Lecture 3 Asset liquidity

Transcription

1 Lecture 3 Asset liquidity Shengxing Zhang LSE October 14, 2015

2 Liquidity, Business Cycles, and Monetary Policy Nobuhiro Kiyotaki and John Moore

3 Overview Amodelofamonetaryeconomywhereassetsaredifferentin there liquidity two frictions: pledgeability resellability links to Tobin s Q-theory, IS-LM curve of Keynes

4 Environment Infinite-horizon, discrete-time two types of agents entrepreneur worker P Preference: E 1 t s=t four objects traded capital nondurable output labor equity fiat money illiquid decrepiates with rate 2 (0, 1) s t u(c s ), u(c) =log c

5 Entrepreneurs technology to produce nondurable output y t = A t k t l 1 t technology to produce capital transforms output to capital, one-to-one the replacement cost of one capital is one output good accessible with probability new capital is available one period later k t+1 = k t + i t two key frictions moral hazard (pledgeability of output as collateral) asset liquidity (liquidity of the financial market)

6 Entrepreneurs: two frictions pledgeability a fraction 2 (0, 1) of new capital is pledgeable a borrowing constraint resaleability of equity equity: a claim of capital the book value of an equity is one output good the market value of an equity: q t Tobin s Q a fraction market value of installed capital/replacement cost of capital 2 (0, 1) of a firm s equity holding can be resold discussion: two parts of return from capital production committed return plegeable as collateral can be thought of as collateralized borrowing uncommitted return issue equity, subject to liquidity friction

7 Entrepreneurs: balance sheet

8 Entrepreneurs: asset portfolio money other entrepreneurs equity unmortgaged capital stock Simplification: an entrepreneur can issue new equity against a fraction t of any uncommitted returns from old capital cash flow of unmortgaged capital and other entrepreneurs equity is the same resaleability of the equity is the same perfect substitutes: no distinction between inside equity and outside equity balance sheet after simplification asset: m t and n t+1 = k t+1 liability: n t, net worth (value of asset - the market value of a firm)

9 Entrepreneurs: constraints flow of funds constraint c t + i t + q t n t+1 + p t m t+1 = r t n t + q t ( n t + i t )+p t m t two liquidity constraints n {z} t+1 + t n {z } t + t i {z} t equity next period equity resale "mortgage" m t+1 0 i t + n t

10 Workers endowment: labor preference: E t P 1 s=t flow of funds constraint: s t U h c 0 s i! 1+ (l s) 0 1+ c 0 t + q t n 0 t+1 + p t m 0 t+1 = w t l 0 t + r t n 0 t + q t n 0 t + p t m 0 t liquidity constraints: n 0 t+1 0, m 0 t+1 0

11 Entrepreneur s problem max {c s,i s,k s+1,n s+1,m s+1 } 8s t E t s.t.k s+1 = i s + k s 1X s=t s t u(c s ) c s + i s + q s n s+1 + p s m s+1 = r s n s + q s ( n s + i s )+p s m s n s+1 (1 )i s +(1 s) n s m s+1, c s, i s 0

12 Worker s problem max {c 0 s,l 0 s,n0 s+1,m0 s+1} 8s t E t 1X s=t s t U apple c 0 s! 1 + (l 0 s) 1+ s.t.c 0 s + q s n 0 s+1 + p s m 0 s+1 = w s l 0 s + r s n 0 s + q s n 0 s+1, m 0 s+1, c 0 s 0 n 0 s + p s m 0 s

13 Definition of equilibrium An equilibrium, given k t,isasequenceofprices{p s, q s, w s } 8s t, {c s, i s, k s+1, n s+1, m s+1 } 8s t and c 0 s, l 0 s, n 0 s+1, m0 s+1 8s t such that: given prices, {c s, i s, k s+1, n s+1, m s+1 } 8s t solves entrepreneurs problem, and cs, 0 ls, 0 ns+1 0, m0 s+1 8s t solves workers problem markets for general output, labor, equity and money clear for all s t

14 When liquidity constraints are not binding If (1 ) + (1 )(1 ), thenintheneighbourhoodof the steady state: the allocation of resources is first best Tobin s q is equal to unity: q t = 1 money has no value: p t = 0 the gross dividend r t w 1

15 When liquidity constraints are binding If (1 ) + < (1 )(1 ), amongsomeadditional conditions, in the neighbourhood of the steady state: the price of money, p t,isstrictlypositive the price of capital, q t,isstrictlygreaterthan1 an entrepreneur with an investment opportunity faces binding liquidity constraints: mt+1 i = 0 nt+1 i =(1 )i t +(1 t) nt i From the flow of funds constraint ct i + (1 q t )i {z } t = r t nt i + tq t nt i + p {z } t mt i down payment revenue from resale

16 When liquidity constraints are binding From the flow of funds constraint ct i + (1 q t )i {z } t = r t nt i + tq t nt i + p {z } t mt i down payment revenue from resale h ct i + qt R nt+1 i = r t nt i + tq t +(1 t)q R t q R t 1 q t 1 < 1, as q t > 1 i n i t + p t m i t qt R (replacement cost): for every unit of investment, an entrepreneur needs a downpayment 1 q t,ofwhichhe retains 1 inside equity. two components for old equity a fraction t is resaleable and is priced at market value q t a fraction 1 t is not resaleable and is priced at effect replacement cost qt R

17 Euler equation u 0 (c t )=E t pt+1 p t (1 )u 0 (c s t+1)+ u 0 (c i t+1) =(1 )E t rt+1 + q t+1 q t u 0 (c s t+1) + E t ( rt+1 + t+1 q t+1 + (1 t+1)q R t+1 q t u 0 (c i t+1) ) u 0 (c i t+1 ) > u0 (c s t+1 ), qr t+1 < 1 < q t+1: equitycarriesan idiosyncratic risk. its effective return is negatively correlated with the idiosyncratic variations in marginal utility that stem from the stochastic investment opportunities. money is free from such a risk

18 Equilibrium return When liquidity constraints are binding equilibrium capital stock is les than first-best the expected rate of return on equity: E t a t+1 K 1 t+1 + q t+1 q t < 1 the expected rate of return on money is yet lower: p t+1 a t+1 K 1 t+1 E t < E + q t+1 t p t the expected return on equity contingent on having an investment opportunity is lower still: E t a t+1 K 1 t+1 + t q t+1 +(1 t+1) q R t+1 q t < E t p t+1 p t q t

19 Equilibrium return Discussion: 1 > Et a t+1 K 1 t+1 + q t+1 q t > E t p t+1 p t > E t a t+1 K 1 t+1 + t q t+1 +(1 t+1) q R t+1 q t Aspectrumofinterestrates!Theyreflecttheliquidity premium of different assets to finance investment. Workers do not need the liquidity for investment: they always sell.

20 Over-the-Counter Markets Duffie, Darrell, Nicolae Gârleanu, and Lasse Heje Pedersen

21 Overview Amodeloftheover-the-countermarkets Amicro-foundedmodelofmarketliquidity(resaleability) Determinent of liquidity search friction bargaining market structure future extension: asymmetric information

22 Environment continuous time, infinite horizon acontinuumofinvestors,withmeasure1 acontinuumofmarketmakerswithmeasure1 asset durable, indivisible fixed supply: s < 1 constant dividend flow numeraire good deep pockets can be stored with return r

23 Environment 1 Preference of investors: E t t e rs (u ij,t + c) dt valuation: i 2{h, l} asset holding j 2{o, n} u ho = 1, u lo = 1, u hn = u ln = 0. preference shock u: Poisson rate to switch from type l to type h d: Poisson rate to switch from type h to type l c: consumption of the numeraire good 1 Preference of dealers: E t t e rs cdt

24 Market structure

25 Market structure Interdealer market competitive, with price M t random matching between investors and dealers Poisson rate for an investor to meet a dealer: Nash bargaining: dealers bargaining power, z B t : bid price, the price when dealers bid from investors A t : ask price,the price dealers ask for to sell the asset to investors Illiquidity: Bid-ask spread: B t < A t delay in trade:

26 Value functions of investors rv lo = 1 + u (V h0 V lo )+ (B + V ln V lo )+ V lo rv ho = 1 + d (V lo V ho )+ V ho rv ln = u (V hn V ln )+ V ln rv hn = d (V ln V hn )+ (V ho V hn A)+ V hn

27 Bargaining and BA spread max A (V ho A V hn ) 1 z (A M) z max B (B + V ln V ln ) 1 z (M B) z A =(V ho V hn )z + M(1 z) B =(V lo V ln )z + M(1 z) A B = z [(V ho V lo ) (V hn V ln )] The spread depends on the difference in value between h type and l type the bargaining power of dealers

28 Law of motions µ lo = uµ lo + d µ ho µ lo µ ho = u µ lo d µ ho + µ hn µ ln = uµ ln + d µ hn + µ lo µ hn = u µ ln d µ hn µ hn

29 Equilibrium definition Asymmetricequilibriumisapathofprices{B t, A t, M t } t 0,apath of distributions µ and a path of value functions V and initial condition µ(0) such that, given the initial condition, given V (t) and µ(t), {B t, A t } t problem at t, 8t given {, equations 0 solves the bargaining }, V satisfies the Hamilton-Jacobi-Bellman µ is follows the laws of motion M t clears the interdealer market at t, 8t

30 Search-Based Endogenous Illiquidity and the Macroeconomy Wei Cui, Sören Radde

31 Overview Introduce endogenous resaleability to Kiyotaki Moore (2012) See Wei Cui s slides

32 References Kiyotaki, N. and Moore, J. (2012). Liquidity, Business Cycles, and Monetary Policy Duffie, D., Gârleanu, N. and Pedersen, L. H. (2005). Over-the-Counter Markets. Econometrica, 73(6), Cui, W. and Radde S. (2014). Search-Based Endogenous Liquidity and the Macroeconomy