Liquidity and asset pricing

Transcription

1 Liquidity and asset pricing Bernt Arne Ødegaard 21 March Liquidity in Asset Pricing Much market microstructure research is concerned with very a microscope view of financial markets, understanding how markets are organized is affecting the price formation process, or how information gets into prices. Most concepts of liquidity is then a result of this process. This is however not the only way to approach liquidity. An alternative is to ask whether liquidity affects asset prices at a more macro level, in a way that one can discern from the crossection of asset returns. A famous call for this merging of the worlds of market microstructure and asset pricing was O Hara (2003) s Presidential Address at the annual AFA meetings. This has resulted in a sizeable literature looking for liquidity in the cross-section of asset returns. Much of this research has identified an empirical liquidity premium in stock returns. Less liquid stocks command a premium. But this is not a settled literature. Let us mention some well known studies. An early paper was Amihud and Mendelson (1986), which show spread measures important for cross sectional returns. They also have a theoretical argument for why spread should be important, namely that traders with longer holding periods will accept holding higher spread stocks. But this is not an equilibrium argument, it just states that if traders take spreads as given, only people with longer expected holding periods will hold the high-spread stocks. It does not adress the source of the spread. Other well known early investigations were Brennan and Subrahmanyam (1996), showing that Kyles lambda estimated from intraday data is important for crossection, and Brennan, Chordia, and Subrahmanyam (1998), showing that trading volume as measure of illiquidity seems priced. Datar, Naik, and Radcliffe (1998) uses turnover (the inverse of holding period) as a measure of liquidity. The problem with most of the literature is that it does not explain why idiosyncratic things such as spreads, should be relevant in an asset pricing settings, which should be limited to systematic sources of risk. Acharya and Pedersen (2005) 1 attempts to model the systematic sources of liquidity risk. The financial crash of 08 has brought home to many the importance of liquidity for asset pricing, and the literature on the intersection of liquidity and asset prices is expanding. We will not go in detail over this literature. In the following we illustrate a couple of standard asset pricing studies of liquidity. 1 See also the survey of Amihud, Mendelson, and Pedersen (2005). 1

2 2 Theoretical approaches How can one build a model where liquidity is incorporated in asset prices? Liquidity should be a property valued by the investor. Will not be valued if markets are frictionless, need some friction that affects investor decisions. Transaction costs Informational inefficienes Grossman and Stiglitz (1980) 2.1 Transaction costs Constantinides (1986) Effect of transaction costs second order. 2.2 Spreads and holding period Early approach, paper of Amihud and Mendelson (1986). Partial equilibrium model, investors provided with a menu of assets which differs in the bid/ask spread. Investors discount future transaction costs when investing. Return depressed by spread. Spread differences induce clienteles: Long term investors spread the high spread over longer periods, can afford to buy the high spread stocks. Empirical implications In the crossection, returns increasing in spreads. Expected returns an increasing and concave function of transaction costs. 2.3 Time variation in liquidity Acharya and Pedersen (2005) model economy with time variation in cost of liquidity. Agents in an OLG model. End up with a model in gross return with three liquidity betas Covariability between assets illiquidity and markets illiquidity. (Usually positive) Exposure to market-wide illiquidity. (Usually negative) Third liquidity beta (usually negative) 2.4 Variation in trading horizon Vayanos (1998) 2.5 Others Huang and Wang (2010) 2

3 3 Liquidity in the crossection at the Oslo Stock Exchange We do a couple of exercises investigating whether liquidity is important for the crossection at the Oslo Stock Exchange (OSE). Do we find signs of liquidity being important? 3.1 Can asset pricing models explain liquidity One way to ask that question is to construct portfolios sorted on a liquidity measure, and see if the standard asset pricing models are sufficient to explain the crossection. Exercise 1. The CAPM is usually written as E[r it ] = r ft + β i (E[r mt ] r ft ) where r ft is the risk free rate, r it the return on an asset, and r mt the market return. Rewriting in excess return form, where we find the excess asset return er it = r it r ft and excess market return er mt = r mt r ft we write the univariate regression. er it = α i + β i er mt + e it A testable implication of the CAPM is that α i = 0 in this regression. As first shown by Black, Jensen, and Scholes (1972) this can be tested by time series regressions. Run these regressions on 10 (ew) spread sorted portfolios at the OSE. Test α i = 0 on a portfolio by portfolio basis. Use an equally weighted market index, and returns data Solution to Exercise 1. Reading in the data and running the regressions > library(sandwich) > Rets <- read.zoo("../../data/relative_spread_portfolios_monthly_ew.txt", + format="%y%m%d",header=true,sep=";") > Rf <- read.zoo("../../data/nibor_monthly.txt",format="%y%m%d", + header=true,sep=";"); > er <- Rets - lag(rf,-1) > Rm <- read.zoo("../../data/market_portfolios_monthly.txt", + header=true,sep=";",format="%y%m%d") > ermew <- Rm$EW - lag(rf,-1) > data <- merge(er,ermew,all=false) > er <- as.matrix(data[,1:10]) > erm <-as.matrix(data[,11]) > reg <- lm(er~erm) Results, All Portfolios 3

4 Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Model 9 Model 10 (Intercept) (0.003) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.003) erm (0.043) (0.030) (0.033) (0.029) (0.033) (0.030) (0.034) (0.040) (0.040) (0.052) R Adj. R Num. obs *** p < 0.001, ** p < 0.01, * p < 0.05, p < 0.1 Note that we reject that the intercept is zero for many of these portfolios 3.2 Can a liquidity measure price risk? Another is to construct a measure similar to the Fama French measures capturing the liquidity risk. Use LIQ from Næs, Skjeltorp, and Ødegaard (2009) Exercise 2. Consider the model E[r i ] r f = E[r m r f ]β i + b liq i LIQ where LIQ is a zero investment portfolio designed to represent liquidity, as described in Næs, Skjeltorp and Ødegaard (2008). er it = α i + β i er mt + +b liq i LIQ t e it Run these regressions on size sorted portfolios at the OSE. Is the LIQ factor useful for pricing the crossection? Use an equally weighted market index, and returns data Solution to Exercise 2. Reading the data etc. > library(zoo) > Rets <- read.zoo("../../data/equity_size_portfolios_monthly_ew.txt", + header=true,sep=";",format="%y%m%d") > Rf <- read.zoo("../../data/nibor_monthly.txt", + format="%y%m%d",header=true,sep=";") > er <- Rets - lag(rf,-1) > Rm <- read.zoo("../../data/market_portfolios_monthly.txt", + format="%y%m%d",header=true,sep=";") > ermew <- Rm$EW - lag(rf,-1) > FF <- read.zoo("../../data/pricing_factors_monthly.txt", + header=true,sep=";",format="%y%m%d") > data <- merge(er,ermew,ff$liq,all=false) > er <- as.matrix(data[,1:10]) > erm <-as.matrix(data[,11]) > LIQ <- as.matrix(data[,12]) > reg <- lm(er~erm + LIQ) Results First five portfolios 4

5 Last five portfolios Model 1 Model 2 Model 3 Model 4 Model 5 (Intercept) (0.00) (0.00) (0.00) (0.00) (0.00) erm (0.05) (0.04) (0.03) (0.04) (0.04) LIQ (0.05) (0.04) (0.04) (0.04) (0.04) R Adj. R Num. obs *** p < 0.001, ** p < 0.01, * p < 0.05, p < 0.1 Model 6 Model 7 Model 8 Model 9 Model 10 (Intercept) (0.00) (0.00) (0.00) (0.00) (0.00) erm (0.03) (0.03) (0.03) (0.03) (0.04) LIQ (0.04) (0.04) (0.04) (0.03) (0.05) R Adj. R Num. obs *** p < 0.001, ** p < 0.01, * p < 0.05, p < 0.1 See that LIQ is significant in most cases. 5

6 4 Literature A couple of useful surveys: Goyal (2012) has a section on liquidity bases asset pricing in his broad survey of cross-sectional asset pricing Amihud et al. (2005) surveys liquidity literature. References Viral A Acharya and Lasse Heje Pedersen. Asset pricing with liquidity risk. Journal of Financial Economics, 77: , Yakov Amihud and Yakov Mendelson. Asset pricing and the bid/ask spread. Journal of Financial Economics, 17: , Yakov Amihud, Haim Mendelson, and Lasse Heje Pedersen. Liquidity and asset prices. Foundations and Trends in Finance, 1(4): , Fisher Black, Michael Jensen, and Myron Scholes. The capital asset pricing model, some empirical tests. In Michael C Jensen, editor, Studies in the theory of capital markets. Preager, Michael J Brennan and Avanidhar Subrahmanyam. Market microstructure and asset pricing: On the compensation for illiquidity in stock returns. Journal of Financial Economics, 41: , Michael J Brennan, Tarun Chordia, and Avanidhar Subrahmanyam. Alternative factor specifications, security characteristics, and the cross-section of expected stock returns. Journal of Financial Economics, 49: , George M Constantinides. Capital market equilibrium with transaction costs. Journal of Political Economy, 94(4): , August Vinay T Datar, Narayan Y Naik, and Robert Radcliffe. Liquidity and stock returns: An alternative test. Journal of Financial Markets, 1: , Amit Goyal. Empirical cross-sectional asset pricing: a survey. Financial Markets and Portfolio Management, 26: 3 38, Sanford Grossman and Joseph Stiglitz. On the impossibility of informationally efficient markets. American Economic Review, Jennifer Huang and Jiang Wang. Market liquidity, asset prices, and welfare. Journal of Financial Economics, 95: , Randi Næs, Johannes Skjeltorp, and Bernt Arne Ødegaard. What factors affect the Oslo Stock Exchange? Working Paper, Norges Bank (Central Bank of Norway), December Maureen O Hara. Presidential adress: Liquidity and price discovery. Journal of Finance, LVIII(4), August D Vayanos. Transaction costs and asset prices: A dynamic equilibrium model. Review of Financial Studies, 11(1): 1 58,