Maturity Transformation and Interest Rate Risk in Large European ...

Table 7: Frequency of ≥ 2% increase in the level of historical (forward or zero) yield curves over anl−month period for various values of l. Subtables (a) and (b) are computed by estimating Nelson-Siegeland Svensson parametric forms respectively at each month-end in the sample, and by then examiningthe longitudinal distribution of β 0 . In each subtable, the first row shows the number of times wherean l−month change in β 0 meet or exceeds 2%, the middle row shows the number of longitudinalobservations on which this count is based, and the final row shows the frequency obtained by dividingthe first row by the second.(a) Nelson-Siegel1 3 6 9 12 15 18 24number ≥ 2% 1 3 5 5 6 6 2 6number observations 166 164 161 158 155 152 149 143frequency (%) 0.60 1.83 3.11 3.16 3.87 3.95 1.34 4.20(b) Svensson1 3 6 9 12 15 18 24number ≥ 2% 4 6 14 19 22 29 36 33number observations 166 164 161 158 155 152 149 143frequency (%) 2.41 3.66 8.70 12.03 14.19 19.08 24.16 23.084.3 How representative is a 2% parallel yield curve shock?In Table 7 we show the frequency of large parallel shifts in the yield curve, under the Nelson-Siegeland Svensson models, over various time horizons. Under the Nelson-Siegel model, such large movesin the yield curve are rare even over 24 months, while under the Svensson model they are much morefrequent. The most relevant time horizons for our purposes are up to 3 months, in which time wemay expect a bank to be relatively unable to make major portfolio adjustments in response to sharpyield curve changes. Based on time horizons of up to 3 months, we might estimate that a 2% parallelupward shift in yield curve occurs with probability between 0.6% and 3.7% in any one month, whichcorresponds to something between a 1 in 14 year event and a 1 in 2 year event. This gives an idea ofthe ‘severity’, or lack thereof, of a 2% shock to the level of the yield curve.In addition, we would like to investigate the extent to which it is reasonable to shock the level ofyield curves without also varying other shape parameters of the yield curve. In particular if slope andlevel changes tend to occur together, then the revaluation effect of a level shock only may under- oroverstate the revaluation effect of a shock to both levels and slope. We present an initial investigationof these relationships between changing parameters in Table 8, where the subtables correspond todifferent time horizons over which we might measure the change in parameters. The correlations arestable between tables. They show that changes in the level and slope of the yield curve, as parametrisedby β 0 and −β 1 , exhibit a strong positive contemporaneous correlation over 1, 3, 6, 9 and 12 months. 32Increases in the level of the Euro yield curve are associated with simultaneous increases in the slopeof the yield curve over all of these time horizons, and the absolute size of the correlation decreaseswith the time horizon. Similary, level and curvature show a strong negative association, suggestingthat yield curves flatten when they shift upward, and the absolute size of this association increaseswith the time horizon. We therefore note, that regardless of the severity of the interest rate shock onewould like to apply (for example a 2% level change), association between level, slope and curvatureare highly prevalent historically. We regard these relationships as evidence against the plausibility ofa parallel yield curve shock. These relationships should be used in a proper assessment of interest raterisk.It is well known that correlation is not a very satisfactory measure of dependence. In a sense,correlation only captures a type of ‘linear’ dependence, which might ignore important and measurable‘non-linear’ relationships. As a robustness check on our correlation estimates, we provide scatterplotsof the levels and month-on-month (l = 1) changes in the β parameters of the Nelson-Siegel model in32 β 0 and β 1 are negatively associated, so that β 0 and −β 1 are positively associated, and hence increases in level arepositively correlated with increases in slope.25