The Macroeconomics of Shadow Banking. January, PDF Free Download

The Macroeconomics of Shadow Banking Alan Moreira Yale SOM Alexi Savov NYU Stern & NBER January, 21

Shadow banking, what is it good for? Three views: 1. Regulatory arbitrage - avoid capital requirements, exploit implicit guarantees 2. Neglected risks - package risky investments as safe, pass on to unsuspecting investors 3. Liquidity transformation - create money-like liquid instruments from a broader set of assets Moreira and Savov (215) 2/34

The liquidity transformation view of shadow banking $ $5 $4 $3 $2 $1 Securitized loans Intermediated funding Liquidity provision Non-agency RMBS Commercial MBS Student Loans Credit Card Other ABS Auto $4 $3 $2 $1 Financial CP Asset-backed CP Repo $5 $4 $3 $2 $1 Large Time Deposits Prime Money Market Funds $ 21 23 25 27 29 211 213 Trillions of USD outstanding $ 21 23 25 27 29 211 213 1. Shadow banking turns risky assets into liquid liabilities expands credit to the economy and liquidity provision to households/institutions 2. Bigger booms, deeper busts tradeoff between growth and fragility $ 21 23 25 27 29 211 213 Moreira and Savov (215) 3/34

Our framework 1. Investors demand liquid securities to consume in high marginal-utility states (liquidity events) - liquidity low shock exposure overcollateralization 2. Intermediaries invest in assets and finance with - money safe always liquid (e.g. government money market fund) - equity residual illiquid (e.g. toxic waste CDO tranche) - shadow money safe except in a crash liquid except in a crash (e.g. Financial CP, ABCP, private-label repo, etc.) 3. Collateral constrains liquidity provision: Money 1 + Shadow money ( 1 Crash loss ) Value of assets in a crash - tradeoff between quantity and fragility of the liquidity supply 4. Uncertainty drives demand for fragile vs. crash-proof liquidity Moreira and Savov (215) 4/34

MODEL ROADMAP 1. Static model for core mechanism, analytical expressions 2. Dynamic model for amplification, cycles, and effects of policy Moreira and Savov (215) 5/34

Static model: preferences, endowment, and information 1. Three dates,, 1 and 2. Investors subject to liquidity events U = max E [z 1 C 1 + C 2 ] - z 1 {1, ψ}, where z 1 = ψ privately-observed liquidity event - z 1 = ψ with probability h, i.i.d. across investors 3. Promises require collateral. Endowed with asset that pays Y 2 = { 1 + µy, prob. 1 λ (normal times) 1 κ Y, prob. λ (crash) - normalize E [Y 2] = 1, λ measures uncertainty - normalize q = 1, assets are the numeraire Moreira and Savov (215) /34

Securities and liquidity Assumption (Liquidity) Investors in a liquidity event trade only claims that they can sell for their present value under public information. We call these liquid claims. 1. Intermediaries buy assets at date and tranche into securities - security x with yield µ x, crash exposure κ x: { r2 x 1 + µx, if Y 2 = 1 + µ = Y (normal times) 1 κ x, if Y 2 = 1 κ Y (crash) 2. Implications of Assumption 1 - Liquid security needs sufficiently low κ x to deter info. production - Security liquid when λ 1 = λ L might not be when λ 1 = λ H Proposition (Securities) Intermediaries optimally issue the following three securities: i. money m with κ m = is liquid for λ 1 { λ L, λ H} (always-liquid); ii. shadow money s with κ s= κ is liquid if λ 1 = λ L (fragile-liquid); iii. equity e with κ e = 1 is illiquid, where < κ < 1 under appropriate parameter restrictions. Moreira and Savov (215) 7/34

Balance sheet view Assets Intermediaries Investors Y 2 Assets Crash exposure κ Y Liabilities Equity e Shadow money s Wealth m + s + e = 1 Normal times liquidity m + s Crash collateral 1 κ Y Money m Crash-proof liquidity m Moreira and Savov (215) 8/34

Equilibrium Equilibrium allocation solves ] max E [h (ψ 1) C 1 + Y 2 m,s (1) subject to m + s 1, the liquidity constraint C 1 { m + s if λ 1 = λ L, prob. 1 p H (λ ) m if λ 1 = λ H, prob. p H (λ ), (2) and the collateral constraint m + s (1 κ) 1 κ Y. (3) Investors weigh - the liquidity advantage of money p H (λ ) against - the collateral advantage of shadow money κ Moreira and Savov (215) 9/34

Equilibrium Proposition (Equilibrium security issuance) Suppose that κ κ Y. Then in equilibrium money and shadow money issuance, m and s, is as follows: i. if p H (λ ) κ, then m = and s = 1 κ Y 1 κ ; ii. if p H (λ ) > κ, then m = 1 κ Y and s =. Trade-off between quantity and stability of the liquidity supply - Low uncertainty, shadow money crowds out money (supply large but fragile) - High uncertainty, only money issued (supply small but stable) Moreira and Savov (215) 1/34

MODEL ROADMAP 1. Static model for analytical expressions 2. Dynamic model for amplification, cycles, and effects of policy Moreira and Savov (215) 11/34

Capital accumulation 1. Two technologies: A high-growth risky; B low-growth safe dk a t /k a t = [ φ a (ι a t ) δ ] dt κ a dz t dk b t /k b t = [ φ b ( ι b t ) δ ] dt - investment ι a t, ι b t ; adjustment cost φ < ; depreciation δ - dz t compensated (mean-zero) Poisson crash, exposure κ a > - intensity λ t, measures uncertainty Moreira and Savov (215) 12/34

Time-varying uncertainty 1. Latent true probability of a crash λ t { λ L, λ H} - follows two-state Markov chain with generator unconditional mean λ and overall transition rate ϕ - agents learn from crashes (dz t) and Brownian news (db t) 2. Bayesian learning time-varying uncertainty λ t = E t [ λ t ] - low after a long quiet period (Great Moderation) - high after a crash (Reinhart-Rogoff) - jumps most from moderately low levels ( Minsky moment ) dλ t = ϕ ( λ λ t ) dt + Σt ( νdb t + 1 λ t dz t ), (4) where Σ t ( λ H λ t ) ( λt λ L) = Var t ( λt ) and ν is the precision of the Brownian signal Moreira and Savov (215) 13/34

Intermediaries and Markets 1. Intermediaries buy assets, set investment, and issue securities to maximize the present value of future profits Moreira and Savov (215) 14/34

Intermediaries and Markets 1. Intermediaries buy assets, set investment, and issue securities to maximize the present value of future profits 2. Assets claims to one unit of capital. Asset prices q i t = q i (λ t, χ t ) dq i t/q i t = µ i q,tdt + σ i q,tdb t κ i q,tdz t, i = a, b 3. Intermediaries tranche assets into securities. With two shocks (dz t,db t ), a generic security x s return has the form dr x t = µ x,t dt + σ x,t db t κ x,t dz t. (5) Now we take the securities and liquidity profiles from before as given i. money m with κ m,t = σ m,t = is liquid with probability 1 (always-liquid); ii. shadow money s with κ s,t = κ and σ s,t = is liquid with probability 1 p H (λ t), where p H (λ t) > (fragile-liquid); iii. equity e with κ e,t = 1 and σ e,t > is illiquid. Moreira and Savov (215) 14/34

Demand for liquidity and securities expected returns [ )] ρv t dt = max E t W t (ψdc m t,s t,dc ψ t ψ dz t + c t dt + E t [dv t ] () t,c t subject to c ψ t c ψ t and the budget and liquidity constraints dw t = drt e + m t (drt m drt e ) + s t (drt s drt e ) c t dt dct ψ dz t W t { dct ψ mt + s t prob. 1 p H (λ t ) m t prob. p H (λ t ). Risk-neutrality implies the problem simplifies to [ ρ = max h(ψ 1) [1 p H (λ t )] m t,s t +p H (λ t ) where F (c ψ t ) = Exp(η) min{c ψ t, m t }df ( c ψ t min{c ψ t, m t + s t }df ( ) c ψ t ) ] + µ W,t. (7) Moreira and Savov (215) 15/34

Demand for liquidity and securities expected returns Proposition (Security expected returns) The expected returns of money (µ m,t ), shadow money (µ s,t ), and equity (µ e,t ) satisfy ( ) µ e,t µ m,t = h (ψ 1) [1 p H (λ t )] e η(mt+st) + p H (λ t ) e ηmt µ s,t µ m,t = h (ψ 1) p H (λ t ) e ηmt. The aggregate discount rate (µ W,t ) satisfies µ W,t = [ρ hη ] (ψ 1) + 1 η (µ e,t µ m,t ). A lower liquidity premium reduces the cost of consuming in a high marginal utility state, increasing savings. Moreira and Savov (215) 1/34

Intermediaries = max m,s,k a,k b,ι a,ι b [ (y a ι a ) k a + ( y b ι b) k b] dt + E t [da t ] +A t [m(µ e,t µ m,t ) + s(µ e,t µ s,t ) µ e,t ] + E t [dv t ], subject to the collateral constraint m t + s t (1 κ) 1 κ A,t, [θ t ] (8) where the aggregate collateral value is the value weighted sum of asset collateral values 1 κ A,t = χ q t (1 κ a k) ( 1 κ a q,t) + (1 χ q t ) ( 1 κ b q,t), (9) - collateral values depend on the endogenous price exposure. - θ low when asset B supply is high or shadow-money money spread µ s,t µ m,t is high - 1 κ b q,t 1 safe asset becomes risk because changes in the collateral premium θ t Moreira and Savov (215) 17/34

Intermediaries and the supply of liquidity Proposition ((Equilibrium security ) issuance) Let M t 1 η log κ 1 p H (λ t) 1 κ p H (λ t). Then in equilibrium issuance follows { } κa,t i. if M t > min κ, 1 κ A,t 1 κ, m t = max {, 1 κ } { } A,t 1 κa,t κ and st = min 1 κ, κ A,t κ ; } ii. if M t min, { κa,t κ, 1 κ A,t 1 κ m t = 1 κ A,t (1 κ) M t and s t = M t ; and iii. if M t <, m t = 1 κ A,t and s t =. M t measures marginal value of first unit of shadow money Moreira and Savov (215) 18/34

Intermediaries and the supply of liquidity Shadow money s t min { 1 κa,t 1 κ }, κ A,t (i) κ Low λ t Moderate λ t (ii) High λ t 1 1 κ (iii) 1 κ A,t Money m t Moreira and Savov (215) 19/34

Intermediaries: asset prices and investment 1. Intermediaries can scale up their balance sheets by issuing more securities and buying more assets. We get a PDE: q i t = y i ι i t ( ) µ W,t θ t [(1 κ i t) (1 κ A,t )] [ µ i q,t + κ ik κi q,tλ t + φ (ι i t) δ ] - term in brackets is the asset expected return: assets with higher collateral value discounted at a lower rate - When collateral becomes scarce (high θ), assets with high collateral value experience flight to quality Moreira and Savov (215) 2/34

1. Parameter values in paper RESULTS 2. Model in closed form up to prices 3. Solve for prices q i (χ, λ), i = a, b numerically using projection methods Moreira and Savov (215) 21/34

Security markets 1 Money m Shadow money s Equity e 1 1.8..4.2 L.2.4..8 H.8..4.2 L.2.4..8 H.8..4.2 L.2.4..8 H (high collateral) @ = :75 @ = :95 (low collateral) 1. Shadow banking booms in low uncertainty-low collateral states - crowds out money creation in booms - disappears when uncertainty rises from a low level (e.g. August 7) 2. Money is produced most when collateral is abundant (low χ). Moreira and Savov (215) 22/34

Discount rates Agg. discount rate Liquidity premium shadow-money money spread.1 µ W µ e µ m µ s µ m.25.25.8..4.2.2.15.1.2.15.1.5 L.2.4..8 H.5 L.2.4..8 H L.2.4..8 H @ = :75 @ = :95 (high collateral) (low collateral) 1. Higher uncertainty causes the shadow-money money spread to rise, shadow banking contracts, lower liquidity supply causes liquidity premium and overall discount rate to rise 2. Discount rates are more uncertainty-sensitive when shadow banking activity is high (low uncertainty, low collateral) Moreira and Savov (215) 23/34

Asset markets.3 Collateral premium θ Asset a price Asset b price 1.4 1.5.2.1 L.2.4..8 H 1.3 1.2 1.1 L.2.4..8 H 1.95.9.85 L.2.4..8 H (high collateral) @ = :75 @ = :95 (low collateral) 1. Higher uncertainty causes the collateral premium to rise, lowers the price of the risky asset and raises the price of the safe asset 2. Riskier asset mix χ means less collateral, lowers q a and raises q b Moreira and Savov (215) 24/34

The macroeconomy.1.8..4.2 Aggregate discount rate Output growth µ W µ y L.2.4..8 H (high collateral).2 -.2 -.4 -. L.2.4..8 H @ = :75 @ = :95 (low collateral) 1. Growth more uncertainty-sensitive when shadow banking is high (collateral and uncertainty are low) 2. Real boom coincides with shadow banking boom Moreira and Savov (215) 25/34

The macro cycle 1 Target capital mix χ.8..4.2 L.2.4..8 H 1. Capital mix drifts towards risky asset during shadow banking boom 2. Capital mix drifts towards safe asset during bust Fragility buildup in booms, collateral mining in bust Moreira and Savov (215) 2/34

Collateral runs Asset a collateral value Asset b collateral value Aggregate collateral value.52 (1 κ a q )(1 κa ) (1 κ b q ) 1 κ A 1.1.5.5.48.4.44 L.2.4..8 H 1.5 1.95 L.2.4..8 H..55.5.45 L.2.4..8 H @ = :75 @ = :95 (high collateral) (low collateral) 1. Collateral values fall as prices fall prices fall more, etc. 2. Amplifies liquidity contraction 3. Flight to quality implies safe assets have excess collateral Moreira and Savov (215) 27/34

Cycles are a product of shadow banking Money m Equity e Aggregate discount rate µ W 1.8..4.2 L.2.4..8 H 1.8..4.2 L.2.4..8 H.8..4.2 L.2.4..8 H Asset a price q a Asset b price q b Aggregate collateral 1 κ A 1.4.98.5 1.2 1.9.94.92..8 L.2.4..8 H.9 L.2.4..8 H Without shadow banking.55 L.2.4..8 H With shadow banking Moreira and Savov (215) 28/34

EFFECTS OF POLICY INTERVENTIONS Moreira and Savov (215) 29/34

QE1 - Large-Scale Asset Purchases 1. Fed buys risky a and sells safe b asset (Ricardian) Announcement effect on a price #1 5!3-5 L.2.4..8 H Ex ante effect on a price q a #1 8!3 4 Announcement effect on b price -.1 -.2 -.3 L.2.4..8 H -.2 Ex ante effect on b price q b 2 L.2.4..8 H (high collateral) -.4 L.2.4..8 H @ = :75 @ = :95 (low collateral) Moreira and Savov (215) 3/34

QE2 - Operation Twist 1. Fed buys long-term safe bonds and sells short-term safe bonds. - long-term safe bond acts as crash hedge due to flight to quality - short-term safe bond safe but not a hedge -1 #1!3 Change in Change in Change in price of asset a price of long safe asset aggregate collateral.2.2-2 -3.15.1-4 L.2.4..8 H.5 L.2.4..8 H -.2 L.2.4..8 H 2. OT reduces the supply of collateral liquidity provision falls discount rates rise, especially for risky/productive assets Moreira and Savov (215) 31/34

Liquidity requirements 1. Limit liquidity mismatch: m t + s t l 1.4 Asset a price.2 Aggregate collateral 1.3. 1.2.58 1.1.5 1 L.2.4..8 H.54 L.2.4..8 H 15% liquidity requirement No liquidity requirement 3. Mitigate collateral runs, enhance financial stability 4. But higher discount rates, lower prices Moreira and Savov (215) 32/34

Monetary policy normalization 1. Pre-crisis view: short-term rate captures monetary policy stance 2. Our framework: Tbill rate = ( ) aggregate discount rate ( ) collateral value θ t of Tbill Tbill rate can be low if collateral premium θ t is high and policy tight 3. Reverse repo facility -... should help to establish a floor on the level of overnight rates. (Dudley, 213) - accommodative, even though pushes the safe rate up - releases collateral to financial system (θ t ) Moreira and Savov (215) 33/34

Takeaways 1. Liquidity transformation and the macro cycle - tradeoff between quantity and fragility of liquidity provision 2. Shadow banking expands liquidity supply in booms - lower discount rates, more investment, more growth - increases economic and financial fragility 3. Framework has implications for - monetary policy, financial stability regulation Moreira and Savov (215) 34/34

APPENDIX Moreira and Savov (215) 35/34

Benchmark parameters This table contains the benchmark values for the model parameters used to produce results for the dynamic model. The investment cost function is parameterized as φ (ι) = 1/γ ( 1 + 2γι 1 ). We use the specification ( implied by the static model for the probability that shadow money becomes illiquid. i.e. p H (λ) = λ λ L) ( / λ H λ L). Description Parameter Value Technology: Asset cash flows y a, y b.138,.1 Depreciation rate δ.1 Exogenous aggregate growth µ.1 Adjustment cost parameter γ 3 Asset crash exposures κ a, κ b.5, Information sensitivity constraint: Crash exposure limit for fragile liquid securities κ.7 Uncertainty: Low/high uncertainty states λ L, λ H.5, 1 Average uncertainty λ.245 Uncertainty rate of mean reversion ϕ.5 Uncertainty news signal precision 1/σ.1 Preferences and liquidity events: Liquidity event frequency h.28 Liquidity event marginal utility ψ 5 Average size of liquidity event 1/η.33 Subjective discounting parameter ρ.37 Moreira and Savov (215) 3/34

Uncertainty shock impulse responses.4 Uncertainty λ Capital mix χ Log output log Y #1!3 #1 2!3.3.2.1 -.5-1 -1.5-2 -4 2 4 8 1 t -2 2 4 8 1 t - 2 4 8 1 t Asset a price q a Asset b price q b Aggregate collateral 1 κ A #1 2!3 #1 8!3 #1 2!3-2 4-4 2-2 - -8-2 -4 2 4 8 1 2 4 8 1 2 4 8 1 t t t Without shadow banking With shadow banking Moreira and Savov (215) 37/34

Crash shock impulse responses Uncertainty λ Capital mix χ Log output log Y.8..4.2 -.1.1 -.1 -.2 -.2 2 4 8 1 2 4 8 1 2 4 8 1 t t t Asset a price q a Asset b price q b Aggregate collateral 1 κ A.5 -.5 -.1.15.1.5.1.5 -.15 -.5 2 4 8 1 2 4 8 1 2 4 8 1 t t t Without shadow banking With shadow banking Moreira and Savov (215) 38/34

The Macroeconomics of Shadow Banking. January, 2016