MPhil F510 Topics in International Finance Petra M. Geraats Lent Course Overview

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1 Course Overview MPhil F510 Topics in International Finance Petra M. Geraats Lent New micro approach to exchange rates 2. Currency crises References: Lyons (2001) Masson (2007) Asset Market versus Microstructure Approach to Exchange Rates Assumptions Asset market Microstructure Information Public Also private Players Homogeneous Heterogeneous Trading Irrelevant Essential Asset market approach: Implicit Walrasian auctioneer collects conditional orders and sets market clearing price. Public information immediately reflected in price. Trading irrelevant. Microstructure approach: Dealer sets price and collects actual orders, acting as buffer between buyers and sellers. Private information gradually revealed through actual orders. Process of price discovery through trading. Lecture 1 MPhil F510 Topics in International Finance Petra M. Geraats Lent 2015 Overview new micro approach to exchange rates and FX market Theory: basic microstructure asset pricing model; portfolio shifts model Empirical evidence Main readings: Lyons (2001), chapter 1, 3 Evans and Lyons (JPE 2002), Order Flow and Exchange Rate Dynamics Supplementary references: Evans (2011), Exchange-Rate Dynamics, Part II & III Sarno and Taylor (2003), Economics of Exchange Rates, ch 9 Vitale (JES 2007), Guided Tour of Market Microstructure Approach to Exchange Rates Microstructure terminology Order flow: net signed transaction value (+ buyer initiated; seller initiated) Bid-ask spread: difference between sell and buy prices Trading mechanism: institutions regarding transactions, price-setting and information disclosure (transparency) Microstructure approach to exchange rates focuses on private information conveyed by order flow. Types of private information held by foreign exchange (FX) dealer: mapping of fundamentals into exchange rates customer order flow (reflecting FX fundamentals, portfolio shifts or liquidity trading) dealer inventory

2 Institutional Characteristics Foreign Exchange Market Basic Microstructure Asset Pricing Model FX market structure: decentralized multiple-dealer market, electronically connected Main financial centers: London (2/5), New York (1/5), Singapore (1/20), Tokyo (1/20) USD vehicle currency (used for transactions between other currencies) Percentage trading shares of currencies: USD EUR JPY GBP other (Source: BIS Triennial Survey, April 2013) Enormous trading volume: FX turnover $5.3 trillion/day (April 2013) Instrument Share of FX turnover Spot transactions 38% FX swaps 42% Other FX derivatives 20% Source: BIS Triennial Survey, April 2013 Rational expectations implicit auction model for risky asset with public signal and private inventory [cf Lyons (2001), ch 4.1]. Assumptions Each trader i [0,1] maximizes CARA utility subject to budget constraint U (W i ) = e W i (1) W i = D i V +R(X i D i )P (2) where W i end-of-period wealth for trader i, D i demand for risky asset {foreign exchange} for trader i, V payoff of risky asset with V N ( 0,σ 2 ) V, i.i.d X i endowment {inventory} of risky asset for trader i, with X i N ( 0,σ 2 ) X P price of risky asset, and unit gross return on risk-free asset R = 1. Counterparty share of FX turnover [bid-ask spread] Interdealer trade 63% 39% - direct [1-2 basis points] - brokered [2-3 basis points] Customer trade [3-7 basis points] - other financial 20% 53% - non financial 17% 9% Source: BIS Triennial Survey, April 2013 No regulation and low trade transparency (no disclosure requirement for FX trades), although imperfect measure of marketwide order flow observed through brokered interdealer trade (operating through electronic interdealer auction market, advertising most competitive buy/sell limit orders and matching buyers/sellers with pre-trade anonymity) Large dealer positions frequent and nontrivial; active inventory management gives quick half-life (about 10 minutes) and zero overnight positions Representative trader observes public signal of fundamentals {e.g. interest rate} where ε N ( 0,σ 2 ε), independent of V and Xi. S = V +ε (3) Perfect competition in market for risky asset (i.e. price taking, non-strategic trading). Equilibrium price P determined by implicit Walrasian auctioneer satisfies: 1 1 D i(p)di = X idi X (4) 0 0 where D i (P) conditional demand {limit} order. Timing: 1. Trader i observes own endowment X i and public signal S. 2. Trade in risky asset at equilibrium price P determined by implicit auction. 3. Risky asset pays off V.

3 Key result Equilibrium price P reflects public signal S of fundamentals and private endowments X: Insights for FX P = σ2 V σ 2 S σ2 εσ 2 V σ 2 X (5) Exchange rate P affected by public information S about FX fundamentals (interest rate differential i i ) private information about inventories X (or liquidity trading) For equilibrium price P = αs βx determined by D = X with demand D = α β S β 1 P, where α,β > 0, order flow proxy: x = α β S X (net buying pressure given P) Microstructure approach: P = α S β X = β x so price explained by order flow. Asset market approach: P = κ S so price explained by public signal and order flow immaterial. Derivation Using W i = D i V +(X i D i )P (2) and information set Ω i = {S,X i } µ i = E[W Ω i ] = D i (E[V Ω i ] P)+X i P σ 2 i = Var[W Ω i] = D 2 i Var[V Ω i] So using (6), (1) yields: u i = D i (E[V Ω i ] P)+X i P 1 2 D2 i Var[V Ω i] Trader i maximizes u i wrt D i subject to (2), given P and Ω i = {S,X i } (price taking, non-strategic behavior) FOC wrt D i : E[V Ω i ] P = D i Var[V Ω i ] Rearranging yields conditional demand D i = E[V Ω i] P Var[V Ω i ] For each trader i, using S = V +ε (3) and normality gives E[V S] = Var[V S] = σ 2 V (7) σ 2 V σ 2 S (8) σ4 V σ 2 = σ2 V σ2 ε σ 2 (9) Constant-Absolute-Risk-Aversion (CARA) utility implies mean-variance utility Expected value of CARA utility U (W) = e θw with coefficient of absolute risk aversion θ and W N ( µ,σ 2) amounts to mean-variance utility Derivation: E[U (W)] = u ( µ,σ 2) = µ 1 2 θσ2 (6) e θw 2πσ 2 e (W µ)2 2σ 2 dw = +2θσ 2 W 2πσ 2 e (W µ)2 2σ 2 dw Factoring: (W µ) 2 +2θσ 2 W = ( W µ+θσ 2) 2 +2σ 2 θ ( µ 1 2 θσ2) So E[U (W)] = e (W µ+θσ2 ) 2 +2σ 2 ( θ µ 1 2 θσ 2) 2σ 2 2πσ 2 dw ( = e θ µ 2 1 θσ2) e (W [µ θσ2 ]) 2 (µ 2σ 2 2πσ 2 dw = e θ 2 1 θσ2) = e θu(µ,σ2 ) Since e x is monotonically increasing in x, u ( µ,σ 2) and E[U (W)] represent same preferences. Properties of normal distribution For x N (E[x],Var[x]) and y N (E[y],Var[y]) jointly normal: E[y x] = E[y]+ Cov[y,x] (x E[x]) Var[x] Var[y x] = Var[y] (Cov{y,x})2 Var[x] Substituting E[V S] = σ2 V σ 2 S (8) and Var[V S] = σ2 V σ2 ε σ 2 (9) into (7): D i = E[V S] P Var[V S] = 1 σ 2 ε Substitute (10) into equilibrium condition (4): Rearranging yields (5): P = σ2 V σ 2 S σ2 εσ 2 V σ 2 X S σ2 σ 2 P (10) ε σ2 V 1 σ 2 S σ2 ε σ 2 εσ 2 P = X V

4 Extensions [Lyons (2001), ch 4] Grosman & Stiglitz (AER 1980): Ratex model with informed and uninformed traders. Uninformed traders use price to infer information about fundamentals. Kyle (Etrica 1985): Model with explicit risk-neutral auctioneer {marketmaker} who sets price for batch of trades subject to expected zero-profit condition, based on order flow from (risk-neutral informed and uninformed) traders. Fundamentals observed by informed traders reflected in order flow that determines price. In multi-period model, strategic informed trader minimizes price impact by spreading trades over time, leading to gradual price adjustment { price discovery }. Glosten & Milgrom (JFE 1985): Model with risk-neutral dealer who quotes bid/ask prices for sequential trades subject to expected zero-profit condition, and learns private information from individual orders (by informed traders), leading to gradual price adjustment {price discovery} and bid-ask spread to protect against informed traders. Lyons (JIE 1997): Simultaneous-trade model with multiple risk-averse dealers who engage in active inventory management through strategic interdealer trading in response to information about fundamentals, customer order flow and own inventory, by passing on inventory imbalances { hot-potato trading }. Dealers observe public signal of fundamentals and interdealer order flow, which are used to adjust (no-arbitrage) price. So, customer orders unrelated to fundamentals affect price. Evans (JIE 2010): Bridging gap between microstructure and asset market models. Realizations of macroeconomic fundamentals first observed as dispersed microeconomic information by individual customers, which gradually gets aggregated and transmitted to FX dealers via order flow and incorporated into exchange rate, before finally becoming evident in published macroeconomic statistics after considerable delay (if at all). Explanation for exchange rate disconnect puzzle (empirical fact that exchange rates and macroeconomic fundamentals appear unrelated)

5 Portfolio Shifts Model Derivation (sketch) Evans & Lyons (JPE 2002) Assumptions Each representative customer i [0,1] maximizes CARA utility (1) over T trading periods subject to budget constraint for t = 1,..,T 1 W i,t+1 = C i,t P t+1 + ( X i,t C i,t ) Pt (11) where C i,t optimal customer demand for foreign exchange (risky asset) P t foreign exchange price in period t (round 3) and V T-period payoff on foreign exchange Maximizing (6) wrt C i,t subject to (11) yields C t = γ ( E[ Pt+1 Ω 3 ] ) t Pt where γ > 0 customer risk parameter and Ω 3 t customer s information set in period t, round 3. All dealers quote common price P 1 nt = P1 t and P nt = P t (due to no-arbitrage) based on common information (incl v t and also x t, resp) Interdealer trade T nt reflects customer order flow Cnt 1, so interdealer order flow x informative about aggregate portfolio shift Ct 1 N n=1 Cnt 1. Price P t adjusted to induce customers to re-absorb portfolio shift. Hence, price adjustment P t affected by change in fundamentals v t and interdealer order flow x t : Representative trader observes change in payoff v t (e.g. interest rate changes) each period t before trading, where V = T+1 t=1 v i.i.d t and v t N ( 0,σ 2 ) v where λ > 0. P t = v t +λ x t Foreign exchange market structure: dealership market with N foreign exchange dealers Empirical Evidence Timing in each period t 0. Payoff increment v t observed i.i.d N ( 0,σ 2 C), where 1. Each dealer n quotes price Pnt 1 and faces customer order flow C1 nt Cnt 1 private information ( portfolio shifts non-dealer customers) 2. Simultaneous interdealer trade (to share inventory risk) with observable interdealer quotesand(net)interdealertradet nt initiatedbydealern, leadingtoobservableinterdealer order flow x = N n=1 T nt 3. Each dealer n quotes price P nt and faces customer order flow C nt (P nt ) Key result Equilibrium price adjustment P t affected by change in fundamentals v t and interdealer order flow x t : P t = v t +λ x t Evans and Lyons (JPE 2002): Evaluation of asset market versus microstructure approach p t =0.51 (0.26) (i t i t) (0.29) x t where R 2 = 0.64 (robust standard errors in parentheses); sample: May-August 1996 p t one-day change in log spot exchange rate (DM/$) (i t i t ) one-day change in overnight $-DM interest differential x measure (buy-sell indicator) of interdealer order flow (from Reuters D electronic trading system used for about 90% of direct interdealer trading) Order flow matters for exchange rate determination. May be explained by positive feedback trading (from price to order flow) Evans and Lyons (AER 2005): Out of sample forecasting of exchange rate based on order flow outperforms macro models and random walk, capturing about 16% of variance of monthly spot rate changes. Evans and Lyons (NBERWP 2007): Order flows forecast future macroeconomic fundamentals.