Asymmeric liquidiy risks and asse pricing Sean Anhonisz and Tālis J. Puniņš Universiy of Technology Sydney 6 h Financial Risks Inernaional Forum on Liquidiy Risk 26 March 2013
Liquidiy level Liquidiy affecs asse prices Inuiion: Invesors care abou ne in-he-pocke reurns (ne of ransacion coss, axes); illiquidiy reduces ne reurns; herefore illiquidiy premium in gross reurns Amihud and Mendelson (1986), Brennan and Subrahmanyam (1996) Liquidiy risk Inuiion: Liquidiy flucuaions cause variaion in gross reurns; some flucuaions are sysemaic and canno be diversified risk premium Acharya and Pedersen (2005): CAPM in ne reurns, gives 3 liquidiy risks: E [ r i, 1 r f ] E [ c i, 1 Cov( ri ] Var( r,, r c ) ) Cov( c Var( r i,, c c ) ) Cov( ri Var( r,, c c ) ) Cov( ci,, r Var( r c ) ) CAPM commonaliy in liquidiy Pasor- Sambaugh Acharya- Pedersen
Bu, empirical evidence on liquidiy risk is mixed Grea deal of variaion in magniude of premium: Pasor and Sambaugh (2003): 7.5% pa Acharya and Pedersen (2005): 1.1% pa (mainly β 4 ) Some sudies find no evidence of a premiu e.g., Hasbrouck (2009) Why? To wha exen does liquidiy risk affec asse prices? This is he broad quesion we seek o shed ligh on in his paper Our approach: Due o asymmery in co-movemens beween reurns and liquidiy we hypohesize ha exising models are misspecified Build more flexibiliy ino liquidiy-adjused CAPM by allowing separae upside and downside risks Le he daa ell us wheher he asymmery maers
Summary of findings Upside and downside liquidiy risks are disinc They command differen cross-secional reurn premiums, which ake opposie signs Combining he wo risks has an offseing effec and leads o mis-esimaion of he imporance of liquidiy risk Asymmeric liquidiy-adjused CAPM has srong empirical suppor: explains a larger proporion of cross-secional variaion in reurns han oher heory-driven models is robus o many conrol variables and permuaions
In invesor preferences Asymmeries Naural o hink of risk in erms of likelihoods of undesirable oucomes Markowiz (1959): invesors care abou downside risk (semi-variance) Kahneman and Tversky (1979): losses cause more disuiliy han gains cause uiliy In comovemens beween reurns and liquidiy ρ(r i,r MKT ) greaer when r MKT <μ Ang and Chen (2002) ρ(liq i,liq MKT ) greaer when r MKT <0 Hameed e al. (2010) ρ(liq i,r MKT ) greaer when r MKT <0 Hameed e al. (2010) ρ(liq MKT,r MKT ) greaer when r MKT <0 Pasor and Sambaugh (2003) In disribuions of reurn and liquidiy shocks Disribuion of reurns and liquidiy shocks are lef skewed (Ang and Chen, 2002; Roll and Subrahmanya 2010)
Causes of asymmeries in liquidiy Downward liquidiy spirals: e.g., liquidiy shock higher margins (reduced funding for inermediaries) less liquidiy provision ec. Brunnermeier and Pedersen (2009), Nagel (2012) evaporaing liquidiy Similar spirals can emerge due o: Tighening of risk managemen (Garleanu and Pedersen, 2007) Traders swich from co-operaion o predaory rading when a rader becomes disressed (Carlin e al., 2007) Traders rush o liquidae following a negaive shock before ohers hi heir loss limis and sell: liquidiy black holes (Morris and Shin, 2004) Fligh o liquidiy Macroeconomic/financial sress aversion o liquidiy shocks invesors swich from illiquid o liquid asses (Acharya e al., 2013)
Liquidiy-adjused asymmeric (LAA) CAPM Using he pricing kernel framework: e E M +1 R i,+1 = 0 e E R i,+1 = Cov e M +1, R i,+1 e E e R +1 Cov M +1, R +1 and making an adjusmen for liquidiy coss of individual socks, C i : e E R i,+1 C i,+1 = Cov e M +1, R i,+1 C i,+1 e Cov M +1, R +1 e E R +1 Simplifying assumpion of no marke liquidiy coss due o: Exensive liquidiy in index fuures and ETFs, i.e., marke liquidiy is no a weighed average of he liquidiy of individual socks Acharya and Pedersen (2005) find very small effecs associaed wih marke liquidiy
Liquidiy-adjused asymmeric (LAA) CAPM Sar from a very general pricing kernel, G M +1 = γ 1, + 1 j 1 j 1 γ j, R +1 j=2 + η k, R +1 K +k 1 k=2 + θ l, K R +1 + l 1 l=2 Add resricions: Degree 2 K = R f Drop he linear erm To obain he LAA-CAPM: M LAA +1 = γ 1, + Η Subsiue kernel ino expeced reurn equaion, use heorem from Anhonisz (2012) o re-express in erms of parial momens Advanages of parial momens: Allow asymmeric preferences around K e + R +1 + e + Θ R +1 Connecs he model wih he lieraure on pricing of downside risks (Hogan and Warren, 1974; Bawa and Lindenberg, 1977) Conribue o recen effors o develop liquidiy-adjused VaR and ES
Liquidiy-adjused asymmeric (LAA) CAPM E R i,+1 = R f,+1 + E c i,+1 + β i,1 λ U + β i,2 λ D + β i,3 λ U + β i,4 λ D Upside reurn risk: Downside reurn risk: Upside liquidiy risk: Downside liquidiy risk: e e β 1,i = CUPM R i,+1, R +1 = 1 n 1 e e β 2,i = CLPM R i,+1, R +1 = 1 n 1 n d=1 n e e β 3,i = CUPM C i,+1, R +1 = 1 n 1 e e β 4,i = CLPM C i,+1, R +1 = 1 n 1 d=1 n e R i,d e R i,d d=1 n d=1 e C i,d e C i,d e + R d e + R d e + R d e + R d
Relaion o Acharya and Pedersen (2005) Relaive o Acharya and Pedersen (2005), we: Replace he linear marke reurn in he pricing kernel wih min and max erms on he marke reurn Do no adjus he marke reurn for marke liquidiy coss
Daa: 1962-2007 Empirical ess of LAA CAPM All NYSE and AMEX common socks; $5 < P < $1000; B/M > 0 Daily reurns/volume (CRSP), accouning variables (Compusa) Approach: Decile sors and Fama MacBeh regressions Esimae beas in rolling 6-monh windows using daily observaions Relae beas o fuure 6-monh realized reurns Repea for every year-monh; ime-series average wih Newey Wes sandard errors
Liquidiy coss, C: Empirical ess of LAA CAPM Sar wih Amihud s (2002) ILLIQ a daily frequency Normalize and scale as per Acharya and Pedersen (2005) Exrac daily innovaions (for risk) using AR(20) model on daily obs Two proxies for expeced illiquidiy (for a levels effec): average of C in pas 6 monhs, and fied value of AR(2) a monhly frequency Conrol variables Fama and French (1993) marke, size and value facor loadings (β MKT, β SMB, β HML ) Carhar (1997) momenum facor loading (β UMD ) Harvey and Siddique (2000) coskewness (β COSKEW ) Jegadeesh (1990) shor-erm reversal (REV) previous 1-mh r Jegadeesh and Timan (1993) momenum (MOM) lagged 11-mh r Ang e al. (2006) idiosyncraic volailiy (IVOL=σ(ε 3-facor model )) Bali e al. (2011) MAX facor (maximum reurn for sock in prev mh) Chordia e al. (2001) σ(monhly urnover)
Decile sors Upside and downside liquidiy risks predic fuure reurns Even afer accouning for marke, size, value and momenum facors
Upside and downside liquidiy risks are disinc High downside reurn risk high upside reurn risk This is no rue for he liquidiy risks, hey are disinc
Fama MacBeh regressions Dependen variable is sock-level fuure 6m excess reurn
Robus o many conrols
Comparison wih oher models LAA-CAPM explains more crosssecional variaion han: (i) oher heory driven models, and (ii) Fama- French 3- facor model
Oher robusness ess Bea esimaion window lengh and frequency of observaions (weekly, monhly) Alernaive measures of liquidiy Value weighing vs equal weighing Sub-period analysis Inclusion of higher order momens
Conclusions Upside and downside liquidiy risks are disinc They command differen cross-secional reurn premiums, which ake opposie signs Combining he wo risks has an offseing effec and leads o mis-esimaion of he imporance of liquidiy risk Asymmeric liquidiy-adjused CAPM has srong empirical suppor: explains a larger proporion of cross-secional variaion in reurns han oher heory-driven models is robus o many conrol variables and permuaions