Another Look at Trading Costs and Short-Term Reversal Profits Wilma de Groot 1, Joop Huij 1,2 and Weili Zhou 1 1) Robeco Quantitative Strategies 2) Rotterdam School of Management http://ssrn.com/abstract=1605049 Quantitative Strategies 1
Motivation of our study Jegadeesh (1990) and Lehman (1990) document that shortterm reversal profits yield more than 20 percent per annum However, the high return is accompanied with the high turnover of the strategy Several studies report that these abnormal returns diminish once transaction costs are taken into account Avramov, Chordia and Goyal (2007) found negative net returns for 1W reversal in the broad U.S. universe over the period 1962-2002 using Keim and Madhaven (1997) model for trading costs Quantitative Strategies 2
Motivation of our study However, high costs may be attributed to: 1.Excessively trading in small cap stocks: Stocks with the highest volatility have the greatest probability to end up in the extreme quantiles, typically expensive micro-caps This effect is especially pronounced in the early 1960s and 70s 2.Naïve trading strategies: Immediately replacing stocks that are no longer losers by newly bottom-ranked stocks may be costly Quantitative Strategies 3
Our research question: What would be the profitability of short-term reversal if we 1.Focus on investable and even mega cap stocks only 2.Deploy a slightly more advanced rebalancing rule However, to answer these questions, we first have to answer the question: what are reasonable (and conservative) trading cost estimates? Quantitative Strategies 4
What do we do in this paper? We use trading cost estimates from Nomura and those from the Keim and Madhaven model We evaluate reversal profits for the 1500, 500 and 100 largest US stocks over the period Jan. 1990 to Dec. 2009 We suggest a slightly more sophisticated portfolio construction approach to reduce unnecessary turnover We investigate the relation between reversal profits and market capitalization of the stock universe We perform a battery of robustness checks Quantitative Strategies 5
What do we find? Trading cost estimates resulting from Keim and Madhaven model should be interpreted with caution in some cases Functional form of relation between market cap and costs causes estimates for the largest and smallest stocks to be biased downwards Reversal profits diminish for the 1500 largest US stocks once trading costs are incorporated The strategy becomes profitable once we switch to the 500 or the 100 largest U.S. stocks A smarter rebalancing rule reduces turnover and costs by 50% Gross returns are similar; net returns up to 40~70 basis points per week Also, effect can be exploited by sizable strategy of USD 150 million; large returns over post-decimalization era; robust to industry effects Quantitative Strategies 6
Data Excluding small/micro caps: we focus on the 1500 largest stocks of the Citigroup US BMI over jan. 1990 to Dec. 2009 (source: Factset Prices) 5 percent smallest (largest) stocks have market cap of USD 400 million (17.1 billion) For comparison, 25 th percentile NYSE stocks was USD 390 million Median trading volumes increased from USD 0.8 mln per day to 18.7 mln, while median mcap from USD 0.3bln to 1.4 bln Ahimud illiquidity measure is below 0.39 in our sample; (in contrast to 10.8 documented by Avramov, Chordia and Goyal as sample of ACG goes back to 1960s and includes micro caps) Quantitative Strategies 7
Trading cost estimates by Keim & Madhaven Cˆ Buy i Cˆ Sell i 0.767 0.336D 0.505 0.058D NASDAQ NASDAQ 0.092Trsize 0.214Trsize i i 1 0.084log mcap 13.807 Pi 1 0.059log mcap 6.537 Pi Keim and Madhaven (1997) model coefficients are based on the period January 1991 through March 1993 using 62,333 trades Estimates include price impact plus commissions Cost can be adjusted for trading style (i.e., technical) Markets have undergone important changes over time, (e.g., quotation in decimals, increases in trading volumes, more competition among brokers, technological improvements) Quantitative Strategies 8
Trading Cost estimates by Nomura Nomura provided us with cost estimates for decile portfolios of stocks sorted on their trading volumes in each quarter during the period January 1990 to December 2009 Model periodically calibrated over 1995 to 2009 using 500,000+ trades per time Bid-ask spread, permanent impact and temporary impact No fixed costs (i.e., taxes and commissions) 1990 to 1994 backfilled with 1500 largest stocks of Russel Index Trades are closed within one day (VWAP) Trade size is one million USD per 2009 (deflated by 10% per year) Quantitative Strategies 9
TC estimates: Keim & Madhaven vs Nomura KM Nomura Calibration once-off periodically recalibrated Sample period 1991-1993 1995-2009 Estimates Input explicit + implicit costs Volume Trade size Exchange implicit costs Mcap Trade size Exchange Price Fit Logarithmic Quadratic Quantitative Strategies 10
Transaction Costs Transaction costs Nomura vs KM: quadratic vs logarithmic fit Nomura KM Volume/Mcap Volume Due to the quadratic fit, Nomura estimates: Cannot become negative Lower for the median group Higher for the extremes (most/least liquid groups) Quantitative Strategies 11
Nomura vs KM cost estimates 1500 Biggest Nomura KM 500 Biggest Nomura KM D1 64 30 D5 15 24 D10 4-20 D1 21 4 D5 5-6 D10 2-27 For the 1500 largest U.S. stocks, Estimates of Nomura are lower for the median group The most/least liquid groups have higher costs For the 500 largest U.S. stocks, KM estimates are negative for the median group The logarithmic fit seems to be more reasonable KM estimates should be interpreted with caution in some cases Quantitative Strategies 12
Reversal profits for the 1500 largest stocks (Deciles) long (bps) short (bps) long-short (bps) t-stat Turnover (%) Gross return 44.3-48.1 92.9 10.1 780 Net return using KM estimates -29.9 23.0-52.8-5.7 " Net return using Nomura estimates -31.4 24.9-56.2-6.1 " Sorts on 1W returns; daily rebalancing; 1day lag for implementation; Gross returns up to 93 basis points per week Turnover of 780% per week; returns diminish after costs by both means Consistent with ACG Quantitative Strategies 13
Reversal profits for the 500 largest stocks (Quintiles) long (bps) short (bps) long-short (bps) t-stat Turnover (%) Gross return 35.3-36.4 71.9 9.1 688 Net return using KM estimates 32.5-33.6 66.4 8.4 " Net return using Nomura estimates 11.8-13.7 25.5 3.2 " Least liquid stocks appear disproportionally expensive to trade Excluding small caps slightly decreases gross returns from 93 to 72 bps Costs are much lower; net returns of more than 25 bps Careful with using KM cost estimates for large caps Still large portion of profits consumed by trading costs and high TO Quantitative Strategies 14
Smart portfolio construction Replacing stocks is only profitable if return difference between old and new stocks is larger than costs Top (second) decile earns 9 (3) bps p.d. Average holding period is 3 days Trading costs should be lower than 18 bps [(9-3) * 3] to be profitable Naive solution would be to increase the holding period However, one runs risk to hold stocks that have already reverted Stocks that have reverted get larger weights Smarter solution should be able to exclude a stock from the portfolio right after the reversal has taken place. Thus, we choose to examine the stock rankings everyday and replace the long/short positions with better choices only when the old rankings are below/above the median (50%). Quantitative Strategies 15
Reversal profits using smart portfolio construction long (bps) short (bps) Turnover halves from 688% to 326%; costs halve from 45 to 21 bps Gross returns are marginally lower; Net returns up to 44 bps per week which are highly significant Effective holding period becomes 5 days long-short (bps) Turnover (%) t-stat Panel A. 1,500 largest stocks Gross return 36.5-44.6 81.5 9.7 321 Net return using KM estimates 6.5-14.4 21.0 2.5 " Net return using Nomura estimates 7.1-14.5 21.7 2.6 " Panel B. 500 largest stocks Gross return 30.7-34.0 65.0 8.7 326 Net return using KM estimates 29.4-32.7 62.3 8.4 " Net return using Nomura estimates 20.4-23.6 44.1 5.9 " Quantitative Strategies 16
Weekly rebalancing short (bps) long-short (bps) long (bps) t-stat Turnover (%) Panel A. Standard reversal strategy for 1,500 largest stocks with a 5-day rebalancing frequency Gross return 23.3-31.7 55.1 7.6 337 Net return using KM estimates -7.3-0.7-6.7-0.9 " Net return using Nomura estimates -7.3-0.3-6.9-1.0 " Panel B. Standard reversal strategy for 500 largest stocks with a 5-day rebalancing frequency Gross return 20.2-23.7 44.0 7.1 310 Net return using KM estimates 18.8-22.5 41.4 6.7 " Net return using Nomura estimates 9.9-13.5 23.4 3.8 " Turnover also halves; but gross returns are substantially lower Reverted stocks have negative expected returns and get larger weight Gross return smart strategy is 82 (65) bps for Big 1500 (500) stocks Quantitative Strategies 17
Reversal profits for the 100 largest stocks (Quintiles) short long-short Turnover short long-short Turnover long (bps) (bps) (bps) t-stat (%) long (bps) (bps) (bps) t-stat (%) Panel A. Smart reversal strategy for 1,500 largest stocks over the period 2000 to 2009 Panel A. Standard reversal strategy for 100 largest stocks Gross return 9.6-31.0 40.7 2.7 321 Gross return 43.7-40.3 84.2 9.8 711 Net Net return return using using KM KM estimates estimates -16.5 42.8-39.4-3.5-13.0 82.5-0.9 9.6 " Net Net return return using using Nomura Nomura estimates estimates -12.3 32.0-28.9-7.0 61.1-5.3-0.4 7.1 " Panel Panel B. B. Smart Smart reversal reversal strategy strategy for for 500 100 largest largest stocks stocks over the period 2000 to 2009 Gross Gross return return 22.2 40.9-36.7-30.7 77.9 53.0 9.4 4.0 337 320 Net Net return return using using KM KM estimates estimates 20.3 40.5-36.3-28.7 77.1 49.2 9.3 3.7 " Net Net return using Nomura estimates 12.0 35.6-31.4-19.8 67.1 31.9 8.1 2.4 " Panel C. Smart reversal strategy for 100 largest stocks over the period 2000 to 2009 Gross return 40.0-38.3 78.6 5.5 329 Net return using KM estimates 39.3-37.5 77.1 5.4 " Net return using Nomura estimates 35.4-33.6 69.3 4.8 " Quantitative Strategies 18
Concluding Comments Cost estimates resulting from the Keim and Madhaven model should be interpreted with caution in some cases (not suitable for the recent period within big caps) Short-term reversal can be profitable after costs once we exclude the micro/small caps from the investment universe Applying a slightly more sophisticated rebalancing rule can effectively reduce the turnover and trading costs by 50% while keep the gross return on the same level We find returns of 40 (70) bps per week net of transaction costs within the 500 (100) largest U.S. stocks Quantitative Strategies 19