On The Risk Situation of Financial Conglomerates: Does Diversification Matter?

Transcription

1 On The Risk Situation of : Does Diversification Matter? Nadine Gatzert and Hato Schmeiser

2 age 2 Outline 1 Introduction 2 Model Framework Stand-alone Institutions 3 Model Framework Solvency Capital, Shortfall Risk 4 Corporate Structures 5 Conglomerate Discount 6 Numerical Analysis 7 Summary

3 age 3 1. Introduction Increasing consolidation activity in the financial sector - Financial conglomerate: financial group providing services and products in different sectors of financial markets - Insurance group: financial group providing services and products in the insurance sector, not necessarily across sectors Corporate Diversification is currently of great interrest to regulators (cf. Solvency II, Swiss Solvency Test), financial group management and to the management of individual group entities

4 age 4 Different conglomerate structures (level of integration, organization form): - Holding company is a representive for the stand-alone case if the entities are separately capitalized and do not have access to each others cash flow - arent-subsidiary model subsidiary s market value is asset for the parent - Integrated conglomerate has one consolidated balance sheet and capital is in general fully fungible between the entities

5 age 5 Conglomeration leads to - Diversification benefit (reduction of risk) Hererby, capital and risk transfer instruments (CRTIs) increase diversification benefit - Conglomerate discount: decrease in shareholder value In literature (cf. paper): - Diversification benefits are calculated without accounting for the conglomerate discount (same capital structure is assumed before and after conglomeration)

6 age 6 But: comprehensive analysis requires competitive situation in a financial conglomerate (risk-adequate returns for shareholder and debtholder) - Hence: capital structure in group context differs from stand-alone case Aim of this paper: 1. Analyze diversification effects in a competitive setting (account for conglomerate discount) 2. Consider holding company, parent-subsidiary, integrated model

7 age 7 Aim of this paper (continued): 3. Include capital and risk transfer instruments (CRTIs) in parent-subsidiary model (guarantees, intra-group retrocession) Analysis of diversification benefits from different perspectives: - Group perspective: diversification benefit, joint default - Individual entity perspective: solvency capital, individual default risk

8 age 8 2. Model Framework Stand-alone Institutions Firm with L(t), A(t) = market value of liabilities, assets - Geometric Brownian motions (under the real-world measure) da() t = µ A( t) dt+ σ A( t) dw ( t) A A A dl() t = µ L( t) dt+ σ L( t) dw ( t) L L L dw dw A L ( ) = ρ A,L dt

9 age 9 D 0 = initial payment of debtholders E 0 = initial payment of equityholders A 0 =D 0 + E 0 invested in capital market - ayoff at t =1 (debtholders) ( ) D = L max L A, ayoff at t =1 (equityholders) ( ) E = A D = max A L,

10 age 10 A fair (or competitive) situation for equityholder and debtholder is given if ( ) Q ( exp( ) ) exp( ) max (,0) E = E r E = E r A L Q ( ) Q ( exp( ) ) exp( ) max (,0) D = E r L E r L A = L Π Q DO Hence, the safety level is measured with the Default ut Option (DO) value ( exp( ) max (,0)) Π = E r L A DO Q 0 1 1

11 age Model Framework Solvency Capital, Shortfall Risk For a given firm capital structure (D 0,E 0 ): - Available economic capital (risk-based capital): RBCt = At Lt - Necessary economic capital (solvency capital SC) = amount of capital needed at t = 0 to meet future obligations over a fixed time horizon for a required confidence level (cf. Swiss Solvency Test): ( exp( ) 1 0 exp( ) 1 0 α ) SC = TVaR = E r RBC RBC r RBC RBC VaR α

12 age 12 - Regulatory requirement: RBC0 SC - Minimum capital requirement (MCR), derived by Solvency I standards: MCR = 0.4 SC Field tests shown that MCR is typically between 10% to 40% of the solvency capital SC; as it is done in Filipovic and Kupper (2007), we choose the upper limit - Shortfall risk: ( ) S = RBC 1 < 0

13 age Corporate Structures Group consisting of two firms ( and S) Joint shortfall of entities within the group: - Exactly one firm defaults S S ( 0, 0) ( 0, 0) = RBC < RBC > + RBC > RBC < I - Both firms default Risk diversification: S ( 0, 0) = RBC < RBC < II 1 1 d group = 1 SC SC + SC + SC, group S, group, solo S, solo

14 age 14 Capital and risk transfer instruments (CRTIs) in parentsubsidiary model (legally binding instruments) - Guarantee: ( ( 1 1 )) T G = min DO S,max A L MCR,0 Transfer from to S is limited (available capital in t = 1) must be at least above the MCR - Quota share retrocession: ( β 1 ( 1 1 )) T R = min L S,max A L MCR,0 - Table: In order to calculate SC, we first need to determine RBC 1 ; RBC 0 is assumed unchanged (and hence does not effect SC)

15 age 15 Table: Risk-based capital at t = 0 and t = 1 for different conglomerate structures Solo (Holding) arent-subsidiary arent-subsidiary Guarantee arent-subsidiary Retrocession S RBC 0 0 t = 0 t = 1 = A0 L S S 0 A0 L0 = A0 L S S 0 = A0 L0 = A0 L S S 0 = A0 L0 = A0 L S S 0 = A0 L0 = A + Integrated 0 0 L A L S 0 0 S RBC RBC 1 RBC 1 = 1 1 S S = A L 1 1 = A L 1 1 S S S ( A1 L1 MCR ) + max,0 = A L 1 1 S S S ( A1 L1 MCR ) + max,0 G T = A L 1 1 S S S ( A1 L1 MCR ) + max,0 T R S S S = A L ( A S L S MCR S ) = min, 1 1 S S S ( A L MCR ) = min, + T G 1 1 S S S ( A L MCR ) = min, + T R 1 1 = A + A L L

16 age Conglomerate Discount - Account for decrease in shareholder value - Safety level (DO value) is assumed to be unchanged; hence, debtholder always pay the same amount D 0 Holding company: corresponds to stand-alone case since we assume that no transfer of assets takes place arent-subsidiary model: - Subsidiary s equity capital unaffected by group building - Fair initial equity capital of parent is reduced

17 age 17 - Fair initial equity capital of parent is reduced due to group-level diversification ( ) E = E e E Q r 0 1 ( 1 1 ( 1 1 ) ) ( max max,0,0 ) r S S S Q = E e A L + A L MCR Integrated conglomerate: Since ( max (,0)) D + D = L + L E e L + L A A S S Q r S only adjust equity capital of firm S such that ( max (,0)) Π = E e L + L A A =Π +Π DO,int Q r S S DO, S DO,

18 age Numerical Analysis Compare diversification effects with and without accounting for conglomerate discount Input parameter: α = 1%, r = 3.5%, β = 5% Firms have same safety level, same size, same asset and liability structure S L0 = L0 = 100 DO D0 = L0 Π 0 = = 99.9 E 0 = 30.1 (fair inital equity capital)

19 age 19 Assets and Liabilities: µ = 0.09 σ = 0.10 A µ = 0.01 σ = 0.10 L S S ( ) ρ( ) ρ A,L = A,L =. ρ S S ( A,L ) ρ( A,L ) A L = = S S ( ) ( ) ρ = ρ A 1,A1 = ρ L 1,L 1 = 0 / 0. 7

20 age 20 Figure: The impact of type of group on fair capital structure ρ = 0 ρ = Fair equity capital S Fair equity capital S 0 Solo -S -S Guarantee -S Retro Integrated 0 Solo -S -S Guarantee -S Retro Integrated Notes: Solo = stand-alone case/holding company model; -S = parent-subsidiary model without CRTIs; -S Guarantee = -S with guarantee; -S Retro = -S with retrocession. Conglomerate discount is stronger with increasing level of integration Capital and risk transfer has no impact on fair capital structure Effects substantially reduced for highly correlated cash flows

21 age 21 Fixed capital structure Fair capital structure Solvency capital Solvency capital Solvency capital S Solvency capital S 0 Solo -S -S Guarantee -S Retro Integrated 0 Solo -S -S Guarantee -S Retro Integrated Shortfall probability S Shortfall probability S 0.4% 0.4% Indiv. shortfall probability 0.3% 0.2% 0.1% S Indiv. shortfall probability 0.3% 0.2% 0.1% S 0.0% Solo -S -S -S Retro Integrated Guarantee 0.0% Solo -S -S Guarantee -S Retro Integrated

22 age 22 Fixed capital structure Fair capital structure Relative diversification benefit Relative diversification benefit Rel. diversification benefit 40% 30% 20% 10% 0% Solo -S -S -S Retro Integrated Guarantee rho = 0 rho = 0.7 Rel. diversification benefit 40% 30% 20% 10% 0% Solo -S -S -S Retro Integrated Guarantee rho = 0 rho = 0.7 Joint shortfall probability Joint shortfall probability 0.7% 0.7% Joint shortfall probability 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 1 2 Joint shortfall probability 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% % Solo -S -S Guarantee -S Retro Integrated 0.0% Solo -S -S Guarantee -S Retro Integrated

23 age Summary Financial conglomerates: - Group solvency requirements decrease with increasing level of integration - Diversification effects and conglomerate discount alleviated when cash flows are highly correlated arent-subsidiary model: - Ownership relation: arent s shortfall probabilities reduced compared to solo case

24 age 24 - Ownership relation (continued): Subsidiary s shortfall risk unaffected by ownership relation - Capital and risk transfer instruments from parent to subsidiary: Do not affect parent s insolvency risk or capital structure (but increase in solvency capital requirements) Reduce subsidiary s shortfall risk and solvency capital requirements

25 age 25 In summary: - Important to account for the conglomerate discount when... measuring diversification benefits in groups... analyzing impact of capital and risk transfer instruments Diversification effects are much lower when the conglomerate discount is taken into account, especially for high correlations - Important information for regulators and group management