Financial Innovation, Collateral and Investment.

Transcription

1 Financial Innovation, Collateral and Investment. A. Fostel (UVA) J. Geanakoplos (Yale) Chicago, October / 103

2 Outline 1 Introduction 2 Model 3 Leverage 4 CDS 5 Over Investment 6 Conclusion 2 / 103

3 Financial innovation was at the center of the recent financial crisis. 3 / 103

4 Leverage and Prices % % Case Shiller % 6.0% 8.0% 10.0% 12.0% 14.0% Down payment for Mortgages- Reverse Scale % Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q2 18.0% Case Shiller Na9onal Home Price Index Avg Down Payment for 50% Lowest Down Payment Subprime/AltA Borrowers Note: Observe that the Down Payment axis has been reversed, because lower down payment requirements are correlated with higher home prices. For every AltA or Subprime first loan originated from Q to Q1 2008, down payment percentage was calculated as appraised value (or sale price if available) minus total mortgage debt, divided by appraised value. For each quarter, the down payment percentages were ranked from highest to lowest, and the average of the bottom half of the list is shown in the diagram. This number is an indicator of down payment required: clearly many homeowners put down more than they had to, and that is why the top half is dropped from the average. A 13% down payment in Q corresponds to leverage of about 7.7, and 2.7% down payment in Q corresponds to leverage of about 37. Note Subprime/AltA Issuance Stopped in Q Source: Geanakoplos (2010). 4 / 103

5 Leverage and Investment % % Investment in Thousands % 6.0% 8.0% 10.0% 12.0% 14.0% Down payment in Mortgages- Reverse Scale % Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q2 18.0% Investment Avg Down Payment for 50% Lowest Down Payment Subprime/AltA Borrowers Note: Observe that the Down Payment axis has been reversed, because lower down payment requirements are correlated with higher home prices. For every AltA or Subprime first loan originated from Q to Q1 2008, down payment percentage was calculated as appraised value (or sale price if available) minus total mortgage debt, divided by appraised value. For each quarter, the down payment percentages were ranked from highest to lowest, and the average of the bottom half of the list is shown in the diagram. This number is an indicator of down payment required: clearly many homeowners put down more than they had to, and that is why the top half is dropped from the average. A 13% down payment in Q corresponds to leverage of about 7.7, and 2.7% down payment in Q corresponds to leverage of about 37. Note Subprime/AltA Issuance Stopped in Q Source: Geanakoplos (2010). 5 / 103

6 Leverage, Prices and Investment The financial crisis was preceded by years in which leverage, prices and investment increased dramatically. Then all collapsed after the crisis. Leverage Cycle. 6 / 103

7 Two Financial Innovations: Credit Default Swaps and Leverage Leverage CDS No'onal Amount in Billions U$S Jun- 00 Oct- 00 Feb- 01 Jun- 01 Oct- 01 Feb- 02 Jun- 02 Oct- 02 Feb- 03 Jun- 03 Oct- 03 Feb- 04 Jun- 04 Oct- 04 Feb- 05 Jun- 05 Oct- 05 Feb- 06 Jun- 06 Oct- 06 Feb- 07 Jun- 07 Oct- 07 Feb- 08 Jun- 08 Oct- 08 Feb- 09 Jun- 09 Oct- 09 Feb- 10 Jun- 10 CDS Avg Leverage for 50% Lowest Down Payment Subprime/AltA Borrowers Source CDS: IBS OTC Derivatives Market Statistics 7 / 103

8 Credit Default Swaps, Prices and Investment Case- Shiller CDS No'onal Amound in Billions U$S Jun- 00 Oct- 00 Feb- 01 Jun- 01 Oct- 01 Feb- 02 Jun- 02 Oct- 02 Feb- 03 Jun- 03 Oct- 03 Feb- 04 Jun- 04 Oct- 04 Feb- 05 Jun- 05 Oct- 05 Feb- 06 Jun- 06 Oct- 06 Feb- 07 Jun- 07 Oct- 07 Feb- 08 Jun- 08 Oct- 08 Feb- 09 Jun- 09 Oct- 09 Feb- 10 Jun- 10 CDS Case Shiller NaAonal Home Price Index Source CDS: IBS OTC Derivatives Market Statistics 8 / 103

9 Credit Default Swaps, Prices and Investment Investment in thousands CDS No'onal Amount in Billions of U$S Jun- 00 Oct- 00 Feb- 01 Jun- 01 Oct- 01 Feb- 02 Jun- 02 Oct- 02 Feb- 03 Jun- 03 Oct- 03 Feb- 04 Jun- 04 Oct- 04 Feb- 05 Jun- 05 Oct- 05 Feb- 06 Jun- 06 Oct- 06 Feb- 07 Jun- 07 Oct- 07 Feb- 08 Jun- 08 Oct- 08 Feb- 09 Jun- 09 Oct- 09 Feb- 10 Jun- 10 CDS Investment Source CDS: IBS OTC Derivatives Market Statistics. Source Investment: Construction new privately owned housing units completed. Department of Commerce. 8 / 103

10 Credit Default Swaps, Prices and Investment Credit Default Swaps (CDS) was a financial innovation that was introduced much later than leverage. Peak in CDS coincides with lower prices and investment. 9 / 103

11 Financial Innovation, Collateral, Prices and Investment We show that financial innovations that change either: -the set of assets that can be used as collateral -or the types of promises that can be backed with the same collateral affect prices and investment. We provide precise predictions. 10 / 103

12 Results I) The ability to leverage an asset generates higher prices and over-investment compared to the Arrow-Debreu level. II) The introduction of CDS generates lower prices and under-investment with respect to the Arrow-Debreu level. It can even destroy competitive equilibrium. III)The ability to leverage an asset never generates marginal under-investment in collateral general equilibrium models. 11 / 103

13 Literature -To collateral in a GE framework we follow the techniques developed by Geanakoplos (1997, 2003,2010), Fostel-Geanakoplos (2008, 2011, 2012, 2012, 2013) -Related to a literature on Leverage as in Araujo et al (2012), Acharya and Viswanathan (2011), Adrian and Shin (2010), Adrian-Boyarchenko (2012), Brunnermeier and Pedersen (2009, Brunnermeier and Sannikov (2011), Gromb and Vayanos (2002), Simsek (2013). -Financial innovations and asset pricing as in Fostel-Geanakoplos (2012b) and Che and Sethi (2011). -Literature on existence: Polemarchakis and Ku (1990), Duffie and Shaffer (86), Geanakoplos and Zame (1997). -Macro /corportate finance literature: Bernanke and Gertler (1989), Kiyotaki and Moore (1997), Holmstrom and Tirole (1997). 12 / 103

14 Outline 1 Introduction 2 Model 3 Leverage 4 CDS 5 Over Investment 6 Conclusion 13 / 103

15 Model Outline Set-up. Arrow Debreu Equilibrium. Financial Innovation and Collateral. 14 / 103

16 Set Up We present a simple GE model with incomplete markets, collateral and production, that we call the C-Model (C*-Model.) In the paper we present a completely general GE model with collateral. 15 / 103

17 Time and Assets Time t = 0, 1. Two states of nature s = U, D at time 1. s=u Y d Y U =1 X d X U =1 Two assets: risky, Y, and riskless, X. Dividends in consumption good. s=0 X can be thought as a durable consumption good or cash, numeraire. Price of Y at t = 0 is p. s=d d Y D< d Y U d X D=1 d D 16 / 103

18 Time and Assets Time t = 0, 1. Two states of nature s = U, D at time 1. s=u Y d Y U =1 X d X U =1 Two assets: risky, Y, and riskless, X. Dividends in consumption good. s=0 X can be thought as a durable consumption good or cash, numeraire. Price of Y at t = 0 is p. s=d d Y D< d Y U d X D=1 d D 16 / 103

19 Time and Assets Time t = 0, 1. Two states of nature s = U, D at time 1. s=u Y d Y U =1 X d X U =1 Two assets: risky, Y, and riskless, X. Dividends in consumption good. s=0 X can be thought as a durable consumption good or cash, numeraire. Price of Y at t = 0 is p. s=d d Y D< d Y U d X D=1 d D 16 / 103

20 Production Agents have access to an intra-period production technology at t = 0 that allows them to invest the riskless asset X and produce the risky asset Y. Z h 0 R2 is the set of feasible intra-period production for agent h H in state 0 (Z h 0 is convex and compact, (0, 0) Z h 0 and Z h 0 = Z 0, h.) Inputs appear as negative components, z x < 0 of z Z h, and outputs as positive components, z y > 0 of z Z h 0. Investment: z x. Denote by Π = z x + pz y the profits from production plan (z x, z y ). 17 / 103

21 Investors Continuum of investors h H = [0, 1]. Risk neutral. No discounting. Consumption only at the end. Expected utility to agent h is U h (c U, c D ) = γu h c U + γd h c D Each agent h H has an endowment x 0 of asset X at time 0. The only source of heterogeneity is in subjective probabilities, γ h U. The higher the h, the more optimistic the investor (γ h U are increasing and continuous). 18 / 103

22 C and C*-Models C-Models are very tractable models. In particular, we can represent the equilibrium in an Edgeworth Box even though we have a continuum of agents. We define a C*-Model as a C-model where: -the space of agents H can be finite or a continuum. -the agents preferences U h = γ h U uh (c U ) + γ h D uh (c D ) can allow for risk aversion. -initial endowments of X at time 0 x h 0 can be arbitrary. 19 / 103

23 Model Outline Set-up. Arrow Debreu Equilibrium. Financial Innovation and Collateral. 20 / 103

24 Arrow-Debreu Benchmark Before focusing on financial innovation, let us consider the Arrow-Debreu economy with production, without any type of collateral considerations. This will be an important benchmark throughout the paper. 21 / 103

25 Arrow-Debreu Equilibrium Since Z h 0 = Z 0, h, then Π h = Π. Because of convexity, wlog we may assume that production plans are the same across agents. Then (z x, z y ) is also the aggregate production. Arrow Debreu equilibrium is easy to solve. 22 / 103

26 The Arrow Debreu Equilibrium h=1 Op(mists: buy Arrow U h 1 Marginal buyer Pessimists: buy Arrow D h=0 23 / 103

27 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Intra- Period Produc:on Possibility Fron:er x 0* (1,1) 45 o O c D 24 / 103

28 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Intra- Period Produc;on Possibility Fron;er Q Economy Total Final Output x 0* (1,1) 45 o O c D 24 / 103

29 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Intra- Period Produc>on Possibility Fron>er Q Economy Total Final Output x 0* (1,1) z Y (d Y U,dY D ) x 0* +z X 45 o O c D 24 / 103

30 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Q (1- h 1 )Q x 0* (1,1) 45 o O c D 24 / 103

31 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Slope q h1 D /q h1 U Q (1- h 1 )Q x 0* (1,1) Price line equal to Indifference curve of h 1 45 o O c D 24 / 103

32 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Slope q h1 D /q h1 U Q (1- h 1 )Q x 0* (1,1) Price line equal to Indifference curve of h 1 45 o O c D 24 / 103

33 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Slope q h1 D /q h1 U Q (1- h 1 )Q x 0* (1,1) Price line equal to Indifference curve of h 1 45 o O c D 24 / 103

34 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Produc>on Possibility Fron>er Q Slope q h1 D /qh1 U x 0* (1,1) (1- h 1 )Q Price line equal to Indifference curve of h 1 45 o O c D 24 / 103

35 The Arrow Debreu Equilibrium: Edgeworth Box c U Y(d Y U,d Y D) Produc>on Possibility Fron>er C z y d Y U+x 0* +z x Q Slope q h1 D /q h1 U x 0* (1,1) (1- h 1 )Q Price line equal to Indifference curve of h 1 45 o O c D 24 / 103

36 Arrow Debreu Equilibrium Summary Optimists consume only in the U state: (z y d Y U + x 0 + z x, 0) Pessimists consume only in the D state: (0, z y d Y D + x 0 + z x ) The marginal buyer determines state prices. 25 / 103

37 Model Outline Set-up. Arrow Debreu Equilibrium. Financial Innovation and Collateral. 26 / 103

38 Financial Contracts and Collateral The heart of our analysis involves contracts and collateral. In Arrow Debreu the question of why agents honor their promises is ignored. We explicitely incorporate in our model repayment enforceability problems. Collateral is the only enforcement mechanism: agents cannot be coerced into honoring their promises except by seizing collateral aggreed upon by contract in advance. 27 / 103

39 Financial Contracts and Collateral A financial contract j is an ordered pair j = ((j U, j D ), c j ) Promise: j = (j U, j D ) denotes the promise in units of consumption good in each final state. Collateral: c j {X, Y } asset used as collateral. 28 / 103

40 Financial Contracts and Collateral We shall suppose every contract is collateralized either by one unit of X or by one unit of Y. Let J = J X J Y be the total set of contracts. 29 / 103

41 Financial Contract Delivery Actual delivery of contract j in each state is (no-recourse): (min(j U, d c j U ), min(j D, d c j D )) We are explicitely assuming repayment enforceability problems. 30 / 103

42 No Cash Flow Problems But crucially, we are assuming away cash flow problems: The value of the collateral in the future, (d c j U, d c j D ): -does not depend on the size of the promise -or on who owns the asset at the end. And every agent knows exactly how the future cash flow depends on the exogenous state of nature. 31 / 103

43 No Cash Flow Problems This eliminates any issues associated with managerial hidden effort or unobserved firm quality. Promises will not be artificially limited. Agents can potentially promise all their future cash flows coming from assets (or firm). 32 / 103

44 Financial Contracts and Borrowing Price of contract j J is πj. An investor can borrow π j today by selling the contract j in exchange for a promise tomorrow. Let ϕ j > 0 (< 0) be the number of contracts j sold (bought) at time / 103

45 Budget Set B h (p, π) = {(x, y, z x, z y, ϕ, c U, c D ) R 2 + R R + R J R 2 + : (x z x x 0 ) + p(y z y ) ϕ j π j j J max(0, ϕ j ) x, max(0, ϕ j ) y j J X j J Y z = (z x, z y ) Z 0 c s = d X s x + d Y s y j J X ϕ j min(j s, d X s ) j J Y ϕ j min(j s, d Y s ), s = U, D} 34 / 103

46 Collateral Equilibrium ((p, π), (x h, y h, z h, ϕ h, c h U, ch D ) h H) such that 1 0 x h dh = 1 0 (x 0 h + zx h )dh 1 0 y h dh = 1 0 zh y dh 1 0 ϕh j dh = 0, j J (x h, y h, z h, ϕ h, cu h, ch D ) Bh (p, π), h (x, y, z, ϕ, c U, c D ) B h (p, π) U h (c U, c D ) U h (cu h, ch D ), h. 35 / 103

47 Financial Innovation and Collateral We regard the use of new kinds of collateral, or new kinds of promises that can be backed by collateral, as financial innovation. Hence, financial innovation in our model is a different set J. We will show how different financial innovations, such as leverage, and CDS can be cast within our model with collateral. 36 / 103

48 Outline 1 Introduction 2 Model 3 Leverage 4 CDS 5 Over Investment 6 Conclusion 37 / 103

49 Leverage-Economy In this case J = J Y, and each j = (j, j) for all j J = J Y. Traded instruments: -risky asset Y and cash X -non-contingent promises j (debt contracts or loans) using the asset Y as collateral. 38 / 103

50 What does it mean to leverage Y? U Asset Y Payoff Family of debt contracts d Y U Residual Debt contract promise j< j* 45 o d Y D D 39 / 103

51 What does it mean to leverage Y? U Asset Y Payoff Family of debt contracts d Y U Residual d Y U -j 45 o Debt contract j>j*=d Y D Arrow U d Y D D 39 / 103

52 What does it mean to leverage Y? U d Asset Y Payoff Residual Family of debt contracts d Y U-d Y D Arrow U 45 o Max min bond j=j*=d Y D d Y D D 39 / 103

53 L-Economy: Endogenous Leverage But which contract is actively traded in equilibrium? 40 / 103

54 L-Economy: Endogenous Leverage The only contract traded in equilibrium is j = dd Y and the risk-less interest rate is equal to zero, so π j = j = dd Y. Geanakoplos (2003) and Fostel-Geanakoplos (JET, 2011). Fostel-Geanakoplos (ECMA, forth) provide a complete characterization showing that in all binomial economies with financial assets we can always assume that the max min contract is the only contract traded. 41 / 103

55 Credit Surface G (97) introduced the concept of Credit Surface: the equilibrium relashionship between LTV j and + r j. 1+r j B orrowers can choose any contract n the Credit Surface provided they ut up the corresponding required ollateral. 1+r A n the Arrow-Debreu budget set, orrowers face in equilibrium a flat redit surface. LTV j* 100% LTV 42 / 103

56 Credit Surface G (97) introduced the concept of Credit Surface: the equilibrium relashionship between LTV j and + r j. 1+r j B orrowers can choose any contract n the Credit Surface provided they ut up the corresponding required ollateral. 1+r A n the Arrow-Debreu budget set, orrowers face in equilibrium a flat redit surface. LTV j* 100% LTV 42 / 103

57 Credit Surface G (97) introduced the concept of Credit Surface: the equilibrium relashionship between LTV j and + r j. 1+r j B orrowers can choose any contract n the Credit Surface provided they ut up the corresponding required ollateral. 1+r A n the Arrow-Debreu budget set, orrowers face in equilibrium a flat redit surface. LTV j* 100% LTV 42 / 103

58 L-Economy: Equilibrium h=1 Op(mists leverage Y using max min bond. They buy Arrow U. h 1 Marginal buyer Pessimists lenders buy max min bond h=0 43 / 103

59 Numerical Example We solve for equilibrium the Arrow Debreu and Leverage economies just described for the following: Production: Z 0 = {z = (z x, z y ) R R + : z y = kz x }, k 0 Beliefs: γ h U = 1 (1 h)2 Parameter values: x 0 = 1, d Y U = 1, d Y D = / 103

60 Numerical Example Equilibrium for k = 1.5. Arrow Debreu Economy L-economy q Y p q U h q D z x 0.92 h z y 1.38 z x z y / 103

61 Numerical Example: Investment Investment in Y: - z x Invesment L- economy Investment AD k 46 / 103

62 Numerical Example: Welfare Welfare L economy AD economy h=0 h^lt_2=.348 h^ad=h^l=.3545 h^lt_1=.388 h=1 h 47 / 103

63 Theoretical Results: Over Valuation and Investment Proposition: Over-Valuation and Investment compared to Arrow Debreu in C-Models. In C-Models p L p A, and z L y z A y. 48 / 103

64 Theoretical Results: Over Valuation and Investment Proposition: Over-Valuation and Investment compared to Arrow Debreu in C*-Models. In C*-Models, p L p A, and z L y z A y. 49 / 103

65 Theoretical Results: Welfare Proposition: Welfare in C*-Models In C*-Models under constant return to scale, Arrow Debreu equilibrium Pareto-dominates Leverage equilibrium. 50 / 103

66 Theoretical Results: Intuition Y can be used as collateral to issue debt. Cash flows from Y can be split into an Arrow U and a riskless part. X cannot be used as collateral. This gives Y an additional collateral value compared to the riskless asset. This gives agents more incentive to produce Y. Agents are worse off over-investing. 51 / 103

67 Theoretical Results: Intuition Marginal Utility of Money for h =.9 in equilibrium at time 0: µ h=.9 = γ U(.9)(d Y U d Y D ) p π j =.99(1.2).67.2 = Payoff value of Y for h =.9 in equilibrium: PVY h=.9.99(1) +.01(.2) = µ h=.9 =.58 < p Hence the Collateral Value of Y for h =.9 in equilibrium: CV h=.9 Y = p PV h=.9 Y = = / 103

68 Theoretical Results: Intuition The utility from holding Y for its dividends alone is less than the utility that could be derived from p dollars; the difference is the utility derived from holding Y as collateral, measured in dollar equivalents. X cannot be used as collateral, so PV X = 1 and hence CV X = 0. Agents have more incentive to produce goods that are better collateral as measured by their collateral values. Investment migrates to better collateral 53 / 103

69 Outline 1 Introduction 2 Model 3 Leverage 4 CDS 5 Over Investment 6 Conclusion 54 / 103

70 What is a CDS? U Y Payoff d Y U CDS Payoff 0 1 D d y D d Y U - dy D 55 / 103

71 CDS and Collateral A seller of a CDS must post collateral typically in the form of money that is worth du Y d D Y when Y pays only d D Y in the down state. We can therefore incorporate CDS into our economy by taking J X to consist of one contract called c promising c = (0, 1). 56 / 103

72 The CDS-Economy In this case J = J X J Y where: -J X consists of the single contract called c promising c = (0, 1) -J Y consists of contracts j = (j, j) as described in the leverage economy. Agents can leverage Y and also can tranche X into Arrow securities. 57 / 103

73 What does it mean to tranche X? Selling a CDS on Y collateralized by X is like selling an Arrow D promise: Sellers of promise c = (0, 1) get the residual which is like the Arrow U which pays 1. Residual Arrow U U 1 Asset X Payoff We call it Tranche X because X is perfectly split into Arrow securities. 45 o 1 Sell Promise Arrow D D 58 / 103

74 What does it mean to tranche X? Selling a CDS on Y collateralized by X is like selling an Arrow D promise: Sellers of promise c = (0, 1) get the residual which is like the Arrow U which pays 1. Residual Arrow U U 1 Asset X Payoff We call it Tranche X because X is perfectly split into Arrow securities. 45 o 1 Sell Promise Arrow D D 58 / 103

75 What does it mean to tranche X? Selling a CDS on Y collateralized by X is like selling an Arrow D promise: Sellers of promise c = (0, 1) get the residual which is like the Arrow U which pays 1. Residual Arrow U U 1 Asset X Payoff We call it Tranche X because X is perfectly split into Arrow securities. 45 o 1 Sell Promise Arrow D D 58 / 103

76 The CDS-Economy Traded instruments: -risky asset Y and cash X. -non-contingent promises (debt contracts) using the asset Y as collateral. -contingent promises (CDS) using the asset X as collateral. The equilibrium regime is as follows: 59 / 103

77 CDS-Economy: Equilibrium h=1 Op(mists: buy all remaining X and Y. Issue bond and CDS (holding the Arrow U) h 1 Marginal buyer Moderates: hold the bond h 2 Marginal buyer Pessimists: buy the CDS 60 / 103

78 Numerical Example We solve for equilibrium in the Arrow Debreu, Leverage and CDS economies just described for the following: Production: Z 0 = {z = (z x, z y ) R R + : z y = kz x }, k 0 Beliefs: γ h U = 1 (1 h)2 Parameter values: x 0 = 1, d Y U = 1, d Y D = / 103

79 Numerical Example Equilibrium for k = 1.5. Arrow Debreu Economy L-economy CDS-economy q Y p p q U h π j q D z x 0.92 π C h z y 1.38 h z x h z y z x 0.14 z y / 103

80 Numerical Example: Investment Investment in Y: - z x Invesment L- economy Investment AD Investment CDS- economy k 63 / 103

81 Numerical Example: Welfare Welfare L economy AD economy CDS economy h=0 h^lt_2=.348 h^ad=h^l=.3545 h^lt_1=.388 h=1 h 64 / 103

82 Under Valuation and Investment Proposition: Under-Investment compared to First Best in C-Models. In C-Models p A p CDS, and zy A concave in h. z CDS y provided that γ h U is 65 / 103

83 Under Valuation and Investment Using X as collateral to sell a CDS splits its cash flows into Arrow securities. Using Y as collateral splits its cash flows into Arrow U and a riskless bond. The collateral value of X is higher than the collateral value of Y. This gives agents less incentive to use X to produce Y. There is no welfare domination: moderate agents in the CDS economy are better off than in the Arrow Debreu economy. 66 / 103

84 Theoretical Results: Intuition Marginal Utility of Money for h =.9 in equilibrium at time 0: µ h=.9 = γ U(.9)(d Y U d Y D ) p π j =.99(1.2) = Payoff value of Y for h =.9 in equilibrium: PVY h=.9.99(1) +.01(.2) = µ h=.9 =.60 < p Hence the Collateral Value of Y for h =.9 in equilibrium: CV h=.9 Y = p PV h=.9 Y =.67.6 = / 103

85 Theoretical Results: Intuition Payoff value of X for h =.9 in equilibrium: PVX h=.9.99(1) +.01(1) = µ h=.9 =.60 Hence the Collateral Value of X for h =.9 in equilibrium: CV h=.9 X = 1 PV h=.9 X = 1.60 =.40. So whereas the collateral value of Y accounts for 10.5% of its price, the collateral value of X accounts for 40% of its price. Agents have more incentive to produce goods that are better collateral as measured by their collateral values. Investment migrates to better collateral 68 / 103

86 CDS and Robust Non-Existence We saw that selling a CDS on Y using X as collateral is like selling an Arrow D using X as collateral. The only difference between a CDS and an Arrow D is that when Y is not produced the CDS is no longer well-defined. It is precisely this difference that can bring about interesting existence problems: introducing CDS can robustly destroy collateral equilibrium in economies with production. Non-Existence 69 / 103

87 Outline 1 Introduction 2 Model 3 Leverage 4 CDS 5 Over Investment 6 Conclusion 70 / 103

88 Outline Geometrical Proof of the Over-Investment Result. Discussion: Over Investment without Cash Flow Problems. Marginal Over-Investment and Collateral Value. 71 / 103

89 Over-Investment in C-Model First we show a geometrical argument in the case of C-Models. 72 / 103

90 L-Economy: Equilibrium h=1 Op(mists leverage Y using max min bond. They buy Arrow U. h 1 Marginal buyer Pessimists lenders buy max min bond h=0 73 / 103

91 L-Economy: Edgeworth Box Y(d Y U,d Y D) Intra- Period Produc1on Possibility Fron1er c U Q Slope q h1 D /qh1 U 45 o x 0* (1,1) (1- h 1 )Q Price line equal to indifference curve of h 1 45 o O c D 74 / 103

92 L-Economy: Edgeworth Box Y(d Y U,d Y D) Intra- Period Produc1on Possibility Fron1er c U Q Slope q h1 D /qh1 U 45 o x 0* (1,1) (1- h 1 )Q Price line equal to indifference curve of h 1 45 o O c D 74 / 103

93 L-Economy: Edgeworth Box Y(d Y U,d Y D) Produc9on Possibility Fron9er c U Q Slope q h1 D /q h1 U z Y d Y D x 0* +z X x 0* +z X 45 o (1- h 1 )Q x 0* (1,1) z Y d Y D C Price line equal to indifference curve of h 1 z Y (d Y U- d Y D) 45 o O c D 74 / 103

94 Over Valuation and Investment Geometrical Proof Y(d Y U,dY D ) ARROW DEBREU Y(d Y U,dY D ) LEVERAGE ECONOMY c U C Q Slope q h1 D /q h1 U c U z Y d Y D x 0* +z X Q Slope q h1 D /qh1 U z y d Y U +x 0* +z x x 0* +z X x 0* (1,1) 45 o (1- h 1 )Q x 0* (1,1) (1- h 1 )Q z Y d Y D C Price line equal to Indifference curve of h 1 z Y (d Y U - dy D ) Price line equal to indifference curve of h 1 45 o 45 o O c D O c D Proof 75 / 103

95 Over Valuation and Investment Geometrical Proof Y(d Y U,dY D ) ARROW DEBREU Y(d Y U,dY D ) LEVERAGE ECONOMY c U C Q Slope q h1 D /q h1 U c U z Y d Y D x 0* +z X Q Slope q h1 D /qh1 U z y d Y U +x 0* +z x x 0* +z X x 0* (1,1) 45 o (1- h 1 )Q x 0* (1,1) (1- h 1 )Q z Y d Y D C Price line equal to Indifference curve of h 1 z Y (d Y U - dy D ) Price line equal to indifference curve of h 1 45 o 45 o O c D O c D Proof 75 / 103

96 Over Valuation and Investment Geometrical Proof Y(d Y U,dY D ) ARROW DEBREU Y(d Y U,dY D ) LEVERAGE ECONOMY c U C Q Slope q h1 D /q h1 U c U z Y d Y D x 0* +z X Q Slope q h1 D /qh1 U z y d Y U +x 0* +z x x 0* +z X x 0* (1,1) 45 o (1- h 1 )Q x 0* (1,1) (1- h 1 )Q z Y d Y D C Price line equal to Indifference curve of h 1 z Y (d Y U - dy D ) Price line equal to indifference curve of h 1 45 o 45 o O c D O c D Proof 75 / 103

97 Over-Investment in C*-Model The geometrical argument in the case of C*-Models is as follows 76 / 103

98 Over-Investment in C*-Model x U Y(d Y U,dY D ) L L e AD N AD AD 45 o O x 77 / 103

99 Over-Investment in C*-Model E(p U ) E N (p U ) E L (p L U) p U E AD (p U ) 78 / 103

100 Outline Geometrical Proof of the Over-Investment Result. Discussion: Over Investment without Cash Flow Problems. Marginal Over-Investment and Collateral Value. 79 / 103

101 Discussion: Over Investment without Cash Flow Problems Over-valuation and over-investment due to leverage may seem surprising. Many macro models (like Kiyotaki-Moore (97), Bernanke-Gertler (89), Mendoza (10)) with financial frictions get the opposite result: lower price and investment with respect the first best allocation. Intuitive: one would expect that the need for collateral would restrict borrowing and hence investment. Why do we get different results? 80 / 103

102 Discussion: Over Investment without Cash Flow Problems The reason for the discrepancy is that in the macro-corporate finance literature it is assumed that there are cash flow problems: The value of the collateral depends on the size of the promise or on who owns the asset at the end. Hence agents cannot pledge the whole future value of the assets they produce. This naturally imposes a limit on borrowing and hence depresses investment. We can clearly see this looking at the Credit Surface implied by models with cash flow problems. 81 / 103

103 Credit Surface All contracts j J = J Y with j = (j, j) have a price in equilibrium, π j. Hence: All contracts define a gross interest rate 1 + r j = j/π j. All contracts have a well defined LTV j = π j p. 82 / 103

104 Credit Surface G (97) introduced the concept of Credit Surface: the equilibrium relashionship between LTV j and + r j. 1+r j B orrowers can choose any contract n the Credit Surface provided they ut up the corresponding required ollateral. 1+r A n the Arrow-Debreu budget set, orrowers face in equilibrium a flat redit surface. LTV j* 100% LTV 83 / 103

105 Credit Surface G (97) introduced the concept of Credit Surface: the equilibrium relashionship between LTV j and + r j. 1+r j B orrowers can choose any contract n the Credit Surface provided they ut up the corresponding required ollateral. 1+r A n the Arrow-Debreu budget set, orrowers face in equilibrium a flat redit surface. LTV j* 100% LTV 83 / 103

106 Credit Surface G (97) introduced the concept of Credit Surface: the equilibrium relashionship between LTV j and + r j. 1+r j B orrowers can choose any contract n the Credit Surface provided they ut up the corresponding required ollateral. 1+r A n the Arrow-Debreu budget set, orrowers face in equilibrium a flat redit surface. LTV j* 100% LTV 83 / 103

107 Discussion: Over Investment without Cash Flow Problems 1+r j B 1+r A π j* p Borrowing π j 84 / 103

108 Discussion: Over Investment without Cash Flow Problems 1+r j B 1+r A p p is fixed at the value of the firm without external financing Borrowing π j 84 / 103

109 Discussion: Over Investment without Cash Flow Problems 1+r j B 1+r A p Borrowing π j p is fixed at the value of the firm without external financing 84 / 103

110 Discussion: Over Investment without Cash Flow Problems In a family of models (C and C*) we show that when we disentangle cash flow problems from repayment enforcement problems we always get over valuation and over investment compared to the Arrow Debreu level. 85 / 103

111 Outline Geometrical Proof of the Over-Investment Result. Discussion: Over Investment without Cash Flow Problems. Marginal Over-Investment and Collateral Value. 86 / 103

112 Marginal Over Investment and Collateral Value Investment and prices can be above or below Arrow Debreu levels in GE collateral models. As we saw in C and C*-models they are above. But in general we don t know. We show that in GE collateral models there is never marginal under investment in equilibrium due to the presence of collateral value. 87 / 103

113 Marginal Over Investment Proposition: No Marginal Under-Investment. There is never marginal-under investment on assets that serve as collateral in collateral general equilibrium models due to non-negative collateral values. 88 / 103

114 Marginal Over Investment and Collateral Value Concept of marginal over-investment is a local measure of inefficiency. Given all spot prices, no agent would prefer to invest an extra unit of money in raising production over the equilibrium level, even if he had access to the best technology available in the economy. 89 / 103

115 Marginal Over Investment and Collateral Value Need to post collateral may constrain borrowers in equilibrium. But when one considers in the same model many durable goods than can be produced with different collateral values, investment migrates to good collateral. Hence, we expose a countervailing force in the incentives to produce: -when only some assets can be used as collateral, they become relatively more valuable, and are therefore produced more. Example 90 / 103

116 Outline 1 Introduction 2 Model 3 Leverage 4 CDS 5 Over Investment 6 Conclusion 91 / 103

117 Conclusion We show that financial innovation affect prices and investment. Leverage can generate higher prices and over-investment compared to the Arrow-Debreu first best level. In C and C*-models it always does. Leverage never generates marginal under-investment in assets that can be used as collateral due to the presence of collateral value. CDS can generate lower prices and under-investment with respect to the Arrow-Debreu first best level. In C-Models always does. And their introduction can even destroy equilibrium. 92 / 103

118 CDS and Robust Non-Existence The only difference between CDS and Arrow D is that when Y ceases to be produced the CDS is no longer well-defined. We show how introducing CDS can robustly destroy collateral equilibrium in economies with production. 93 / 103

119 CDS and Robust Non-Existence Suppose we introduce into the L-economy a CDS. We call this the LC-economy. Equilibrium in the LC-economy equals: -equilibrium in the LT -economy if Y is produced. -equilibrium in the L-economy if Y is not produced. Thus, if all LT -equilibria involve no production of Y and all L-equilibria involve production of Y, then there cannot exist a LC-equilibrium. 94 / 103

120 CDS and Robust Non-Existence Constant return to scale production: Z 0 = {z = (z x, z y ) R R + : z y = kz x }, k 0. Consider any k (1, 1.4). Rest of parameters and beliefs as before. Then LC-equilibrium does not exist. 95 / 103

121 CDS and Robust Non-Existence Y Volume CDS volume High CDS volume with low underlying Y volume Y Volume L- economy Y Volume AD Y Volume LT- economy CDS volume L=LT=AD No produc?on Non- existence region for CDS LC=LT with produc?on k 96 / 103

122 CDS and Robust Non-Existence The equilibrium in the LC economy does not exist for a robust set of parameters. Back 97 / 103

123 Over Valuation and Investment Geometrical Proof In the L-economy, optimists collectively consume z L y (d Y U d Y D ) in state U while in the Arrow Debreu economy they consume z A y d Y U + (x 0 + za x ). The latter is evidently much bigger, at least as long as z A y z L y. So suppose, contrary to what we want to prove, that Arrow-Debreu output were at least as high, z A y z L y and p A p L. 98 / 103

124 Over Valuation and Investment Geometrical Proof c U Y(d Y U,d Y D) Q A Q L x 0* (1,1) 45 o O c D 99 / 103

125 Over Valuation and Investment Geometrical Proof c U Y(d Y U,d Y D) Q A Slope q hl1 D /q hl1 U Q L z L y(d Y U- d Y D) x 0* (1,1) (1- h 1L )Q L 45 o O c D 99 / 103

126 Over Valuation and Investment Geometrical Proof c U Y(d Y U,d Y D) Q A Slope q hl1 D /q hl1 U Q L z L y(d Y U- d Y D) x 0* (1,1) (1- h 1L )Q L (1- h 1L )Q A 45 o O c D 99 / 103

127 Over Valuation and Investment Geometrical Proof c U Y(d Y U,d Y D) Q A Slope q hl1 D /q hl1 U Q L z L y(d Y U- d Y D) x 0* (1,1) (1- h 1L )Q L (1- h 1L )Q A (1- h 1A )Q A 45 o O c D 99 / 103

128 Over Valuation and Investment Geometrical Proof c U Y(d Y U,d Y D) Q A Slope q hl1 D /q hl1 U Q L z L y(d Y U- d Y D) x 0* (1,1) (1- h 1L )Q L (1- h 1L )Q A (1- h 1A )Q A 45 o O c D 99 / 103

129 Over Valuation and Investment Geometrical Proof c U Y(d Y U,d Y D) Q A Slope q hl1 D /q hl1 U Q L z L y(d Y U- d Y D) x 0* (1,1) z A y dy U +x 0* +za x (1- h 1L )Q L (1- h 1L )Q A (1- h 1A )Q A 45 o O c D 99 / 103

130 Over Valuation and Investment Geometrical Proof Back 100 / 103

131 Marginal Over Investment and Collateral Value Will illustrate the concept with our previous numerical example that also has zero consumption at time 0. Consider our numerical example with production Z 0 = {z = (z x, z y ) R R + : z y = kz x }, k = 1.5, beliefs: γ h U = 1 (1 h)2 and x 0 = 1, d Y U = 1, d Y D =.2. In the L-economy equilibrium is given by h 1 =.35, p =.67, z x =.92 and z y = / 103

132 Marginal Over Investment and Collateral Value To fix ideas let s consider one of the optimists h =.9. Marginal Utility of Money for h =.9 in equilibrium at time 0: µ h=.9 =.99(1.2).67.2 = 1.70 Marginal Expected Utility of a dollar invested on Y for h =.9 in equilibrium:.99(1.5) +.01(.2).1.5 = / 103

133 Marginal Over Investment and Collateral Value There is marginal over-investment in equilibrium. No agent would use an extra unit of cash in producing the asset if he could not also borrow to do it. In fact, the agents do not borrow to buy the asset, they buy the asset because it allows them to borrow (and hence consume only in the up state). KM(97) despite cash flow problems also had marginal over-investment in equilibrium. Back 103 / 103