Bubbles and Crises by F. Allen and D. Gale (2000) Bernhard Schmidpeter

Transcription

1 by F. Allen and D. Gale (2

2 Motivation As history shows, financial crises often follow the burst of an asset price bubble (e.g. Dutch Tulipmania, South Sea bubble, Japan in the 8s and 9s etc. Common precursors to most financial crises in the past were financial liberalization and credit expansion (see Kaminsky and einhart (996; 999 Understanding asset price bubbles requires an asset pricing theory different from standard ones 2/7

3 Innovation of the Paper Allen and Gale apply risk shifting and asset substitution which is familiar from corporate finance and credit rationing literature (see e.g. Jensen and Meckling (976; Stiglitz and Weiss (98 to an asset pricing context They explore the influence of credit expansion on the creation of asset price bubbles 3/7

4 the eal Sector Model: There are two dates t=,2, and a single consumption good at each date There is a continuum of small and risk neutral investors. Investors have no initial wealth but can borrow from banks to finance the investments There is a continuum of risk neutral banks. The representative bank has > units of a consumption good to lend anks and investors only use simple debt contracts, i.e. they cannot condition the terms of the loan on the size of the loan or asset returns. anks cannot observe the investment decision anks supply their loanable funds inelastically and the interest rate adjusts to clear the market 4/7

5 the eal Sector Model: There exist two kinds of assets: A safe asset which pays a fixed return rxto the investor at date 2 if xunits of the consumption good is invested at date with f (x=r and f(x satisfies the neo-classical assumptions A risky asset which pays xunits at date 2 if xunits were invested at date. is a random variable with continuous positive density h(and support [, MA ] and mean M. The risky asset is in fixed supply normalized to There is a non-pecuniary cost of investing in the risky asset c(x with c (x> and c (x> 5/7

6 the eal Sector Optimization problem of an investor with limited liability The liquidation value of the investor s portfolio is r s + r( + P s and the investor chooses to default if <rp= The maximization problem of the investor becomes max Max = The market clearing conditions are S r = f '( rp ( rp h ( d c ( = Clearing condition for risky asset + P = s Clearing condition for loan market Clearing condition for capital goods 6/7

7 the eal Sector Equilibrium An equilibrium is described by the variables (r, P, S, where the portfolio ( S, solves the maximization problem and the market clearing conditions are satisfied Substituting the market clearing condition for the risky asset as into the first order condition the equilibrium is determined by Max ( rp h( d = c'( and r = f '( P 7/7

8 the eal Sector Optimization problem of an investor with unlimited liability The maximization problem of the investor now becomes max Max ( rp h( d c( Using the first order conditions of the maximization problem and using the market clearing condition for the risky asset the fundamental price of one unit of the risky asset is P = [ E[ ] c'(] r 8/7

9 the eal Sector Limited liability and bubbles Comparing the outcomes we get P = [ E[ ] c'(] [ r r Max h( d c'( = Pr( P with strict inequality if Pr(<>, i.e. there exists a positive probability that the investor defaults on her loan The possibility of default for the investor (risk shifting leads to prices above the fundamental value Introducing a mean preserving spread even increases the size of the bubble and the probability of default increases (due to the decrease of the fundamental value 9/7

10 the Financial Sector Model: There are three dates t=,,2 and a single consumption good at each date Again there exist two kinds of asset (risky and safe as in the previous model The amount of credit available is now partially controlled by the central bank. At date the level of is treated as a random variable with positive and continuous density k( on the support [, Max ]. The price of the risky asset at date, P ( becomes a random variable depending on The owner of the risky asset receives S x at date 2, where S is a certain return /7

11 the Financial Sector Optimization problem of an investor with limited liability The investor is on the verge of default if The maximization problem of the investor becomes max max [ P ( rp ] k( d c( The market clearing conditions are r S = s P ( = rp = Clearing condition for risky asset + P f '( = Clearing condition for loan market Clearing condition for capital goods /7

12 the Financial Sector Equilibrium An equilibrium is described by the variables (r, P, S,, where the portfolio ( S, solves the maximization problem and the market clearing conditions are satisfied Substituting the market clearing condition for the risky asset as well as the budget constraint into the first order condition the equilibrium is determined by r and P ( max = and ( P ( r r f '( P = P P k( d = c'( 2/7

13 the Financial Sector Optimization problem of an investor with unlimited liability The maximization problem of the investor now becomes max Max [ P ( rp ] h( d c( Using the first order conditions of the maximization problem and using the market clearing condition for the risky asset the fundamental price of one unit of the risky asset is P = [ E[ P ( ] c'(] r 3/7

14 the Financial Sector Limited liability, credit expansion and bubbles Comparing the outcome of the case with limited with the case of unlimited liability we get P = [ E[ P ( r ] c'(] [ r Max P ( k( Pr( d c'( = P with strict inequality if there is a positive probability of default The uncertainty about the credit expansion takes place of the uncertainty about A higher variance of (e.g. due to financial liberalization increases the size of the bubble and possibility of default 4/7

15 the Financial Sector Financial Fragility Using the solutions of the maximization problem of the (limited liability investor max [ P ( ( ] ( = P k d c'( if transaction costs become small the left hand side has to decrease This happens only if and hence there will be a max crash unless the credit expansion is close to the upper bound If transactions costs become vanishing small a financial crises may occur even in expansionary financial systems 5/7

16 Summary Limited liability and uncertainty about future pay off leads to risk shifting behavior of investors and asset prices above the fundamental value Uncertainty about future monetary policy can drive asset prices When transaction costs are small, crisis may occur even with expansionary credit policy Crucial: orrowers have limited liability 6/7

17 Literature Kaminsky, G. and einhardt, C. (996. anking and balance-ofpayment crises: models and evidence., Working Paper, oard of Governors of the Federal eserve ank, Washington D.C. Kaminsky, G. and einhardt, C. (99. The twin crises: the causes of banking and balance of payment problems., American Economic eview, vol. 89, pp Jensen, M. and Meckling, W. (976. Theory of the firm: managerial behaviour, agency cost and ownership structure. Journal of Financial Economics, vol. 3, pp Sitglitz, J. and Weiss, A. (98. Credit rationing in markets with imperfect information., American Economic eview, vol. 7, pp /7