2010 Another Look at Trading Costs and Short-term Reversal Profits

8/10/2019 2010 Another Look at Trading Costs and Short-term Reversal Profits

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Quantitative Strategies 121 May 2010

Another Look at Trading Costs andShort-Term Reversal Profits

Wilma de Groot1, Joop Huij1,2 and Weili Zhou1

1) Robeco Quantitative Strategies2) Rotterdam School of Management

http://ssrn.com/abstract=1605049
http://ssrn.com/abstract=1605049http://ssrn.com/abstract=1605049


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Motivation of our study

Jegadeesh (1990) and Lehman (1990) document that short-term reversal profits yield more than 20 percent per annum

However, the high return is accompanied with the highturnover of the strategy

Several studies report that these abnormal returns diminishonce 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 1962-2002using Keim and Madhaven (1997) model for trading costs


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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 toend up in the extreme quantiles, typically expensive micro-caps

This effect is especially pronounced in the early 1960s and 70s

2.Nave trading strategies:

Immediately replacing stocks that are no longer losers by newlybottom-ranked stocks may be costly


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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 answerthe question: what are reasonable (and conservative) tradingcost estimates?


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What do we do in this paper?

We use trading cost estimates from Nomura and thosefrom the Keim and Madhaven model

We evaluate reversal profits for the 1500, 500 and 100largest US stocks over the period Jan. 1990 to Dec. 2009

We suggest a slightly more sophisticated portfolioconstruction approach to reduce unnecessary turnover

We investigate the relation between reversal profits andmarket capitalization of the stock universe

We perform a battery of robustness checks


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What do we find?

Trading cost estimates resulting from Keim and Madhaven model shouldbe interpreted with caution in some cases

Functional form of relation between market cap and costs causes estimates forthe largest and smallest stocks to be biased downwards

Reversal profits diminish for the 1500 largest US stocks once tradingcosts are incorporated

The strategy becomes profitable once we switch to the 500 or the 100largest 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; largereturns over post-decimalization era; robust to industry effects


7/19Quantitative Strategies 721 May 2010

Data

Excluding small/micro caps: we focus on the 1500 largest stocksof the Citigroup US BMI over jan. 1990 to Dec. 2009 (source:Factset Prices)

5 percent smallest (largest) stocks have market cap of USD 400million (17.1 billion)

For comparison, 25th 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 Goyalas sample of ACG goes back to 1960s and includes micro caps)



Trading cost estimates by Keim & Madhaven

Keim and Madhaven (1997) model coefficients are based on theperiod 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, morecompetition among brokers, technological improvements)

i

i

NASDAQi

Buy

PmcapTrsizeDC

1807.13log084.0092.0336.0767.0

i

i

NASDAQi

Sell

P

mcapTrsizeDC 1

537.6log059.0214.0058.0505.0



Trading Cost estimates by Nomura

Nomura provided us with cost estimates for decile portfolios ofstocks sorted on their trading volumes in each quarter during theperiod 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)



TC estimates: Keim & Madhaven vs Nomura

KM Nomura

Calibration once-off periodicallyrecalibrated

Sample period 1991-1993 1995-2009

Estimatesexplicit +

implicit costsimplicit costs

Input

Volume

Trade size

Exchange

McapTrade size

Exchange

Price

Fit Logarithmic Quadratic



Nomura vs KM: quadratic vs logarithmic fit

Due to the quadratic fit, Nomura estimates:

Cannot become negative Lower for the median group Higher for the extremes (most/least liquid groups)

Volume

Transactio

nc

osts

Nomura

KM

Volume/Mcap

Transaction

Costs



Nomura vs KM cost estimates

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

1500Biggest

Nomura KM

D1 64 30

D5 15 24D10 4 -20

500Biggest

Nomura KM

D1 21 4

D5 5 -6D10 2 -27



Reversal profits for the 1500 largest stocks

(Deciles)

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

Return

long (bps)

Return

short

(bps)

Return

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 "



Reversal profits for the 500 largest stocks

(Quintiles)

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

Return

long (bps)

Return

short

(bps)

Return

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 "



Smart portfolio construction

Replacing stocks is only profitable if return difference between oldand 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 theportfolio right after the reversal has taken place.

Thus, we choose to examine the stock rankings everyday andreplace the long/short positions with better choices only when theold rankings are below/above the median (50%).



Reversal profits using smart portfolio

construction

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 weekwhich are highly significant

Effective holding period becomes 5 days

Return

long (bps)

short

(bps)

long-short

(bps) t-stat

Turnover

(%)Panel A. 1,500 largest stocksGross return 36.5 -44.6 81.5 9.7 321



Panel B. 500 largest stocks

Gross return 30.7 -34.0 65.0 8.7 326





Weekly rebalancing

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

Return

long (bps)

Return

short

(bps)

Return

long-short

(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




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Concluding Comments

Cost estimates resulting from the Keim and Madhaven model shouldbe interpreted with caution in some cases (not suitable for the recentperiod within big caps)

Short-term reversal can be profitable after costs once we exclude themicro/small caps from the investment universe

Applying a slightly more sophisticated rebalancing rule can effectivelyreduce the turnover and trading costs by 50% while keep the grossreturn on the same level

We find returns of 40 (70) bps per week net of transaction costswithin the 500 (100) largest U.S. stocks

Documents

2010 Another Look at Trading Costs and Short-term Reversal Profits