LECTURE 12: FRICTIONAL FINANCE

Transcription

1 Lecture 12 Frictional Finance (1) Markus K. Brunnermeier LECTURE 12: FRICTIONAL FINANCE

2 Lecture 12 Frictional Finance (2) Frictionless Finance Endowment Economy Households 1 Households 2 income will decline positive endowment shock (unexpected pay raise) borrowing/lending insuring Single Representative Household income will rise negative endowment shock (unexpected health expense) Aggregate endowment income/shock (no trading) Intertemporal Elasticity of Substitution (incentive to smooth consumption) Risk aversion

3 Lecture 12 Frictional Finance (3) Frictional Finance Production Economy Households Firms various marginal investor Financial Markets Households Firms C-Banks I-Banks Broker/Dealers Hedge Funds Pension Funds Insurance Companies frictions, frictions, frictions Money Market Funds frictions, frictions, frictions Private Equity funds Mutual Funds Etc. Funding liquidity need for each institution

4 Lecture 12 Frictional Finance (4) Analogy to Physics Frictionless Physics Gravity (Newton/Einstein) Drop of stone = drop of feather Frictions Aviation Finance Arrow-Debreu Finance Law of one price Good benchmark! Finance Price impact/transaction costs Market illiquidity Collateral/margins/haircuts Funding liquidity

5 Lecture 12 Frictional Finance (5) Relative vs. Absolute Asset Pricing Relative asset pricing No (risk-free) arbitrage Bounds on Prices Absolute asset pricing Needed whenever replication strategy is not perfect Additional risk requires a risk premium which needs to be priced! Marginal investor representative agent Wealth/consumption of subgroup with expertise matters!

6 Lecture 12 Frictional Finance (6) Forms of Frictions 1. Extra dollar costs 2. Waiting costs due to search frictions 3. quantity constraint Lagrange multiplier λ Market Liquidity Funding Liquidity

7 Lecture 12 Frictional Finance (7) Leverage and Margins Financing a long position of x t j+ > 0 shares at price p t j = 100: Borrow $90 dollar per share; Margin/haircut: m t j+ = = 10 Capital use: $10x t j+ Financing a short position of x j t > 0 shares: Borrow securities, and lend collateral of $110 dollar per share Short-sell securities at price of 100 Margin/haircut: m j j t = = 10 Capital use: $10x t Positions frequently marked to market payment of x t j p t j p t 1 j plus interest margins potentially adjusted more later on this Margins/haircuts must be financed with capital: x j+ t m j+ t + x j t m j j t W t where x j = x j+ j t x t with perfect cross-margining M t x 1 J t,, x t W t

8 Lecture 12 Frictional Finance (8) A Liquidity Concepts Funding liquidity Can t roll over short term debt Margin-funding is recalled L

9 Lecture 12 Frictional Finance (9) A Liquidity Concepts Market liquidity Funding liquidity Can only sell assets at Can t roll over short term debt fire-sale prices Margin-funding is recalled L

10 Lecture 12 Frictional Finance (10) A Liquidity Concepts Market liquidity Funding liquidity Can only sell assets at Can t roll over short term debt fire-sale prices Margin-funding is recalled L measures quantity price quantity price static Trading volume Bid-ask Unsecured vs. collateralize funding TED spread (term spread) VIX Downside correlation Haircuts/ margins/ltv dynamic Debt maturity to Asset maturity Asset market liq

11 Lecture 12 Frictional Finance (11) Market and Funding Liquidity Step 1: exogenous margin requirement (funding liquidity) Derive modified CAPM Step 2: Endogenous margins as a function of future volatility Liquidity spirals (adverse feedback loops between market and funding liquidity)

12 Lecture 12 Frictional Finance (12) Margins Value at Risk (VaR) How are margins set by brokers/exchanges? Value at Risk: Pr p t+1 p t m = 1% 1% Value at Risk

13 Lecture 12 Frictional Finance (13) Exogenous Margin constraints Cross section of stocks better explained by liquidityadjusted CAPM

14 Lecture 12 Frictional Finance (14) Model of Funding Liquidity Overlapping generations economy: max x x E t P t r f P t γi 2 x Σ t x Portfolio constraint: m j t x j j j P t Lagrange multiplier ψ W t i Solution given by FOC x i = 1 γ i Σ t 1 [E t P t r f P t ψ t D m t P t ] D( ) makes a vector into a diagonal matrix

15 Lecture 12 Frictional Finance (15) Equilibrium Competitive equilibrium with net supply x i x i = x Equilibrium price, with 1 1 γ i and φ = γ γ i γ b P t = D 1 + r f + ψ t φm t 1 Et P t+1 γσ t x

16 Lecture 12 Frictional Finance (16) Margin CAPM Equilibrium required return s E t r t+1 = r f + β s s t λ t + ψ t φ t m t Lagrange multiplier ψ t Fraction of constrained agents φ t Margin requirement m t Risk premium λ t = E t r M t+1 r f ψ t

17 Lecture 12 Frictional Finance (17) Margin CAPM For high margin securities, required return increases when balance sheets are constrained

18 Lecture 12 Frictional Finance (18) Endogenous Margin Constraint Loss and Margin Spiral Fire sales Shock to capital Loss of net worth Precaution + tighter margins volatility price

19 Lecture 12 Frictional Finance (20) Brunnermeier-Pedersen Model Time: t = 0,1,2 One asset with final asset payoff v (later: assets j=1,...,j) Market illiquidity measure: Λ t = E t v p t (deviation from fair value due to selling/buying pressure) Agents Initial customers with supply S z, E t v p t at t = 1,2 Complementary customers demand D(z, E 2 [v] p 2 ) at t = 2 Risk-neutral dealers provide immediacy and face capital constraint x m σ, Λ W Λ max 0, B + x 0 E 1 v Λ cash price of stock holding

20 Lecture 12 Frictional Finance (21) Financiers margin setting Margins are set based on Value-at-Risk Financiers do not know whether price move is due to Likely, movement in fundamental Rare, Selling/buying pressure by customers who suffered asynchronous endowment shocks. m 1 j+ = Φ 1 1 π σ 2 = σ + θ Δp 1 = m 1 j 21

21 Lecture 12 Frictional Finance (22) Margin Spiral Increased Vol. p 1 v t = v t 1 + Δv t = v t 1 + σ t ε t σ t+1 = σ + θ Δv t m 1 m t Selling pressure initial customers complementary customers

22 Lecture 12 Frictional Finance (23) Margin Spiral Increased Vol. customers supply x 1 < W 1 m 1 = W 1 σ + θ Δp 1

23 Lecture 12 Frictional Finance (24) Margin Spiral Increased Vol. customers supply x 1 < W 1 m 1 = W 1 σ + θ Δp 1

24 Lecture 12 Frictional Finance (25) Margin Spiral Increased Vol. customers supply x 1 < W 1 m 1 = W 1 σ + θ Δp 1

25 Lecture 12 Frictional Finance (26) Multiple Assets Dealer maximizes expected profit per capital use Expected profit E 1 v j p j = Λ j Capital use m j Dealers Invest only in securities with highest ratio Λj Hence, illiquidity/margin ratio Λj j is constant m m j

26 Lecture 12 Frictional Finance (27) Commonality & Flight to Quality Commonality Since funding liquidity is driving common factor Flight to Quality Quality=Liquidity Assets with lower fund vol. have better liquidity Flight liquidity differential widens when funding liquidity becomes tight

27 Lecture 12 Frictional Finance (28) Flight to Quality m 2 =Volatility of Security2 = 2 > 1 = Volatility of Security1=m (B) 1 (B) B

28 Lecture 12 Frictional Finance (29) Summary Financial Frictions matter Relative asset pricing bounds on asset prices Marginal investor matters Can vary from asset to asset (depending on expertise) Funding Liquidity constraint Lagrange multiplier modifies CAPM Market Liquidity is impaired feeds back to Funding Liquidity (collateral)