U. Carlos III de Madrid CEMFI. Meeting of the BIS Network on Banking and Asset Management Basel, 9 September 2014

Transcription

1 Search hfor Yield David Martinez-MieraMiera Rafael Reullo U. Carlos III de Madrid CEMFI Meeting of the BIS Network on Banking and Asset Management Basel, 9 Setember 2014

2 Motivation (i) Over the ast decade a combination of diverse forces has created a significant increase in the global suly of saving, a global saving glut, which hels to exlain both the increase in the U.S. current account deficit i and the relatively lti l low level of long-term real interest rates in the world today. Ben Bernanke (2005)

3 Motivation (ii) An environment of low interest rates following a eriod of high rates is articularly yroblematic, for not only does the incentive of some articiants to search for yield go u, but also asset rices are given the initial i i imetus, which h can lead to an uward siral, creating the conditions for a shar and messy realignment. Raghu Rajan (2005)

4 Summing u Global savings glut Low interest rates Search for yield Higher risk-taking

5 Summing u Bernanke Global savings glut Low interest rates Search for yield Higher risk-taking

6 Summing u Global savings glut Rajan Low interest rates Search for yield Higher risk-taking

7 Summing u Global savings glut Low interest rates Search for yield Higher risk-taking This aer

8 Overview of model Three tyes of agents Entrereneurs require funds for their risky rojects Banks fund entrereneurs rojects Investors rovide funds to the banks Banks monitor entrereneur s rojects Reduces robability of failure Monitoring is costly and not observed by investors Moral hazard roblem

9 Two tyes of contracts Contracts with ositive monitoring Banks that originate-to-hold Traditional banking system Contracts with zero monitoring Market finance or banks that originate-to-distribute to Shadow banking system

10 Main results Equilibrium allocation of savings features Zero monitoring for safer entrereneurs Positive monitoring for riskier entrereneurs An increase in the suly of savings Reduces interest rates and interest rate sreads Reduces monitoring incentives Increases robability of failure of traditional banks Exands relative size of shadow banking system

11 Roadma A model of bank finance Search for yield Extensions Short- vs long-run effects of savings glut Risk-averse investors Endogenous booms and busts Concluding remarks

12 Part t1 A model of bank finance

13 Model setu Two dates (t = 0, 1) Agents: Set of otential entrereneurs Set of risk-neutral investors Single risk-neutral bank Entrereneurs have rojects that require bank kfinance Bank has to raise funds from investors Investors require exected return R 0

14 Entrereneurs Each entrereneur has risky roject R, with rob. 1 + m Unit investment Return = 0, with rob. m where m [0, ] is monitoring by lending bank Monitoring i reduces robability bili of failure

15 Bank monitoring Monitoring is not observed by investors Moral hazard roblem Monitoring entails cost cm ( ) For numerical results assume γ 2 cm ( ) = m, with γ > 0 2

16 Bank Bank can only fund one roject Short side of the market Loan rate equal to success return R Bank raises funds from investors Limited liability Borrowing rate denoted B

17 Otimal contract between bank and investors [ ] ( B, m ) = arg max ( Bm, )(1 + m)( R B) c( m) subject to bank s incentive comatibility constraint (IC) arg max (1 )( ) ( ) m = m + m R B c m bank s articiation constraint (PCB) (1 + m )( R B ) c( m ) 0 and di investors articiation i i constraint (PCI) (1 + m ) B = R 0

18 Characterization of otimal contract (i) Bank s IC constraint m = argmax (1 + m R B c m m )( ) ( ) Interior solution characterized by FOC R B = c'( m ) Marginal revenue (intermediation margin) = marginal cost

19 Characterization of otimal contract (ii) Investors PC Substituting it into FOC Key equation (1 + ) = m B R 0 R B = c'( m ) c'( m ) + B = R R 0 c'( m ) m = R

20 Proosition 1 Bank finance is feasible if loan rate R satisfies R 0 R R= min m [0, ] c'( m) m Otimal monitoring m given by highest value of m that satisfies R 0 c '( m ) m R

21 A case with ositive monitoring R0 c'( m) m R R 0 m m

22 Another case with ositive monitoring R R0 c'( m) m R R 0 m m

23 Proosition 2 If bank finance is feasible and we have interior solution Monitoring is decreasing in funding cost R 0 Monitoring is increasing in loan rate R Monitoring i is increasing i in sreadrr R 0

24 Effect of a decrease in loan rate R R0 c'( m) m R 1 R R 2 m 0 m m m 2 m 1

25 Effect of a decrease in loan rate R R0 c'( m) m R 1 R2 = R m 2 = 0 m 1 m

26 Summing u m Monitoring deends on interest rate sread R R 0 Lower sreads lead to Lower monitoring and higher default risk Possible switch from ositive to zero monitoring Form originate-to-holdto to originate-to-distributeto Results assume exogenous interest rates General equilibrium model

27 Part t2 Search for yield

28 Model setu Two dates (t = 0, 1) Agents: Set of otential entrereneurs Set of risk-neutral investors Set of risk-neutral banks Entrereneurs have rojects that require bank kfinance Banks have to raise funds from investors Investors have a fixed aggregate suly of savings w

29 Entrereneurs Continuum of entrereneurs of observable tyes [0,1] Each entrereneur of tye has risky roject Unit investment Return R, with rob. 1 + m = 0, with rob. m where m [0, ] is monitoring i by lending bank

30 Entrereneurs and banks Single bank for each tye of entrereneur All entrereneurs of tye borrow from this bank Loan market is contestable Equilibrium loan rate is lowest feasible rate Returns of entrereneurs of tye are erfectly correlated Portfolio return coincides with single roject return

31 Equilibrium loan rates These assumtions imly R 0 R = R = min m [0, ] c'( m) m Entrereneurs of tye borrow at the lowest feasible rate Otherwise another bank would undercut incumbent

32 Equilibrium with ositive monitoring R R0 c'( m) m R = R m 0 m

33 Equilibrium with zero monitoring R R0 c'( m) m R = R m = 0 m

34 Investment returns Success return R is a decreasing function of investment x R = R ( x ), with R'( x ) < 0 For numerical results assume Rx 1/ σ ( ) = ( x), with σ > 1

35 Equilibrium An equilibrium is investment allocation { } such that 1. Interest rates satisfy x R = R( x ) = R, for all [0,1] 2. The market clears 1 0 x d = w

36 Proosition 3 There is a marginal tye = R0 c 1 / ''(0) Banks lending to tyes will choose Banks lending to tyes > will choose m = 0 m > 0

37 Comment on Proosition 3 (i) Loan rate for riskier tyes satisfies R R c m which imlies > 1 + m R0 = = min m [0, ] '( ) + R0 c''( m ) 0 2 (1 + m ) =

38 Comment on Proosition 3 (ii) If monitoring cost function is quadratic this condition becomes R R c ''( m ) = = γ 2 2 (1 + m) (1 + m) m = 1 R / γ = 0 Originate-to-hold banks have same robability of failure Equal to the tye of marginal entrereneur

39 Equilibrium investment allocation x x 0 Originate-to-distribute Originate-to-hold

40 Equilibrium loan rates R R R 0 0 Originate-to-distribute Originate-to-hold

41 Equilibrium robabilities of bank failure m m 0 Originate-to-distribute Originate-to-hold

42 Proosition 4 Increase in aggregate suly of savings w leads to Reduction in interest rates R Reduction in interest rate sreads 0 Increase in bank klending and dbank size R R x Exansion of originate-to-distribute region [0, ] Increase in robability of failure of originate-to-hold banks

43 Equilibrium investment allocation x x x 0

44 Equilibrium loan rates R R R 0 R R 0 0

45 Equilibrium robabilities of bank failure m m m 0

46 Two effects of savings glut Extensive margin effect Originate-to-hold banks lend to riskier borrowers Intensive margin effect > Originate-to-hold banks take more risk m = m = >

47 Co-movement of sreads and monitoring Effects on sreads of change in R 0 By enveloe theorem dr d R0 1 = '( ) c m + = dr dr m m Hence we have dr ( R) 1 = 1> 0 dr m Savings glut leads to a reduction in safe rate which imlies a reduction in sreads R R 0 R 0

48 Co-movement of sreads and monitoring Effects on monitoring of change in R 0 Zero sloe condition at m R0 c''( m ) 0 (1 + m ) = 2 Differentiating this condition gives dm 0 dr > 0 Savings glut leads to a reduction in safe rate R which imlies a reduction in monitoring which could go to the corner m = 0 R 0 m

49 Effect of a reduction in safe rate R 1 0 R = R c '( m ) + R m m 0 m

50 Effect of a reduction in safe rate R R = R m 0 m

51 Effect of a reduction in safe rate R R = R m = 0 m

52 Summing u Model of the effects of savings glut Partial equilibrium (moral hazard) model of bank finance General equilibrium model of interest rates Results show link between savings glut and Interest rates and interest rate sreads Increases robability of failure of traditional banks Increase in relative size of shadow banking system

53 Part t3 Extensions

54 Part t3 (i) Short- vs long-run effects of savings glut

55 Short-run run effects of savings glut Suose that originate-to-hold banks cannot increase x Due to some caacity constraint (e.g. caital requirements)

56 Results If traditional banks cannot exand Greater increase in shadow banking system Greater reduction in safe rate Wider sreads for traditional i banks They become safer! The effect will only be temorary They become riskier as soon as constraint is relaxed

57 Connection with Shin (2012) Key role of Euroean global banks intermediating dollar funds Taing the wholesale funding market in the US The culrit of the easy credit conditions in the US u to 2007 may have been the global banking glut rather than the global lsavings glut.

58 Part 3 (ii) Risk-averse investors

59 Risk-averse investors Continuum of risk-averse investors of mass w Unit wealth Utility function uc () = c α, with ih0 < α < 1 Assume that they can only invest in one asset Indifferent between funding all tyes of banks Look at effects of a reduction in risk aversion

60 Results If investors are less risk-averse Higher loan rates for safer entrereneurs Lower loan rates for riskier entrereneurs Narrower sreads for traditional i lbanks They become riskier Key difference with effect of savings glut The safe rate R 0 goes u (instead of down)

61 Part 3 (iii) Endogenous booms and busts

62 A simle dynamic model Suose that suly of funds w t+1 at date t + 1 is the outcome of Investment of funds w t at date t t Realization of a systematic risk factor z t Single risk factor of Vasicek (2002) Effect of shocks determined by correlation across tyes Correlation arameter ρ (0,1)

63 Endogenous booms and busts Good realizations of systematic risk factor lead to Accumulation of savings (boom state) Reduction in sreads & higher robabilities of failure Banking system vulnerable to bad realization i of risk factor Bad realizations of systematic risk factor lead to Reduction in savings (bust state) Increase in sreads & lower robabilities of failure Restart rocess that generates another boom

64 Two samle aths of savings w t ρ = 0.2 ρ = 0.7 t

65 Concluding remarks

66 Summing u Simle model to exlain effects of savings glut Focus on key role of bank intermediation Main result: If savings glut is accomanied by banking glut Higher risk-taking by banks Results consistent with a number of stylized dfacts More work needs to be done!

67 Role of macro-rudential olicy Macroeconomic variables can have effects on systemic risk Macro-rudential olicy may ylay significant role Policy should not focus narrowly on credit growth As in latest regulation of Basel Committee (Basel III) Broader macro-finance ersective would be required More work needs to be done!

68 What about monetary olicy? Our story has nothing to do with monetary olicy Real model Interestingly, we show that build-u of risk may take some time Interest rates have to be too low for too long As noted by many critics of Fed olicy Broader money-macro-finance ersective would be required More work needs to be done also here!

69 References Bernanke, B. (2005), The Global Saving Glut and the U.S. Current Account Deficit, Sandridge Lecture, Richmond, Virginia. Caballero, R., E. Farhi, and P.-O. Gourinchas (2008), An Equilibrium Model of f Global limbalances and Low Interest trates, AER. Holmström, B., and J. Tirole (1997), Financial Intermediation, Loanable Funds, and the Real Sector, Quarterly Journal of Economics. Huberman, G., and R. Reullo (2013), Moral Hazard and Debt Maturity, CEMFI Working Paer No Rajan, R. (2005), Has Financial Develoment Made the World Riskier?, Proceedings of the Jackson Hole Conference. Shin, H. S. (2012), Global Banking Glut and Loan Risk Premium, IMF Economic Review.