Economic Valuation of Liquidity Timing Dennis Karstanje 1,2 Elvira Sojli 1,3 Wing Wah Tham 1 Michel van der Wel 1,2,4 1 Erasmus University Rotterdam 2 Tinbergen Institute 3 Duisenberg School of Finance 4 CREATES March 2013 6th Financial Risks International Forum, Paris Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 1 / 19
Motivation (1) Definition of liquidity "The ability to trade large size quickly, at low cost, when you want to trade." (Harris, 2003) Liquidity is unobservable Large number of liquidity proxies is available Which liquidity proxy is best for liquidity timing? Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 2 / 19
Motivation (2) Liquidity can be timed Amihud (JFM 2002) Jones (2002) Baker and Stein (JFM 2004) Bekaert, Harvey, and Lundblad (RFS 2007) Liquidity timing has economic value Baker and Stein (JFM 2004) Cao, Chen, Liang, and Lo (JFE 2012) Large number of liquidity proxies is available Which liquidity proxy should a liquidity timer use? Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 3 / 19
Related literature Time series effect of liquidity on returns Amihud (2002); Jones (2002); Bekaert, Harvey, and Lundblad (2007) Why may liquidity predict returns Amihud and Mendelson (1986); Vayanos (1998); Baker and Stein (2004) Comparison of liquidity proxies Goyenko, Holden, and Trzcinka (2009); Hasbrouck (2009) Economic evaluation West, Edison, and Cho (1993); Fleming, Kirby, and Ostdiek (2001); Della-Corte, Sarno, and Tsiakas (2009); Thornton and Valente (2012) Asset allocation Jagannathan and Ma (2003); Campbell and Thompson (2008) Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 4 / 19
Our approach Our methodology in three steps: 1 Predict expected excess returns Construct liquidity series Formulate model for liquidity Formulate model for returns 2 Asset Allocation Get investment weights 3 Evaluate Economic Value Sharpe ratio Performance fee Transaction costs Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 5 / 19
Preview results In our empirical analysis, the Zeros measure of Lesmond, Ogden, and Trzincka (1999) performs best Our findings are robust to various set-ups and parameter specifications Our ranking of liquidity measures based on economic value is different from ranking based on statistical criteria Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 6 / 19
Liquidity measures Roll (1984) measure The effective bid-ask spread is inversely related to the covariance between subsequent price changes. Effective Tick (Holden, 2009, and Goyenko et al., 2009) Observable price clusters can be used to infer the spread. Zeros (Lesmond et al., 1999) The proportion of days with zero returns. High-Low (Corwin and Schultz, 2012) The high-low ratio reflects both a stock s variance and its bid-ask spread. Illiquidity Ratio (ILR) (Amihud, 2002) The daily price response associated with one dollar of trading volume, the price impact of a trade. Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 7 / 19
Model for liquidity and returns We model the level of liquidity using an AR(2) model Conditional expected excess returns are driven by liquidity: E t [r k,t+1 r f,t ] = δ 0,t +δ 1,t E t [LIQ k,t+1 ] = δ 0,t +δ 1,t (φ 0,t +φ 1,t LIQ k,t +φ 2,t LIQ k,t 1 ) = β 0,t +β 1,t LIQ k,t +β 2,t LIQ k,t 1 Estimate β-coefficients using a moving window Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 8 / 19
Mean variance framework We use dynamic trading strategies to asses the economic value of liquidity timing An investor invests every month in K risky assets and one riskless asset The solution is given by: max w t { rs,t+1 t = w tr k,t+1 t +(1 w t 1)r f,t } s.t. (σ s) 2 = w tσ t+1 t w t, w t = σ s Σ 1 ( ) t+1 t rk,t+1 t 1r f,t, Qt with Q t = ( ) ( ) r k,t+1 t 1r f,t Σ 1 t+1 t rk,t+1 t 1r f,t. Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 9 / 19
Evaluation Sharpe ratio Performance fee Break-even transaction costs Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 10 / 19
Data Common stocks listed on NYSE 1947-2008 After filtering, the data set consists of 4,348 stocks Sort stocks into 10 size portfolios based on end-of-month market capitalization Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 11 / 19
Main result table Sharpe Switching fee Excess Ratio ILR Eff. Tick Roll Zeros τ 1 τ A return Volatility Panel A. 10 year window ILR 0.13 1.4 0.6 1.50% 11.88% Eff.Tick -0.07-206 - - -0.79% 11.41% Roll -0.04-192 14 - - -0.49% 11.77% Zeros 0.38 287 494 480 4.2 2.0 4.55% 12.05% High-Low -0.16-350 -144-158 -638 - - -1.94% 11.99% Panel B. Combination of windows (5, 10, and 20 year window) ILR 0.27 2.8 1.3 3.14% 11.54% Eff.Tick -0.13-478 - - -1.54% 11.81% Roll 0.06-246 232 0.8 0.4 0.72% 11.69% Zeros 0.51 265 742 510 5.5 2.6 6.04% 11.79% High-Low -0.09-456 22-210 -720 - - -1.15% 12.15% ILR=illiquidity ratio; Eff.Tick=Effective Tick; τ 1 and τ A are break-even transaction costs; both the fee and the transaction costs are expressed in basispoints Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 12 / 19
Figure cumulative returns 600% 400% 300% 200% ILR Effective Tick Roll Zeros High-Low 100% 0% -50% -70% 1970 1975 1980 1985 1990 1995 2000 2005 Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 13 / 19
Robustness overview Correct for control variables Alternative return predictors and cross-sectional predictors Risk adjusted returns Three Fama-French factors, Carhart momentum factor, and Pastor-Stambaugh liquidity factor Alternative benchmarks Prevailing mean strategy, 1/N strategy, volatility timing strategy Market microstructure noise bias adjustment Asparouhova, Bessembinder, and Kalcheva (2010, 2012) Sensitivity analysis on the parameters δ and σ s The ranking is robust, the Zeros strategy keeps outperforming the other strategies Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 14 / 19
Control variables Correct for alternative return predictors of excess returns: dividend price ratio, dividend yield, earning price ratio, dividend payout ratio, stock variance, book-to-market ratio, term-spread, default yield spread, inflation, and net equity expansion Provided by Welch and Goyal (2008) Add control variables to prediction model E t [r k,t+1 r f,t ] = β 0,t +β 1,t LIQ k,t +β 2,t LIQ k,t 1 + N n=1 γ n,tf n,t Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 15 / 19
Sharpe ratios of control variable strategies control without with liquidity variable liquidity ILR Eff. Tick Roll Zeros High-Low d/p 0.19 0.20-0.13-0.08 0.42-0.18 d/y 0.28 0.28-0.05-0.02 0.43-0.10 e/p 0.15 0.29 0.07-0.07 0.44-0.21 d/e 0.09 0.33-0.05 0.06 0.54-0.16 svar 0.06 0.27-0.04 0.03 0.34-0.24 b/m 0.07 0.16-0.04-0.12 0.47-0.12 tms 0.18 0.29-0.07 0.03 0.45-0.20 dfy 0.26 0.22-0.03 0.06 0.44-0.07 dfr 0.15 0.29-0.11 0.07 0.46-0.07 dfr 0.14 0.24-0.11 0.06 0.47-0.10 ntis 0.42 0.40-0.03 0.24 0.62-0.02 all 0.25 0.25 0.10-0.01 0.30-0.24 none 0.27-0.13 0.06 0.51-0.09 Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 16 / 19
Risk-adjusted returns Alpha Volatility t-stat Panel A. 10Y window ILR 1.64% 12.94% 2.65 Eff.Tick -1.14% 11.80% -2.01 Roll -0.75% 12.47% -1.25 Zeros 5.79% 12.72% 9.50 High-Low -3.58% 12.62% -5.92 Panel B. Combination of windows ILR 3.36% 12.48% 5.62 Eff.Tick -2.12% 12.40% -3.56 Roll 0.70% 12.43% 1.17 Zeros 7.01% 12.63% 11.59 High-Low -2.98% 12.72% -4.90 Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 17 / 19
Why Zeros is better The Zeros strategy shows better performance during extreme negative market returns. bottom 1% bottom 5% bottom 10% top 10% top 5% top 1% ILR -1.35% -0.79% -0.42% 1.00% 1.64% 2.14% Eff.Tick -0.02% -1.59% -0.72% 0.41% 0.20% -0.13% Roll -2.67% -1.50% 0.18% 0.21% 0.63% 0.46% Zeros 2.50% 1.22% 1.11% 0.56% 1.14% 1.76% High-Low -1.43% -0.12% 0.42% 0.47% 0.96% 1.45% Quality of predicted returns Jagannathan and Ma (2003) Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 18 / 19
Summary Which liquidity proxy should a liquidity timer use to forecast excess returns Build on the findings of Amihud (2002) and Jones (2002) who show that liquidity is predictable and that liquidity significantly predicts future excess returns We form optimal portfolios in a mean-variance framework using return prediction conditional on the different liquidity measures The Zeros measure of Lesmond et al. (1999) outperforms the other liquidity measures This result is robust to different specifications and parameter settings Our ranking differs from the ranking of Goyenko et al. (2009) based on statistical criteria Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 19 / 19
Summary Which liquidity proxy should a liquidity timer use to forecast excess returns Build on the findings of Amihud (2002) and Jones (2002) who show that liquidity is predictable and that liquidity significantly predicts future excess returns We form optimal portfolios in a mean-variance framework using return prediction conditional on the different liquidity measures The Zeros measure of Lesmond et al. (1999) outperforms the other liquidity measures This result is robust to different specifications and parameter settings Our ranking differs from the ranking of Goyenko et al. (2009) based on statistical criteria Karstanje et al. (EUR) Economic Valuation of Liquidity Timing 6th Financial Risks Int. Forum 19 / 19