' (1998-2007)  Whole sample (1857-2007) Golden Decade' (1998-2007)  Density 0.80  Density 0.80  0.70  0.70  0.60  0.60  0.50  0.50  0.40  0.40  0.30  0.30  0.20  0.20  0.10  0.10 0.00  0.00 -5  0  BIS Review 18/2009  5 10 15 Unemployment (%)  20  -40  -20  0  20  40  -0.10  Annual Earnings Growth (%)  11  Chart 5: Probability density estimates  Chart 6: Probability density estimates  for UK Base rate  for UK House Price Inflation  Whole sample (1857-2007) Golden Decade' (1998-2007)  Whole sample (1954-1997) Golden Decade' (1998-2007)  Density 0.40  Density 0.08  0.35  0.07  0.30  0.06  0.25  0.05  0.20  0.04  0.15  0.03  0.10  0.02  0.05  0.01  0.00 -5  0  5 10 Base rate (%)  15  20  0.00 -20  0 20 40 House Price Inflation (%)  60  -0.01  Chart 7: Probability density estimate for  Chart 8: Probability density estimate for  FTSE All-Share Index  UK 2.5% coupon consol yield Density  Whole sample (Jul 1700 - Nov 2008)  Whole sample (Jan 1693 - Nov 2008)  'Golden Decade' (Jun 97 - Jun 07)  0.24  'Golden Decade' (Jun 97 - Jun 07)  Density 0.10 0.09 0.08  0.20  0.07 0.16  0.06 0.05  0.12  (a) (b) (c) (d)  (c)(d) 0.08 (a)  (b)  0.04 0.03  (e)  0.02  0.04  0.01 0.00 -80  -60  -40  -20 0 20 40 Price return (%)  60  80  Sources: Global Financial Data and Bank calculations.