The High Idiosyncratic Volatility Low Return Puzzle

Transcription

1 The High Idiosyncratic Volatility Low Return Puzzle Hai Lu, Kevin Wang, and Xiaolu Wang Joseph L. Rotman School of Management University of Toronto NTU International Conference, December, 2008

2 What is the puzzle? Ang, Holdrick, Xing, and Zhang, Journal of Finance, 2006 AHXZ find that high idiosyncratic volatility (ivol) stocks have low returns. It is about cross-sectional differences in stock returns. What is ivol (or how is it measured)? Constructed with the Fama-French three factor model Obtained by daily return regressions in each month Defined as the standard deviation of the residuals 1

3 The Basic Result of AHXZ: month-t ivol quintile t-stat (5-1) month-(t + 1) return FF-3 alpha

4 What do we do in this paper? Basic idea The effect is nonlinear - mostly concentrated in the highest ivol quintile. The highest ivol quintile contains two types of stocks: Stocks with regularly high ivol Stocks with temporarily high ivol 3

5 YAHOO INC (NasdaqGS) Range: 1d 5d 3m 6m 1y 2y 5y max Type: Bar Line Cdl Scale: Linear Log Size: M L Temporarily high ivol - An example Compare: YHOO vs S&P Nasdaq Dow Compare Want more control over the chart? Try our Interactive Chart. Splits:02-Sep-97 [3:2], 03-Aug-98 [2:1], 08-Feb-99 [2:1], 14-Feb-00 [2:1], 12-May-04 [2:1] 4 Last Trade: Trade Time: Mar 14 Day's Range: wk Range:

6 What have we got? What are we trying to get? The highest ivol quintile contains two types of stocks: A group of small, illiquid, low-priced stocks display strong reversal. A group of relatively large and liquid stocks generates the puzzle. In particular, losing stocks in this group exhibit drift. Work-in-progress: What explains low return of the second group? Analysts forecasts dispersion and/or effects of corporate news 5

7 Why is it interesting? Two different views of the ivol effect: Very robust - AHXZ Not robust at all - Bali and Cakici (2008) Sensitive to weighting-scheme. Sensitive to data frequency used to estimate ivol. Our goal is to explain both. Now we can explain the sensitivity results of Bali and Cakici. We are trying to explain how the second group generates the AHXZ finding. 6

8 re reported in the lower panel. size represents the average stock market capitalization by the end of month t. eports the average book-to-market ratio. turnover reports the average monthly turnover. illiquidity reports the av onthly Amihud (2002) illiquidity measure. price reports the average stock price in each size group. Panel A is f tocks in the idiosyncratic volatility quintile 5. Panel B is for stocks with ranking-month (month t) return < 0. Pa s for stocks with ranking-month (month t) return > 0. Table 3 - Panel A A. All stocks in the idiosyncratic volatility quintile 5 value-weighted equally-weighted size rank number t t+1 t t [3.34] 2.10 [4.44] 0.59 [0.98] 3.18 [6.32] [8.62] 0.38 [0.86] 5.26 [8.30] 0.47 [1.05] [11.12] [-0.23] 7.53 [10.74] [-0.14] size rank size B/M turnover illiquidity price

9 t+1). Panel B reports the equally-weighted portfolio returns. Panel C reports the average idiosyncratic volatility in roup. Table 6 - Panel A A. Value-weighted portfolio returns size rank ivol rank t t+1 t t+1 t t+1 t t+1 t t [7.17] [0.85] [11.22] [-3.63] [11.84] [-4.88] [11.01] [-4.40] [9.07] [-2.84] B. Equally-weighted portfolio returns size rank

10 [4.40] [3.55] [11.04] [-3.44] [11.90] [-4.89] [11.37] [-4.63] [9.20] [-3.24] Table 6 - Panel C C. Average idiosyncratic volatility size rank ivol rank t t+1 t t+1 t t+1 t t+1 t t

11 Table 9 (Continued) Table 9 - Panels C and D C. Returns (using the group of small stocks in the quintile 5) L N [0.85] 0.47 [1.14] 0.62 [1.47] 0.75 [1.75] [1.15] 0.62 [1.50] 0.76 [1.79] 0.85 [1.96] [1.63] 0.79 [1.89] 0.90 [2.13] 0.96 [2.22] [1.90] 0.91 [2.18] 0.99 [2.35] 1.02 [2.38] [2.14] 0.99 [2.38] 1.07 [2.53] 1.07 [2.50] D. FF-3 alphas (using the group of small stocks in the quintile 5) L N [-1.24] [-0.74] [-0.21] 0.07 [0.27] [-0.78] [-0.17] 0.08 [0.31] 0.15 [0.60] [-0.09] 0.09 [0.39] 0.19 [0.78] 0.25 [0.99] [0.37] 0.19 [0.80] 0.28 [1.11] 0.33 [1.31] [0.75] 0.28 [1.16] 0.36 [1.45] 0.40 [1.57] E. Returns (using the group of large stocks in quintile 5) L N [-3.16] [-3.04] [-3.17] [-2.32] 10

12 [-0.78] [-0.17] 0.08 [0.31] 0.15 [0.60] [-0.09] 0.09 [0.39] 0.19 [0.78] 0.25 [0.99] [0.37] 0.19 [0.80] 0.28 [1.11] 0.33 [1.31] [0.75] 0.28 [1.16] 0.36 [1.45] 0.40 [1.57] Table 9 - Panels E and F E. Returns (using the group of large stocks in quintile 5) L N [-3.16] [-3.04] [-3.17] [-2.32] [-2.43] [-2.47] [-2.32] [-1.70] [-2.05] [-2.01] [-1.84] [-1.41] [-1.67] [-1.64] [-1.55] [-1.33] [-1.44] [-1.41] [-1.36] [-1.26] F. FF-3 alphas (using the group of large stocks in the quintile 5) L N [-6.52] [-6.44] [-6.65] [-5.46] [-5.80] [-5.85] [-5.46] [-4.50] [-5.75] [-5.33] [-4.92] [-4.09] [-5.23] [-4.93] [-4.55] [-3.95] [-4.96] [-4.71] [-4.29] [-3.88] 11

13 For the second group in the ivol quintile 5, both winning and losing stocks have negative holding period returns. Disagreement = Overpricing What can generate disagreement? Hong and Stein (2007, JEP): Gradual information flow Limited attention Heterogeneous priors Miller (1977), Harrison and Kreps (1978), and Scheinkman and Xiong (2003) Opinion divergence and short-sale constraint lead to overpricing. Trading volume and the degree of overpricing are positively correlated. 12

14 ranking and the holding month. Robust Newey-West t-statistics are reported in square brackets. The bottom panel reports average stock size and average number of forecasts ( est ) made by analysts in a given month The sample period is from January 1976 to December Panel B reports the results for first sorting o idiosyncratic volatility, and on analyst forecast Table dispersion Panel B B. Stocks with at least three analysts making forecasts analyst dispersion rank value-weighted portfolio return ivol rank t t+1 t t+1 t t+1 t t+1 t t [4.84] [-0.40] [5.23] [-0.91] [5.64] [-1.25] [5.67] [-1.88] [6.54] [-2.82] equally-weighted portfolio return ivol rank t t+1 t t+1 t t+1 t t+1 t t

15 Summary We find that the division of the highest ivol quintile is useful. Sensitivity to variation of the empirical procedure is annoying. It should be understood in any serious attempt to explain the effect. What to do next? Focus on shocks to explore temporarily high volatility. In fact, we have a new paper: The Long Memory in Stock Price Shocks 14