Cross Sectional Variation of Stock Returns: Idiosyncratic Risk and Liquidity

Transcription

1 Cross Sectional Variation of Stock Returns: Idiosyncratic Risk and Liquidity by Matthew Spiegel Xiaotong (Vivian) Wang

2 Cross Sectional Returns via Market Microstructure Liquidity Returns Liquidity varies across stocks. More liquidity is better. Duh! People should be willing to accept lower returns in exchange for higher liquidity levels.

3 Asset Pricing Research Volatility Returns If the CAPM assumptions do not hold exactly, idiosyncratic risk may be priced. Ex. Merton (1987).

4 Conversation Between Asset Pricing and Market Microstructure? Volatility Returns Liquidity Returns Volatility Liquidity

5 Idiosyncratic Risk?? Liquidity Theory implies idiosyncratic risk and liquidity should be negatively correlated Asset Pricing: Merton (1998) Inventory Control: Ho and Stoll (1980) Spiegel and Subrahmanyam (1995) Question: Are past empirical results relating returns to liquidity and idiosyncratic risk due to one, the other, or in some measure to both?

6 Innovation Volatility Liquidity Returns

7 Question: Which Picture is Right? Volatility Liquidity Returns Volatility Liquidity Returns Volatility Liquidity Returns

8 Questions? Idiosyncratic risk Cross sectional return variation. Liquidity Cross sectional return variation. Idiosyncratic risk Liquidity To what degree is the cross sectional variation in returns due to idiosyncratic risk or liquidity? Do some measures explain more than others?

9 Answers: Acting Alone EGARCH idiosyncratic risk strongly positively correlated with out of sample returns. OLS idiosyncratic risk uncorrelated with out of sample returns. Cost and reflective liquidity measures correlated with returns. Cost based: bid-ask spread Reflective: volume

10 Answers: Acting Together Controlling for idiosyncratic risk cost based liquidity measures play a minor role in cross sectional returns Controlling for idiosyncratic risk volume plays a strong role in cross sectional returns. Controlling for liquidity EGARCH measured idiosyncratic risk plays a major role.

11 Data Monthly from CRSP. Nice because fewer microstructure issues than daily data. Find idiosyncratic risk is positively related to returns. Opposite of Ang et al. finding using daily data. Do not explore why the monthly and daily data produce different answers.

12 Measures Need liquidity and idiosyncratic risk measures. No kidding! For liquidity use estimates provided on Joel Hasbrouck s web page. For idiosyncratic risk use EGARCH model.

13 Estimating Liquidity (Hasbrouck 2005) Hasbrouck s Gibbs Sampler estimate of Roll s (1984) effective Cost (bid ask spread): r = cδ q + u c t t t < = 0 otherwise cov ( r ) ( ) t, rt 1 if cov rt, rt 1 0.

14 Forecasting Idiosyncratic Risk OLS vs. EGARCH OLS estimates of Idiosyncratic Risk (Idio) ( ) R R = α + β R R + β SMB + β HML + ε i t ft i imkt, mktt, ft ismb, t ihml, t it, EGARCH estimation of Idiosyncratic Risk (Eidio) ( ) R R = α + β R R + β SMB + β HML + ε ε i t ft i imkt, MKTt, ft ismb, t ihml, t it, = h v it, it, t p ( ) ln h = ω + δ ln h + η v E v + ψ v q i, t i i, m i, t m i, n t n t n i t n m= 1 m= 1

15 OLS EGARCH Contest Use 60 months of data (1 to 60) to estimate each model. Each model forecasts month 61 idiosyncratic risk. OLS = Idio, EGARCH = Eidio. Use OLS model to produce an estimate of month 61 idiosyncratic risk with data from month 2 to 61. Closest forecast in average absolute value across stocks wins! Note: Horse Race strongly rigged to favor OLS.

16 Eidio Wins in 483 out of 505 Months EGARCH Jan-62 Jan-64 Jan-66 Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Forecast Error OLS Date Idio Eidio

17 Relationship Between Idiosyncratic Risk, Size and Liquidity Strong relationships across these three factors known to influence stock returns.

18 Size, Illiquidity as Idiosyncratic Risk Increases Portfolios Sorted by Idiosyncratic Risk Illiquidity (Gibbs*10^3) Size (log(mktcap)) 0 P P10

19 Illiquidity and Idiosyncratic Risk Table 4: Regression of Illiquidity (Gibbs) on Eidio Pooled OLS Eidio Size Adjusted R^2 Edio significant w/ or w/o Size 0.006*** *** *** 0.15 Edio explains as much as Size.

20 Now for the Real Tests In sample: Who really cares? Out of sample: Potential to make actual money! Everybody cares!

21 Portfolio Construction Based on previous month s Eidio form 10 portfolios Hold this portfolio for 1 month. Repeat

22 Yellow: t>2. +,++ Rank Corr. Sig. 5%, 1%. Rank CAPM Carhart-4 Alpha ++ FF-3 Alpha + Alpha ++ OLS FF-3 Alpha Portfolios Sorted by Idiosyncratic Risk: Monthly Rebalance 1Low -0.47% -0.42% -0.30% -0.01% % -0.02% -0.01% -0.05% % 0.14% 0.12% 0.01% % 0.15% 0.19% 0.10% % -0.01% 0.07% 0.05% % 0.07% 0.08% 0.15% % 0.11% 0.09% 0.14% % 0.11% 0.15% 0.09% % 0.60% 0.86% -0.03% 10High 0.96% 1.06% 1.27% -0.77% p10-p1 1.43% 1.49% 1.58%

23 Yellow: t>2. +,++ Rank Corr. Sig. 5%, 1%. Rank CAPM Alpha ++ FF-3 Alpha + Carhart-4 Alpha ++ Portfolios Sorted by Eidio: Yearly Rebalance 1Low -0.17% -0.85% -0.89% % -0.51% -3.21% % -2.48% -1.46% % -3.07% -0.15% % -1.34% -0.20% % -1.45% -1.87% % 1.12% 1.57% % 6.74% 6.96% % 10.75% 9.87% 10High 25.97% 24.78% 25.01% p10-p % 25.63% 25.90%

24 Yellow: t>2. +,++ Rank Corr. Sig. 5%, 1%. Rank CAPM Alpha FF-3 Alpha Panel A: Portfolios Sorted by Gibbs Sampler Carhart-4 Alpha 1Low 1.83% 0.93% -0.81% % -0.19% 1.51% % -2.52% -1.47% % -0.34% 1.84% % -3.40% -1.16% % -1.52% 3.25% % -4.18% -2.79% % -2.04% 1.63% % -2.74% -2.51% 10High 7.99% 2.24% 1.77% p10-p1 6.16% 1.30% 2.58%

25 Yellow: t>2. +,++ Rank Corr. Sig. 5%, 1%. Rank CAPM Alpha -- FF-3 Alpha Carhart-4 Alpha Panel A: Sorted by $ Volume Rebalanced Annually 1Low 9.75% 3.49% 2.99% % 0.87% -0.11% % 1.35% 1.65% % 1.21% 1.82% % -0.99% -0.47% % -0.87% 0.38% % -0.64% -0.41% % -0.63% 0.18% % -0.29% -0.57% 10High -0.50% -0.32% -0.06% p1-p % 3.81% 3.06%

26 Two Way Sorts Controls for one factor to see if the other factor continues to explain cross sectional stock returns. Portfolios hold only stocks in the control decile and then sort on the factor of interest. Three primary findings Controlling for Eidio the bid-ask spread has little explanatory power. Controlling for any other factor Eidio, and $ Volume continue to have significant explanatory power.

27 Bid-Ask Spread Out of Sample Annual Alphas [t-stat][rank Corr. Sig. ++,- -=1%; +,-=5%] Quintile Size Control Eidio Control Equal Most of the return is from small cap and high Eidio firms % [4.10][++] 3.83% [1.72][++] -1.76% [-1.21] -6.20% [-8.00][- -] -1.11% [-1.02][-] 3.12% [1.84][+] -6.77% [-2.87][- -] -9.05% [-4.42][-] -7.41% [-5.47] -1.40% [-1.54][-] 34.46% [3.78] 1.96% [0.81]

28 $ Volume Out of Sample Annual Alphas [t-stat][rank Corr. Sig. ++,- -=1%; +,-=5%] Quintile Size Control Eidio Control Equal 20.70% [4.10][- -] 15.83% [6.17] [- -] 13.32% [5.99] [- -] 6.08% [3.70] [-] 0.07% [0.05] 11.20% [9.51] [- -] 1.45% [0.78] [- -] 3.35% [2.30] [- -] 8.91% [3.57] [- -] 9.09% [3.10] [-] 11.37% [3.95] [- -] 6.83% [5.15] [- -]

29 Eidio Out of Sample Monthly Alphas [t-stat][rank Corr. Sig. ++,- -=1%; +,-=5%] Quintile Size Control Bid-Ask Control Equal 2.31% [4.92][++] 2.07% [4.97] [++] 1.62% [3.26] [++] 0.81% [4.59] [++] 0.57% [2.18] [++] 1.48% [6.10] [++] 0.91% [2.43] [++] 0.91% [2.25] [++] 1.19% [4.63] [++] 1.05% [4.87] [++] 0.70% [4.21] [++] 0.95% [6.78] [++]

30 Regression Analysis Regression risk adjusted return (alpha) on different characteristics Controls For: Size, Liquidity (various measures), Idiosyncratic Risk, Lagged returns (momentum), and Dollar volume In the table note that liquidity is not significant when Eidio is included in the regression.

31 Fama-Macbeth Regression of Alpha on Characteristics Alpha (Bid-Ask Current Yr.) Alpha (Bid-Ask Previous Yr.) Eidio *** *** Bid-Ask *** *** ** Lmv *** *** *** retlag ** ** *** *** retlag ** ** *** *** retlag ** * *** *** Nyamdvol *** *** *** *** Nasdvol *** *** * *** Adjusted R

32 Missing Factor? Are the high idiosyncratic risk portfolio returns due to a missing risk factor? If so then high Eidio portfolios should have higher volatilities. Missing risk factors should be correlated across the stocks and thus not diversify away.

33 Eidio Portfolio Risk and Return (All Firms No Liquidity Measure Restriction) Port1 (low) Port2 Port3 Port4 Port5 mean % 0.086% 0.118% 0.377% 0.671% s.d % 8.349% 7.627% 7.045% 6.398% Sharpe Port6 Port7 Port8 Port9 Port10 (high) mean 0.753% 0.857% 0.825% 0.964% 1.077% s.d % 5.191% 4.293% 3.681% 7.218% Sharpe Mean s.d. Sharpe Spear s.d. P-value Market.458% 4.483%

34 Connor-Korajczyk Factors +++,--- = rank corr. sig. 1%, ++, -- = rank corr. sig. 5%, +, - = rank corr. sig. 10% Rank CK α Factor (low) -0.47% [1.19] [3.55] [0.94] [1.18] [0.58] [0.12] [1.70] % [0.02] [3.36] [0.89] [0.01] [0.16] [0.87] [0.59] % [0.14] [2.05] [1.46] [0.49] [1.85] [0.29] [0.62] % [0.95] [0.37] [1.74] [0.55] [2.59] [1.94] [0.73] % [2.13] [1.23] [1.26] [0.54] [0.80] [0.54] [0.72]

35 Connor-Korajczyk Factors +++,--- = rank corr. sig. 1%, ++, -- = rank corr. sig. 5%, +, - = rank corr. sig. 10% Rank CK α Factor (low) -0.47% [1.19] [3.55] [0.94] [1.18] [0.58] [0.12] [1.70] % [0.02] [3.36] [0.89] [0.01] [0.16] [0.87] [0.59] % [2.13] [1.23] [1.26] [0.54] [0.80] [0.54] [0.72] % [5.67] [1.02] [0.49] [1.06] [0.58] [1.49] [0.31] 10 (high) 1.08% [3.34] [0.06] [0.20] [0.32] [0.75] [0.66] [2.64] Avg. fac. r -0.91% 2.09% 8.83% 6.17% -3.27% 2.04% Right Way

36 Period Specific Results Are the results due to a particular time period? Results by decade. Results by economic environment Expansions vs. recessions. High vs. low volatility periods.

37 Sub-Period Analysis Time Ranking on Idiosyncratic Risk Sub-Period 1 Low 10High 10-1 Jan Dec % 1.10% 1.21% [-0.57] [1.74] [1.65] Jan Dec % 1.06% 1.46% [-3.84] [2.76] [3.67] Jan Dec % 1.01% 1.43% [-3.74] [3.41] [3.76] Jan Dec % 0.55% 1.15% [-2.31] [1.81] [1.78]

38 Sub-Period Analysis Economic Environment Ranking on Idiosyncratic Risk Sub-Period 1 Low 10High 10-1 NBER Expansions -0.31% 0.77% 1.08% [-2.59] [1.76] [2.46] NBER Recessions -0.76% 2.38% 3.15% [-2.51] [2.25] [2.74] Stable Periods -0.78% 0.98% 1.76% [-2.25] [1.09] [2.29] Volatile Periods -0.39% 1.18% 1.57% [-3.12] [2.67] [3.43]

39 Real Time 2007 Results /3/2007 2/3/2007 3/3/2007 4/3/2007 5/3/2007 6/3/2007 7/3/2007 8/3/2007 9/3/ /3/2007 Eidio Wilshire 5000 Eidio: 14.69% ytd, Wilshire 5K: 10.87% ytd

40 One Factor Conclusions: Cross Sectional Returns OLS idiosyncratic risk estimates have little explanatory. EGARCH has significant explanatory power. Carhart alpha of 25% per year for high risk portfolios Cost based measures have little explanatory power. Dollar volume has significant explanatory power. Carhart alpha of 3% for low volume stocks.

41 Multi-Factor Conclusions: Cross Sectional Returns Liquidity and idiosyncratic Risk are negatively correlated. Controlling for liquidity (however measured) Eidio has out of sample predictive power. Controlling for Eidio cost based liquidity measures have little cross sectional explanatory power. Controlling for Eidio dollar volume has substantial cross sectional explanatory power.