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Price Impact Costs and the Limit of Arbitrage

Price Impact Costs and the Limit of Arbitrage. Zhiwu Chen Werner Stanzl Masahiro Watanabe. Arbitrageur. Price Anomalies. Market Anomalies. Size effect (Banz, 1981; Fama & French, 1993) Smaller size, larger returns  Long small-size & short big-size stocks

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Price Impact Costs and the Limit of Arbitrage

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  1. Price Impact Costs and the Limit of Arbitrage Zhiwu Chen Werner Stanzl Masahiro Watanabe

  2. Arbitrageur Price Anomalies

  3. Market Anomalies • Size effect (Banz, 1981; Fama & French, 1993) Smaller size, larger returns  Long small-size & short big-size stocks • B/M (value) effect (Basu, 1983; FF 1993 Lakonishok et al., 1994; LaPorta et al., 1997) Higher B/M, greater returns  Long high-B/M & short low-B/M stocks • Momentum (Levy, 1967; Jegadeesh & Titman, 1993 & 2001) Return continuation  Long past winners & short past losers

  4. Empirical Price Impact Literature • Linear Price Impact Breen, Hodrick & Korajczyk (2001) Sadka (2002) • Nonlinear (Concave) Price Impact Hasbrouck (1991) Hausman, Lo & MacKinlay (1992) Keim and Madhavan (1996) Knez and Ready (1996)

  5. Data • TAQ Price impact estimation 1/1993-6/1993: Oldest available • CRSP Return & portfolio formation 7/1963-12/2001: Covers Fama & French (1993) and Jegadeesh & Titman (1993) • Compustat Accounting information 4th Quarter, 1962 - 4th Qtr, 2001 • TASS Estimation of actual hedge fund size Covers 1330 hedge funds as of 5/2000

  6. Estimation of Price-Impact Function • Price Impact where Qt = Quote midpoint at transaction time t Vt = Dollar trading volume at t • Nonlinearity b/w log ( = 0) & linear ( = 1) functions inclusive • The only method that can be applied to almost all stocks without overfitting to outliers • Nonlinear least squares, purchases and sales separately • Matching & trade direction: Lee & Ready (1991) Method • Discard the top one-percentile trades

  7. Example: FHT Figure 1 • Overfitting problem except for the Box-Cox model

  8. Figure 2 Estimated Price Impacts

  9. Estimates for Individual Stocks Table 2

  10. Figure 3 Box-Cox vs. Linear PI Functions

  11. Table 3 Linear vs. Nonlinear PI Functions

  12. Portfolio PI Functions by Size Table 4 • For both buys and sells, • Slope coefficient b decreases with size • Concavity coefficient  has a U-shape

  13. Price Impacts by Size Decile Figure 4 • Buy trades have positive price impacts, sells negative • Absolute price impact increases with the size of trade • Price impact monotonically decreases with firm size

  14. Implementation of Strategies • Set up a long-short portfolio based on each strategy • Measure excess return after cost, where volume to compute PIs converted to year 1993 dollars • Since price impact increases in fund size, there is a maximal fund size at which excess return after cost = 0 • The maximal fund size reported in year 2001 dollars

  15. Investment Strategy Criteria • Portfolios are formed annually, semiannually, or quarterly • Value of long position = Value of short position • Rebalance when stocks are either added to or dropped from a portfolio; also when weights change • Commisions: 15 bp for purchases and sales 25 bp for short-selling • Short-sale rebate: 80% of Fed Fund Rate • Maximum $ volume / trade: 1% of market cap Maximum holding: 5% of market cap

  16. Portfolio Accounting • Initial fund size: 0 • At the beginning of period t1, invest bt= t-1 – PILt– PISt– TCLt– TCSt Volume to compute PIs converted to year 1993 dollars • At the end of period t, t = (1 + rl,t– rs,t+ 0.8 rFF,t) bt • Excess return after cost Rt = t / t-1 – 1 – rFF,t • Break-even fund size • Below, 0 is reported in year 2001 dollars

  17. Size Strategy Table 5 • Huge, but is this really attainable?

  18. Trading and Holding Restrictions Figure 5 • Realistically implemented size strategies will not accommodate more than several hundred million dollars

  19. Higher Rebalancing Frequencies Figure 6 • The potential benefit of “fine tuning” does not cover higher price impact costs

  20. Book-to-Market Strategy Table 7

  21. Momentum Strategies (in $ millions) Table 9: Maximum fund sizes, non-overlapping strategies • Momentum strategies could accommodate billions of dollars if no trading restrictions are imposed

  22. At a glance… Table 6

  23. Combined/No-small-stock Strategies Size-B/M Combined Strategy (Table 10) • Smaller break-even fund sizes than the size-only strategy because of higher turnover in the long position • Because of this and the smaller # stocks in both the long and short positions, the 1% trade-size and 5% position-size restrictions will make the fund sizes even smaller than those for size-only strategies in Figure 5 No-small-stock B/M Strategy (Table 11) • Restricts the available stocks to only those in the biggest 5 deciles • Mediocre performance, due to much lower returns before cost than with all stocks

  24. No-small-stock Momentum Strategy Table 12, VW 12/12 non-overlapping strategy • Still works. • Both the EW & VW strategies accommodate b/w $1 and 3 billions with the 1% trade-size restriction.

  25. Actual Hedge Fund Size Table 13

  26. Conclusions • Price impact reduces returns substantially • For size and B/M strategies, only about one hundred million dollars can be accommodated under realistic trading restrictions • This is marginal compared to the actual hedge fund size • However, some momentum strategies may be implemented profitably with about one billion dollars • Market is minimally efficient to allow for size & B/M anomaly; persistence of momentum is still a challenge

  27. Future Research • “Working” the order • VWAP • Time variation in liquidity suggests change in price impacts • Change in other costs (bid-ask spread, short sale carry cost, transactions fees)

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