Size Matters, if You Control Your Junk

Discussion of: Size Matters, if You Control Your Junk by: Cliff Asness, Andrea Frazzini, Ronen Israel, Tobias Moskowitz, and Lasse H. Pedersen Kent Daniel Columbia Business School & NBER AFA Meetings 7 January, 2017

Outline Size Anomaly History History The quality measure Seasonalities Explanations

Non-linearities The Size Anomaly early evidence Banz (1981) presents evidence of a strong size (market cap) effect that is not explained by the loading on the market portfolio Keim (1983) shows that this effect is all in January From Keim (1983):

Non-linearities EW Size Decile Portfolio Returns Portfolio Value (Dollars) 10 7 10 6 10 5 10 4 10 3 10 2 d01 d02 d03 d04 d05 d06 d07 d08 d09 d10 Size Decile Portfolios (EW) -- Cumulative Returns, 1926:07-2016:11 $1,824,735 $3,057 10 1 10 0 10-1 1929 1939 1949 1959 1969 1979 1989 1999 2009 date

Non-linearities EW Size Decile Portfolio Returns Over the 1926:07-2016:11 period, the smallest size-decile portfolio outperforms the largest by 92 bps/month. r Jan = 909 bps/month; r non Jan = 17 bps/month, However, both Banz (1981) and Keim (1983) used equal-weighted portfolios Specifically, Banz (1981) uses the 25 size/beta-sorted, EW portfolios of Black and Scholes (1974). AFIMP note the discrepancy between their results and those of Banz, and argue that the discrepancy is probably the result of CRSP errors that were corrected. Most of the difference results from AFIMP using VW portfolios.

EW Portfolio Return Bias Price 2 1 Non-linearities Asset A Asset B 1 2 3 R EW,2 = (1/2) ( 50%) +(1/2) (+100%) = 25% R EW,3 = (1/2) (+100%) +(1/2) ( 50%) = 25% Gain R EW,2 = InitialCost Gain R EW,3 = InitialCost = (1/4) ( 1)+(1/2) (+1) (1/4) 2+(1/2) 1 = 25% = (1/2) (+1)+(1/4) ( 1) (1/2) 1+(1/4) 2 = 25% To avoid this bias, AFIMP use all VW portfolios.

Non-linearities EW Size Decile Portfolio Returns Portfolio Value (Dollars) 10 7 10 6 10 5 10 4 10 3 10 2 d01 d02 d03 d04 d05 d06 d07 d08 d09 d10 Size Decile Portfolios (EW) -- Cumulative Returns, 1926:07-2016:11 $1,824,735 $3,057 10 1 10 0 10-1 1929 1939 1949 1959 1969 1979 1989 1999 2009 date

Non-linearities VW Size Decile Portfolio Returns Portfolio Value (Dollars) 10 7 10 6 10 5 10 4 10 3 10 2 d01 d02 d03 d04 d05 d06 d07 d08 d09 d10 Size Decile Portfolios (VW) -- Cumulative Returns, 1926:07-2016:11 $37,182 $3,293 10 1 10 0 10-1 1929 1939 1949 1959 1969 1979 1989 1999 2009 date

Size Decile Portfolio Returns Non-linearities Portfolio Value (Dollars) 10 7 10 6 10 5 10 4 10 3 10 2 Hedged Size Decile Portfolios (VW) -- Cumulative Returns, 1926:07-2016:11 d01 ( ˆα = 2. 3%, t = 1. 0) d02 ( ˆα = 1. 0%, t = 0. 6) d03 ( ˆα = 1. 3%, t = 1. 0) d04 ( ˆα = 1. 4%, t = 1. 2) d05 ( ˆα = 1. 1%, t = 1. 1) d06 ( ˆα = 1. 4%, t = 1. 8) d07 ( ˆα = 0. 9%, t = 1. 3) d08 ( ˆα = 0. 8%, t = 1. 5) d09 ( ˆα = 0. 4%, t = 1. 0) d10 ( ˆα = 0. 1%, t = 0. 3) RF 10 1 $24.07 $18.09 10 0 10-1 1929 1939 1949 1959 1969 1979 1989 1999 2009 date

Size Decile Portfolio Returns Non-linearities 0.4 Small Decile - Large Decile (VW), Annual Returns, 1975-1990 0.3 0.2 Calendar Year Return Difference 0.1 0.0 0.1 0.2 0.3 0.4 1975 1976 1977 1978 1979 1980 1981 1982 year 1983 1984 1985 1986 1987 1988 1989 1990 Some have argued that the small-cap effect has been arbitraged away post-1980 This plot shows the annual returns from end of the authors Golden Age period (1957-1979), and the start of the Embarassment period (1980-1999).

Size Decile Portfolio Returns Non-linearities 1.0 Small Decile - Large Decile (VW), Annual Returns, 1975-1990 0.8 0.6 Calendar Year Return Difference 0.4 0.2 0.0 0.2 0.4 0.6 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 year

10 6 10 5 10 4 Non-linearities Cumulative Returns & CAPM αs, FF25 Portfolios, 1926:07-2016:11 BigVal ( ˆα = 1. 3%/yr) BigGro ( ˆα = 0. 1%/yr) Mkt ( ˆα = 0. 0%/yr) Portfolio Value 10 3 10 2 10 1 10 0 10-1 10-2 1934 1944 1954 1964 1974 date 1984 1994 2004 2014

10 6 10 5 Non-linearities Cumulative Returns & CAPM αs, FF25 Portfolios, 1926:07-2016:11 BigVal ( ˆα = 1. 3%/yr) BigGro ( ˆα = 0. 1%/yr) 10 4 Portfolio Value 10 3 10 2 10 1 10 0 10-1 10-2 1934 1944 1954 1964 1974 date 1984 1994 2004 2014

10 6 10 5 10 4 Non-linearities Cumulative Returns & CAPM αs, FF25 Portfolios, 1926:07-2016:11 BigVal ( ˆα = 1. 3%/yr) BigGro ( ˆα = 0. 1%/yr) SmlVal ( ˆα = 5. 6%/yr) SmlGro ( ˆα = 6. 0%/yr) Portfolio Value 10 3 10 2 10 1 10 0 10-1 10-2 1934 1944 1954 1964 1974 date 1984 1994 2004 2014

Quality Size Anomaly History Measuring Quality January & Variability This paper is based on the Asness, Frazzini, and Pedersen (2014, AFP) Quality measure. The motivation for the AFP quality measure is the Gordon Growth Model: Defined in this way, Value i,t = e i,t δ i r i g i Quality i,t = Profitability i Payout i ( Safety i ) Growth i Quality( ) x j > 0 x j.

Calculating Quality: Size Anomaly History Measuring Quality January & Variability Quality is a z-scored combination of the four components: Quality = z(profitability + Payout + Safety + Growth) where each component is based on z-scored combinations of various instruments: Profitability = z(z gpoa + z roe + z cfoa + z gmar + z acc ) Payout = z(z eiss + z diss + z npop ) Safety = z(z bab + z ivol + z o + z z + z evol ) Growth = z(z gpoa + z roe + z roa + z cfoa + z acc )

Quality, Price and Returns Measuring Quality January & Variability AFP s empirical evidence suggests that the price/quality relationship is too weak. This means that quality should explain return, consistent with AFP s evidence However, on average small firms tend to be junky.

Measuring Quality Size & Figure 5: Distribution of Quality/Junk Among Large and Small Stocks January & Variability The first figure plots the fraction of the number of stocks over time across five quality categories that make up the 20 percent of smallest stocks. The second figure plots the fraction of the number of stocks over time across five quality categories that make up the 20 percent of largest stocks. Quality Distribution for Small Firms 100.0% Quality Distribution Among Smallest Stocks %Junk %Q2 %Q3 %Q4 %Quality 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% 6/1/1957 9/1/1958 12/1/1959 3/1/1961 6/1/1962 9/1/1963 12/1/1964 3/1/1966 6/1/1967 9/1/1968 12/1/1969 3/1/1971 6/1/1972 9/1/1973 12/1/1974 3/1/1976 6/1/1977 9/1/1978 12/1/1979 3/1/1981 6/1/1982 9/1/1983 12/1/1984 3/1/1986 6/1/1987 9/1/1988 12/1/1989 3/1/1991 6/1/1992 9/1/1993 12/1/1994 3/1/1996 6/1/1997 9/1/1998 12/1/1999 3/1/2001 6/1/2002 9/1/2003 12/1/2004 3/1/2006 6/1/2007 9/1/2008 12/1/2009 3/1/2011 6/1/2012 9/1/2013 Quality Kent Daniel Distribution Columbia Among AFIMP Biggest Size Matters Stocks 2017 AFA Meetings

20.0% 10.0% Size Anomaly History Measuring Quality January & Variability 0.0% Quality Distribution for Big Firms 6/1/1957 9/1/1958 12/1/1959 3/1/1961 6/1/1962 9/1/1963 12/1/1964 3/1/1966 6/1/1967 9/1/1968 12/1/1969 3/1/1971 6/1/1972 9/1/1973 12/1/1974 3/1/1976 6/1/1977 9/1/1978 12/1/1979 3/1/1981 6/1/1982 9/1/1983 12/1/1984 3/1/1986 6/1/1987 9/1/1988 12/1/1989 3/1/1991 6/1/1992 9/1/1993 12/1/1994 3/1/1996 6/1/1997 9/1/1998 12/1/1999 3/1/2001 6/1/2002 9/1/2003 12/1/2004 3/1/2006 6/1/2007 9/1/2008 12/1/2009 3/1/2011 6/1/2012 9/1/2013 100.0% Quality Distribution Among Biggest Stocks %Junk %Q2 %Q3 %Q4 %Quality 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% 6/1/1957 9/1/1958 12/1/1959 3/1/1961 6/1/1962 9/1/1963 12/1/1964 3/1/1966 6/1/1967 9/1/1968 12/1/1969 3/1/1971 6/1/1972 9/1/1973 12/1/1974 3/1/1976 6/1/1977 9/1/1978 12/1/1979 3/1/1981 6/1/1982 9/1/1983 12/1/1984 3/1/1986 6/1/1987 9/1/1988 12/1/1989 3/1/1991 6/1/1992 9/1/1993 12/1/1994 3/1/1996 6/1/1997 9/1/1998 12/1/1999 3/1/2001 6/1/2002 9/1/2003 12/1/2004 3/1/2006 6/1/2007 9/1/2008 12/1/2009 3/1/2011 6/1/2012 9/1/2013

Quality, Price and Returns Measuring Quality January & Variability Table 3: Size and Junk Double Sorts The table reports results from time-series regression tests of 25 portfolios sorted on size (market cap) and quality/junk as defined by Asness, Frazzini, and Pedersen (2014). The 25 portfolios are formed from independent sorts of stocks into five quintiles using size and quality/junk. The average returns in excess of the monthly T-bill rate and their t-statistics are reported over the sample period from July 1957 to December 2012. Also reported are summary statistics from time-series regressions of the 25 portfolios on each of the following factor models: (i) the Fama and French (1993) factors RMRF, SMB, and HML plus UMD; (ii) the Fama and French (2014) five factor model, consisting of RMRF, SMB, HML, RMW, and CMA; and (iii) the Fama and French (1993) factors plus UMD Given and the the quality flat composite size-return factor, QMJ. At the relationship, bottom of the table we report this summary must statistics mean on Fama and that French s SMB factor, taken from Ken French s website, as well as an SMB factor adjusted for quality, which we non-junk call SMBQ, small which is an firms average of the earn small high minus big returns. within each quality/junk quintile, averaged equally across the five quality/junk groups. Reported are the annualized means and Sharpe ratios of SMB, SMBQ, as and, well as RMRF, that HML, big-junk UMD, and QMJ, firms along with earn their correlations really with all low of the other returns. factors. Small 2 3 4 Big Small - Big Excess returns Junk 0.35% 0.42% 0.44% 0.40% 0.12% 0.23% 2 0.84% 0.73% 0.68% 0.56% 0.37% 0.46% 3 0.87% 0.77% 0.74% 0.59% 0.34% 0.54% 4 0.89% 0.86% 0.76% 0.77% 0.47% 0.42% Quality 0.97% 0.89% 0.83% 0.78% 0.53% 0.44% Quality - Junk 0.62% 0.47% 0.39% 0.38% 0.42% t -statistics Junk 1.18 1.46 1.65 1.59 0.50 1.21 2 3.40 3.12 3.18 2.80 1.99 3.02 3 3.80 3.56 3.74 3.19 1.93 3.44 4 4.15 4.09 3.95 4.10 2.72 2.82 Quality 4.55 4.23 4.11 4.08 3.23 2.87 Quality - Junk 4.78 3.82 3.37 3.19 2.78 Annual correlation with mean Sharpe SMB RMRF HML UMD QMJ SMBQ Kent 5.0% Daniel Columbia 0.39 0.85AFIMP 0.15 Size Matters 0.02 2017 AFA -0.18Meetings -0.31

January-Periodic Returns Measuring Quality January & Variability One of the intriguing findings here is that the variability of the Size Q premium is far smaller than the size premium. An ancillary finding is the finding that the Table 4: Seasonal Patterns and the Size Premium January-component of the Q premium is smaller and less variable. The table reports regression results for the size premium (SMB) on the factors RMRF, its lagged value, HML, and UMD and the composite quality factor from Asness, Frazzini, and Pedersen (2014), where the alphas are estimated for the months of January and non-january separately using dummy variables for those months. Also reported is the difference between January and other months, along with a t-statistic on that difference in the last column. Results are reported over four sample periods: the full quality sample period (July 1957 to December 2012), and the golden age (July 1957 to December 1979), embarrassment (January 1980 to December 1999), and resurrection (January 2000 to December 2012) periods for the size premium. SMB =. +. + RMRF + 1RMRF 1+ hhml + mumd + qqmj + t Non Jan Jan t t t t t t α Non-Jan. t (α) α Jan. t (α) β t (β) β-1 t (β-1) h t (h) m t (m) q t (q) R 2 Jan. diff t (diff) Quality sample -0.0004-0.32 0.0209 5.59 0.16 6.21 0.13 5.29-0.19-4.68 0.02 0.90 0.18 0.0213 5.46 0.0038 3.62 0.0157 4.74-0.03-1.28 0.10 4.77-0.26-7.10 0.07 3.08-0.71-14.37 0.38 0.0119 3.42 Golden age -0.0001-0.08 0.0354 6.34 0.25 6.95 0.14 4.02-0.10-1.41-0.03-0.67 0.34 0.0355 6.13 0.0033 2.42 0.0359 7.61 0.05 1.55 0.14 4.75-0.38-6.02-0.01-0.21 0.55 0.0326 6.67-0.94-11.27 Embarrassment -0.0016-0.89 0.0045 0.79 0.03 0.79 0.18 5.01-0.25-3.67-0.07-1.46 0.19 0.0061 1.04 0.0058 3.35-0.0013-0.27-0.14-3.42 0.15 4.87-0.42-6.81-0.06-1.51-0.86-9.12 0.40-0.0071-1.37 Resurrection 0.0041 1.50 0.0180 1.98 0.27 4.44 0.09 1.55-0.33-4.22 0.15 3.22 0.26 0.0139 1.45 0.0091 3.86 0.0069 0.90-0.18-2.40-0.03-0.58-0.18-2.68 0.17 4.33 0.49-0.0022-0.27-0.84-8.19

SMB returns by month Measuring Quality January & Variability 2.5 SMB Mean Monthly Returns, 1956:07-2012:12 2.0 1.5 Mean Monthly Return (%) 1.0 0.5 0.0 0.5 1.0 1.5 Jan Feb Mar Apr May Jun month Jul Aug Sep Oct Nov Dec

QMJ returns by month Measuring Quality January & Variability 1.5 QMJ Mean Monthly Returns, 1956:07-2012:12 1.0 Mean Monthly Return (%) 0.5 0.0 0.5 1.0 1.5 Jan Feb Mar Apr May Jun month Jul Aug Sep Oct Nov Dec

Vas ist das? Size Anomaly History Explanations T-Costs Liquidity Shocks The empirical finding that Size Q earns a premium begs the question of what is causing this premium. 1 It is either: A premium that is related to covariance with marginal utility of all investors A result of biased expectations on the part of some or all investors. The authors explore a number of different possible explanations: risk-based behavioral liquidity/average t-costs time-varying liquidity 1 See Roll (1983)

Table 8: Liquidity level: Size, Junk, and Trading Costs Reported are average statistics on liquidity Size Anomaly and trading History cost measures Explanations for the 25 portfolios sorted on size (market cap) and quality/junk from Table 3. We report Size the & average Qualitybid-ask T-Costs spread as a percentage of share price (Panel A) and the market impact cost per dollar traded estimated from Frazzini, Liquidity Israel, Shocks and Moskowitz (2015) assuming a constant fund net asset value (NAV) of $1 billion plus one half of the effective bid-ask spread, all expressed in basis points (Panel B). The trading cost data cover the period January 2000 to December 2012. Is it average tcosts? Panel A: % Bid/Ask Spread Small 2 3 4 Big Junk 3.1% 0.9% 0.3% 0.2% 0.1% 2 3.4% 1.0% 0.3% 0.2% 0.1% 3 3.8% 1.1% 0.3% 0.1% 0.1% 4 3.4% 1.2% 0.3% 0.1% 0.1% Quality 2.5% 1.2% 0.3% 0.1% 0.1% Panel B: Market Impact Cost per dollar traded (bps) Small 2 3 4 Big Junk 33.98 20.46 15.50 12.47 6.61 2 35.76 21.10 15.51 12.09 5.70 3 38.15 21.74 15.49 12.08 4.88 4 36.43 22.34 15.56 12.02 4.50 Quality 33.04 22.14 15.58 11.89 4.42 Particularly given the strong persistence in size and quality, the t-costs associated with buying small quality/selling large junk appears small

Liquidity shocks? Size Anomaly History Explanations T-Costs Liquidity Shocks Table 9: Can Liquidity Risk Explain Size Controlling for Quality? This table reports regression results for the size premium, SMB, on the factors RMRF, HML, UMD, the quality factor QMJ, and two proxies for liquidity risk. Specifically, IML is the return of a portfolio that is long illiquid stocks and shorts liquid stocks, where liquidity is assessed by on the Amihud measure (Amihud, 2014). Likewise, LIQ is the decile spread in portfolios sorted on bid-ask spreads. The sample is 1956 to 2012. alpha RMRF HML UMD QMJ IML LIQ 0.20% 0.17-0.15 0.00 (1.70) (6.49) (-3.64) (-0.10) -0.19% 0.26-0.35 0.07 0.79 (-2.70) (16.01) (-13.07) (3.97) (33.47) 0.65% -0.09-0.24 0.06-0.84 (6.64) (-3.58) (-6.69) (2.45) (-18.04) 0.16% 0.07-0.38 0.10-0.56 0.68 (2.72) (4.44) (-17.65) (7.14) (-19.55) (34.94) 0.12% 0.06-0.34 0.09-0.51 0.70 0.10 (2.03) (3.54) (-15.53) (6.82) (-17.59) (36.56) (6.53) The authors argue that what explains the premium is likely time-varying t-costs.. However, the same magnitudes argument, applied here, would I suspect rule this out as an explanation. Also: Liquidity is endogenous. In an Acharya and Pedersen (2005) like framework, there has to be a reason why the set of investors who are exposed to the shocks to the illiquid securities choose to hold the small stocks.

References I Size Anomaly History Explanations T-Costs Liquidity Shocks Acharya, Viral V., and Lasse H. Pedersen, 2005, Asset Pricing with Liquidity Risk, Journal of Financial Economics 77, 375 410. Asness, Clifford S, Andrea Frazzini, and Lasse H Pedersen, 2014, Quality minus junk, AQR Capital Management working paper. Banz, Rolf W., 1981, The relationship between return and market value of common stocks, Journal of Financial Economics 9, 3 18. Black, Fischer, and Myron Scholes, 1974, The effects of dividend yield and dividend policy on common stock prices and returns, Journal of financial economics 1, 1 22. Keim, Donald B., 1983, Size-related anomalies and stock return seasonality: Further evidence, Journal of Financial Economics 12, 13 32. Roll, Richard W., 1983, Vas ist das?, Journal of Portfolio Management 9, 18 28.