The Common Factor in Idiosyncratic Volatility: Quantitative Asset Pricing Implications Bryan Kelly University of Chicago Booth School of Business (with Bernard Herskovic, Hanno Lustig, and Stijn Van Nieuwerburgh)
Average Firm Volatility Campbell et al. (2001) Have Individual Stocks Become More Volatile? Panel A. Firm volatility % % Z 8 E X t Z K R 8 % $ 5 % 8 % S 8 Panel B. Firm volatility, MA(12) Figure 4. Annualized firm-level volatility FIRM. The top panel shows the annualized vari- ance within each month of daily firm returns relative to the firm's industry, calculated using equations (20)-(22), for the period from July 1962 to December 1997. The bottom panel shows a backwards 12-month moving average of FIRM. NBER-dated recessions are shaded in gray to iIlustrate cyclicaI movements in volatility. stock market has become more volatile over the sample but on a firm level instead of a market or industry level. Apart from the trend, the plot of FIRM looks similar to MKT and IND. Firm-level volatility seems to be higher in NBER-dated recessions and the crash also has a significant effect. Looking at the three volatility plots together, it is clear that the different volatility measures tend to move together, particularly at lower frequencies. For example, all three volatility measures increase during the oil price shocks in the early to mid-1970s. However, there are also some periods in which the volatility measures move differently. For example, IND is very high com- pared to its long-term mean during the early 1980s while MKT and FIRM
Average Firm Volatility Idiosyncratic Volatility by Size Quintile 1.6 1 (Small) 2 3 4 1.4 5 (Large) 1.2 1 0.8 0.6 0.4 0.2 1930 1940 1950 1960 1970 1980 1990 2000 2010
This Paper ◮ Strong comovement of individual stock return volatilities ◮ Idiosyncratic volatility ◮ Firm cash flows ◮ Shocks to this common component of idiosyncratic volatility (CIV) are priced ◮ Idiosyncratic volatility ◮ Sorting stocks on their CIV-beta produces return spread of about 6% ◮ Survives typical battery of factors ◮ Establish empirical connection between CIV and household income risk ◮ Model with heterogeneous investors whose income risk is linked to firm performance accounts for all three facts
Outline 1. Common idiosyncratic volatility (CIV) facts 2. Firm risk and household risk 3. CIV and stock returns 4. Heterogeneous agent model with common idiosyncratic volatility 5. Firm volatility in dynamic networks
Volatility Factor Structure Facts: 1. Firm-level volatility obeys a strong factor structure ◮ Both in returns and in cash-flow growth rates ◮ Both total volatility and residual volatility 2. Not due to omitted factors in return/growth rate model ◮ Among uncorrelated residuals (e.g. from 10 PCs), strong factor structure in volatilities remains intact 3. A common idiosyncratic volatility factor (CIV) captures much of the covariation (factor is not market volatility) i F t + σ 2 = γ 0 , i + γ ′ i , t ε i , t r i , t σ 2 σ 2 = i + δ i CIV t + ν i , t i , t * Return to discussion of potential mechanisms at the end
Firm-Level Volatility Matters Why might this matter? ◮ Pass-through in labor markets: substantial fraction of firm-level volatility ends up being passed through to workers What can investors do? ◮ Build portfolios that hedge their income risk This paper: Commonality in firm vol + = Important price effects Labor income pass-through
The Basic Volatility Facts
Calculations Return volatility (year-firm panel, CRSP 1926-2010) ◮ “Total” volatility: Std dev of daily stock returns within calendar year ◮ “Idiosyncratic” volatility: Daily factor model in each calendar year r i , t = γ 0 , i + γ ′ i F t + ε i , t ◮ F t can be mkt, FF3, 5PCs, 10PCs ◮ Extensions: Monthly panel, monthly returns, portfolios, etc. Fundamental volatility (year-firm panel, CRSP/Compustat 1975-2010) ◮ “Total” volatility: Std dev of 20 qtrly yoy sales growth observations for calendar years τ − 4 to τ ◮ “Idiosyncratic” volatility: Qtrly factor model in 5-year window (PCs) ◮ Extensions: Cash flows, estimation window, etc.
Common Factor in Total and Residual Volatility Panel A: Total Volatility by Size Quintile Panel B: Idiosyncratic Volatility by Size Quintile 1 (Small) 1.6 1 (Small) 1.8 2 2 3 3 4 4 1.4 1.6 5 (Large) 5 (Large) 1.4 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 1930 1940 1950 1960 1970 1980 1990 2000 2010 1930 1940 1950 1960 1970 1980 1990 2000 2010
Common Factor in Total and Residual Volatility Panel A: Total Volatility by Industry Panel B: Idiosyncratic Volatility by Industry Consumer Goods Consumer Goods Manufacturing Manufacturing 1 High Tech 0.9 High Tech Healthcare Healthcare Other (finance, services, etc.) Other (finance, services, etc.) 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 1930 1940 1950 1960 1970 1980 1990 2000 2010 1930 1940 1950 1960 1970 1980 1990 2000 2010
Again, These are Residual Volatilities For each stock i 1. Run time series regression r i , t = α i + β M r M , t + β ′ FF FF t + any other factors you want + ε i , t 2. Study residuals ε i , t ◮ Check if they cross-correlated ◮ Build their variances ◮ Does their volatility comove?
Correlation and Volatility Average Pairwise Correlation Average Volatility Total Total 1 MM Residuals MM Residuals 0.4 FF Residuals FF Residuals 5 PC Residuals 5 PC Residuals 0.9 0.35 0.8 0.3 0.7 0.25 0.6 0.2 0.5 0.15 0.4 0.1 0.3 0.05 0.2 0 1930 1940 1950 1960 1970 1980 1990 2000 2010 1930 1940 1950 1960 1970 1980 1990 2000 2010
Comovement in Fundamental Volatilities Panel A: Total Volatility by Size Quintile Panel B: Total Volatility by Industry 0.6 1 (Small) Consumer Goods 0.4 2 Manufacturing 3 High Tech 0.55 4 Healthcare 5 (Large) Other (finance, services, etc.) 0.5 0.35 0.45 0.3 0.4 0.35 0.25 0.3 0.2 0.25 0.2 0.15 0.15 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010 Panel C: Idiosyncratic Volatility by Size Quintile Panel D: Idiosyncratic Volatility by Industry 1 (Small) Consumer Goods 0.22 2 Manufacturing 0.3 3 High Tech 4 Healthcare 5 (Large) Other (finance, services, etc.) 0.2 0.25 0.18 0.16 0.2 0.14 0.12 0.15 0.1 0.1 0.08 0.06 1975 1980 1985 1990 1995 2000 2005 2010 1975 1980 1985 1990 1995 2000 2005 2010
Quantifying the Factor Structure ◮ Panel regression of firm vol on equally-weighted average vol across firms Panel A: Returns Total MM FF 5 PCs Loading (average) 1.012 1.024 1.032 1.031 Intercept (average) 0.006 0.005 0.004 0.004 R 2 (average univariate) 0.362 0.347 0.346 0.348 R 2 (pooled) 0.345 0.337 0.339 0.347 Panel B: Sales Growth Total (5yr) 1 PC (5yr) 5 PCs (5yr) Total (1yr) Loading (average) 0.885 1.149 1.249 0.884 Intercept (average) 0.044 -0.018 -0.024 0.030 R2 (average univariate) 0.293 0.299 0.299 0.178 R2 (pooled) 0.303 0.315 0.304 0.168
CIV, MV, and CIV Innovations Panel A: Volatility Level Panel B: Volatility Changes 0.9 0.4 CIV CIV MV CIV orth. 0.8 0.3 0.7 0.2 0.6 0.1 0.5 0.4 0 0.3 −0.1 0.2 −0.2 0.1 0 −0.3 1926 1937 1949 1961 1973 1985 1997 2010 1926 1937 1949 1961 1973 1985 1997 2010 ◮ Common idios. volatility (CIV) and market volatility (MV) correlated ◮ Nonetheless, shocks to CIV and shocks to MV are distinct: 67% correlation between CIV changes and CIV changes orthogonalized to MV changes
Implications of Volatility Comovement ◮ This talk: Equity risk premia ◮ Ongoing work: ◮ Valuing and hedging options book ◮ Understanding and valuing joint tail risk
Outline 1. Common idiosyncratic volatility (CIV) facts 2. Firm risk and household risk 3. CIV and stock returns 4. Heterogeneous agent model with common idiosyncratic volatility 5. Firm volatility in dynamic networks
CIV and Individual Income Risk ◮ Many of persistent, idiosyncratic income shocks experienced by households begin with firm/employer from which income is derived ◮ Job displacement: “a plant closing, an employer going out of business, a layoff from which he/she was not recalled” (Kletzer 1989,1990) ◮ Firm-specific human capital “... cost of and the return to the investment will be shared by the worker and the employer” (Becker 1962) ◮ Direct exposure to equity risk of employer for incentive reasons... (Jensen and Meckling 1976, Murphy 1985, Morck, Shleifer, and Vishny 1988, Kole 1995, etc.) ◮ ...and for non-incentive reasons (Benartzi 2001, Cohen 2009, Van Nieuwerburgh and Veldkamp 2006)
CIV and Individual Income Risk ◮ Consensus view in the literature: Households can’t fully insulate their consumption from persistent shocks to labor income. > 40% of permanent labor income shocks are passed to consumption (Cochrane 1991, Attanasio and Davis 1996, Blundell, Pistaferri, and Preston 2008, Heathcote, Storesletten, and Violante 2013) ◮ Firms provide employees with some temporary insurance against idiosyncratic shocks, little protection against persistent shocks which ultimately affect compensation through wages or layoffs (Berk, Stanton, and Zechner 2010, Lustig, Syverson, and Nieuwerburgh 2011)
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