The optimal capital requirement for UK banks: a moral hazard perspective

1. The optimal capital requirement for UK banks:a moral hazard perspective Supervisor: Marcus Miller Dmitry Kuvshinov 29 January 2013

2. About me • Worked for Bank of England 2007-2013 • 2007-10: statistics, measuring banks’ contribution to the economy • 2011-13: financial stability, prudential regulation • Design liquidity regulations in Basel • Re-evaluate the role of risk weights • Work on macro-prudential tools (time-varying capital, risk weights, leverage) • Studied EIFE at Warwick 2010-11 • Dissertation on bank capital and gambling • PhD next Autumn 2

3. Outline • Motivation • Methodology • Can capital prevent gambling? • The optimal capital ratio • Cost of higher capital requirements • Policy recommendations 3

4. Motivation • Recent crisis has been very costly • Present value loss: 130 – 520% of 2009 UK GDP • Excessive risk taking was a key cause of the crisis • Stricter capital requirements to moderate future crises 4

5. Motivation 5

6. Motivation 6

7. Methodology

8. Role of bank capital • Equity, or capital, is a form of bank liability • Special: value changes depending on the value of the bank (loans – deposits) • Regulators set a minimum ratio of equity/assets • why? 8

9. Role of bank capital • Two roles: • Increase resilience (loss absorption buffer) • Limit risk taking (skin in the game) 9

10. Role of bank capital • Risk-taking incentives: • Banks have limited liability • So “downside” is limited to the value of their equity • Gamble: “Heads I win, tails you lose” • In a well-functioning market, depositors would react to this “residual risk” not absorbed by bank equity • But depositors are insured, or uninformed • Higher capital requirements force banks to absorb a larger proportion of the loss, deter gambling • Skin in the game 10

11. Calibrating optimal capital ratios • Existing studies of optimal capital ratios focus on purpose 1): loss-absorbency • Capital increases resilience to exogenous shocks • Compare benefits of resilience vs cost of raising capital • But this ignores incentive effects of capital • My dissertation focused on 2): incentives 11

12. My dissertation – what’s new? • Calculate the optimal level of capital in a moral hazard set up • “optimal” means “the minimum amount of capital that will prevent banks from gambling” • How to do it? • Calibrate a theoretical model • Use Hellmann, Murdock and Stiglitz (2000); further: HMS • Important: focus on long term, steady-state capital 12

13. The Model • Set-up: • Banks obtain funding via deposits D or equity k • Then invest all funds into a safe or gambling asset • Safe return α with certainty • Gambling return γ > α with probability θ and β < α w prob (1 – θ) • Market failure • Deposit insurance => limited downside on gambles • Asymmetric information => banks actions not observable ex ante 13

14. Banks’ problem • Banks maximise discounted profits (franchise value V) • Per-period expected profits πg if gamble, and πp if prudent • Discounted profits: • Vg =πg/(1-δθ) if gamble, Vp =πp/(1-δ) if prudent (δ: discount factor) • For no gambling, need Vg ≤ Vp G= ((1+k) – r)-k P= (1+k) -k –r 14

15. Banks’ problem • No Gambling Condition: • If not regulated, banks hold no capital and gamble • Optimal to set k = 0 • Then , invest in the gambling asset • Capture the upside of the gamble, whilst downside falls on insured deposits 15

16. Calibrations

17. Can capital prevent gambling? • Capital increases skin in the game => discourages gambling • Capital is costly => erodes banks’ profitability => banks are less worried about going bust => encourages gambling • Capital discourages gambling if: • (derived from NGC) • Capital less effective if: • Banks are far-sighted • Capital is costly • Returns to gambling are high 17

18. Calibration parameters 18

19. Can capital prevent gambling? • Need δ < 0.94 for capital to be effective • Estimates based on Haldane (2011) suggest δ = 0.86 • Also HMS model too conservative in its estimation • No risk weights, no real-time monitoring, some technical features understate the benefits of capital • Conclusion: capital requirements deter gambling 19

20. The optimal capital ratio • Simplest case: assume perfect competition • Solving for optimal capital • Zero profit => πp= πg = 0 • Banks compete to offer the highest deposit rate possible • Can work out the deposit rates offered given zero profit for either prudent or gambling investment, rg and rp rg=(1+k)–(/)k) rp=(1+k)-k 20

21. The optimal capital ratio • Solving for optimal capital • Both rg and rp vary with capital – they decrease as k increases • But rgdecreases by more due to “skin in the game” • Optimal capital where rg = rp, no incentive to “deviate” to gambling 21

22. The optimal capital ratio – perfect competition • rg: gambling banks’ deposit rate • rp : prudent banks ’ deposit rate 22

23. The optimal capital ratio – perfect competition • Optimal capital ratio of 40% RWA • NB: important to use risk weights to discourage gambling • Sensitivity to calibration parameters: • Not sensitive to cost of capital • Sensitive to probability of gamble succeeding • Very sensitive to tail risk in the gamble 23

24. Extensions

25. Real-time monitoring • Probability 1 – φ of being caught gambling • If caught, get fined a proportion of capital = x*k • This reduces the expected return on gambling => lower incentive to gamble => lower capital requirements • Capital lower: i). The higher the fine (x) ii). The higher the probability of detection (φ) 26

26. Real-time monitoring • Can be an effective gambling deterrent • But need strong punishment 27

27. Imperfect competition • Introduce a monopoly bank • Lost gamble = lost future profits • So lower incentive to gamble, and lower optimal capital • IF the monopolist is allowed to fail when gamble fails • But in practice a monopolist would be “too big to fail” 28

28. Too Big to Fail • Market concentration C, share of pure monopoly profits captured • Bail-out probability τ(C), increasing in C • τ(C) = 0 for 0 ≤ C ≤ C small banks allowed to fail • τ(1) = 1 pure monopolist always bailed out • No Gambling Condition modified: • Lower effective probability of gamble failing • Vp is the franchise value of a prudent monopolist 29

29. Imperfect Competition and Too Big to Fail • Imperfect competition can reduce optimal capital requirements, but not by much 30

30. Summary – capital ratios necessary to deter gambling 31

31. The cost of higher capital requirements

32. Cost of higher capital requirements • Estimate the cost of equity at a given capital requirement, and the effect on bank funding costs • Follows Miles et al (2011) and Bank of England (2011) • Basic idea • Price of equity reflects fluctuations in asset values • As equity increases, asset fluctuations spread over a larger “base” • So equity becomes less volatile/risky • Therefore the “price” of equity should fall (Modigliani-Miller offset) • Investors accept a lower return in exchange for less risk 33

33. Cost of capital – regression • From CAPM can derive: • Can estimate (1) and (2) as a panel regression (UK banks over time) • Miles et al (2011) focus on (1) • BoE (2011) uses (1) + extra variables • NPL share in total assets • VIX volatility index 35

34. Regression specification • Use data for RBS, Lloyds, HSBC and Barclays, 1997 – 2010 (half-yearly) • A balanced panel, similar to BoE (2011) • Use log-log specification (2), pooled OLS • Hausman and LM tests in favour of pooled OLS • Linear specification (1) is heteroskedastic and fails functional form test • MacKinnon-White-Davidson Pe test: logs better than levels • VIX and NPL variables not significant, so excluded • Result: Modigliani-Miller offset of around ½ • Offset stronger than the linear specification used in Miles et al and BoE 36

35. Regression results 37

36. Cost of capital requirements • For example, impose a 40% RWA requirement (up from 7.5%) • Leverage falls from 25 to 7.5 (mechanical) • Equity beta falls from 1.6 to 0.84 (estimated regression) • Cost of equity falls from 13% to 9% (balance sheet model) • Banks’ funding cost rises from 5.3% to 5.6% (balance sheet model) • Corporate borrowing costs increase by 10bps (balance sheet model) • GDP falls by 0.25% (production function) • Present value of GDP lost = 10% • BoE (2010): reduce crisis probability by 1pp => PV GDP gain of 55% • Conclude: a strong argument for much higher capital than Basel 38

37. Policy recommendations • Correcting banks’ incentives is likely to require much higher capital than Basel • Capital requirements alone probably insufficient • Prohibition of certain activities, i.e. taking on tail risk • Real-time monitoring • Effective resolution to prevent “too big to fail” • Other issues to think about • Risk weights to reduce costs on prudent banks • Long-term focus in bank compensation schemes • Can argue that the ICB report goes some way in meeting these • Structural reform + loss-absorbency of 20% 40

38. Summary • Empirical cost-benefit analysis of capital requirements so far does not model incentive effects • Calibrations here are crude, but illustrate the need for higher capital requirements than Basel to prevent gambling • Capital of 25 – 40% RWA required • Such capital requirements would not be costly in the longer term • Need other policies to accompany this • Real-time monitoring and structural separation important