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

Table 5: Summary statistics for the yield curve data, in percentage points.series mean sd min max series mean sd min maxEONIA Index 2.47 1.44 0.08 5.16 EUSA3 Curncy 3.23 1.26 0.47 5.59EUR001M Index 2.52 1.43 0.11 5.05 EUSA30 Curncy 4.45 1.05 1.86 6.22EUR001W Index 2.45 1.44 0.08 4.89 EUSA35 Curncy 3.81 0.80 1.86 5.05EUR002M Index 2.59 1.43 0.15 5.13 EUSA4 Curncy 3.40 1.21 0.60 5.65EUR003M Index 2.67 1.40 0.19 5.28 EUSA40 Curncy 4.12 0.92 1.87 5.99EUR004M Index 2.70 1.38 0.23 5.32 EUSA45 Curncy 3.84 0.82 1.88 5.14EUR005M Index 2.74 1.36 0.28 5.36 EUSA5 Curncy 3.56 1.16 0.77 5.71EUR006M Index 2.77 1.34 0.32 5.38 EUSA50 Curncy 4.07 0.90 1.89 5.74EUSA1 Curncy 2.87 1.36 0.33 5.38 EUSA6 Curncy 3.70 1.13 0.95 5.76EUSA10 Curncy 4.09 1.04 1.56 5.95 EUSA7 Curncy 3.82 1.10 1.12 5.82EUSA11 Curncy 4.07 1.01 1.68 5.98 EUSA8 Curncy 3.92 1.08 1.29 5.86EUSA12 Curncy 4.22 1.01 1.79 6.06 EUSA9 Curncy 4.01 1.06 1.43 5.89EUSA15 Curncy 4.35 1.00 1.91 6.16 EUSWG Curncy 2.72 1.53 0.32 5.35EUSA1F Curncy 2.92 1.34 0.35 5.43 EUSWH Curncy 2.73 1.52 0.32 5.30EUSA2 Curncy 3.04 1.31 0.38 5.52 EUSWI Curncy 2.74 1.49 0.32 5.31EUSA20 Curncy 4.46 1.01 1.92 6.22 EUSWJ Curncy 2.74 1.52 0.32 5.33EUSA25 Curncy 4.43 1.03 1.90 6.22 EUSWK Curncy 2.75 1.52 0.32 5.343 Method3.1 A theory of maturity transformation and its relation to interest rateriskConsider a financial institution that enters into contractual arrangements with other parties. Thesecontractual agreements bind the institution into making and receiving payments many years intothe future. Let us imagine that there are finitely many characteristics of these future cashflowsthat are relevant for determining the price today of transferring these rights and obligations toother institutions. We could call this set of characteristics Ω, and we could write Ω = X × T forsome finite sets X and T with T ⊂ R + to record the fact that among these characteristics will bethe contractual maturity or repricing date of each cashflow (T ). The financial institution is thereforedefined by its asset and liability cashflow streams { }{ }A x,t ∈ R : (x, t) ∈ X × T ⊂ R N × R + andLx,t ∈ R : (x, t) ∈ X × T ⊂ R N × R + respectively, where x ∈ X ⊂ R N is an indexing set 18 andt ∈ T ⊂ R + is time into the future. 19 We can define the net asset stream or equity stream using afunctional application of the accounting identity E {E x,t A x,t − L x,t : (x, t) ∈ X × T }. The equitystream can be thought of as the future profit or future net cashflow in the firm emerging over time inevery tradable claim x ∈ X.We can say that an institution engages in net asset transformation if ∃(x, t), (x ′ , t ′ ) ∈ X × T suchthat E x,t ≠ E x ′ ,t′, or in words, if there are differences in its borrowing and lending across characteristicsin X × T . We give a graphical representation of transformation in Figure 6 , where an intermediaryis a net borrower of some tradable claims and a net lender of others. Maturity transformation is thena special case of net asset transformation and could be defined local to some x ∈ X or globally in allx ∈ X . An intermediary engages in local maturity transformation at x ∈ X if ∃t, t ′ ∈ T such thatE x,t ≠ E x,t ′, which says that the intermediary transforms assets of type x ∈ X from various maturitiesinto other maturities, while an intermediary engages in global maturity transformation if ∃t, t ′ ∈ Tsuch that ∑ x E x,t ≠ ∑ x E x,t ′. We can further talk of positive or negative maturity transformation,18 The index x ∈ X could be thought of as measurable time-invariant classifications of assets and liabilities relevant tothe price of a contract. Formally, X = Ω\T . Examples are sector, geographic, and ratings-based classifications of assetsand liabilities. In the context of assessing the revaluation effect of changes in asset prices or interest rates, we assumethat we have a complete market so that we can treat every element x ∈ X as a tradable claim with a measurable price.We will require that X be finite, or in other words |X| < ∞. The indexing set X is relevant for grouping assets andliabilities that are traded together, have similar prices (which may or may not be related to others through substitutioneffects) and whose risk characteristics are therefore similar.19 We will require |T | < ∞, which does not in principle preclude the institution from holding non-maturing assets likestocks.15