In order to make any claims with respect to a failure of the efficient market hypothesis, empirical studies need to prove, at least, that anomalies present an economically profitable trading opportunity. That is, there must be significant expected (ex ante) profits after taking into account trading costs (and adjustment for risk). Of course, the role of trading costs is not new, but at least as old as the market anomaly literature. Nevertheless, much of the literature only pays lip service to trading costs, or ignores it entirely, or provides misleading estimates of its size by focusing on only a small component or focusing on low estimates for the most frequently traded and largest stocks.
How much does it cost to trade common stock and implement trading strategies? Representative estimates of trading costs are difficult to obtain, because the costs are frequently not directly observable in existing historical databases and costs tend to vary over time, across different types of stock, across different exchange trading systems, and of course across countries. Below I provide some of the estimates, with a focus on the United States.
Trading costs are made up of several components: bid-ask spread (buy vs. sell prices), price impact of trading, broker commissions and other fees, taxes, short-sale costs, carry-costs (borrowing money to invest). Note that most trading cost studies assume that trading costs refer to round-trip or turnaround (buy and sell) transactions. The actual net-of-cost future return formula would be 100% * [(1-c)/Pt * (Pt+1)(1-c) -1] = 100% * [(1+rt+1)(1-c)2 -1] with c the estimated one-way fraction trading cost. The use of rt+1 - 2*c is an approximation. However, to implement a trading strategy with an assumed zero-investment portfolio an investor may actually have to execute 4 buy and sell transactions (sell reference portfolio, buy anomaly portfolio, sell anomaly portfolio, buy back reference portfolio). Otherwise, the trading strategy return would have to take into account the interest rate costs of borrowing money to invest in the anomaly, plus a premium for the equity risk.
Note that because many, if not all, stock market anomalies appear to be related to small, low price and illiquid stocks, the higher trading cost estimates are generally the most relevant ones. A volume-weighted estimate such as by Berkowitz et al (1988) is insufficient because it overemphasizes the lower trading costs of the liquid and large stocks.
Cooper, Gutierrez and Marcum (2005 Appendix A) apply a particularly promising approach to estimating trading costs. Their estimates combine available evidence on both the cross-section variation and the time-series variation of trading costs.
Step 1. Applying the Keim and Madhavan (1997) regression estimates of determinants of stock specific trading costs (i.e. share price, exchange, market value, type of trader and trading style). The Keim and Madhavan estimates are for the years 1991-1993.
Step 2. Adjusting for the substantial decline in trading costs over time, using a scaling factor based on the yearly trading cost estimates (1980-1992) provided by Stoll (1995).
Estimates of bid-ask spreads and commission rates
Stoll and Whaley (1983, Table 5) provided quoted bid-ask spreads and regulated minimum commission costs for NYSE stocks for the years 1960 through 1979. Estimates are given below for transactions of average size in 10 market capitalization stock portfolios. The 1960-1979 average values are:
Portfolio 1 smallest, portfolio 10 largest, EW equal weighted market index, VW value weighted market index. Effective May 1, 1975 all minimum commission rules were abolished and commissions became subject to negotiation between NYSE member firms and customers. Over individual years bid-ask spreads for P1 varied from 1.69% to 5.08% and commission rates for P1 varied from 1.26% to 3.23%.
Estimated average trading costs for a single buy or sell transaction of average size are 1/2*2.93+1.92 = 3.38% in P1 and 1.36 in P10. Most trading cost studies assume that trading costs refer to round-trip or turnaround (buy and sell) transactions. Transaction costs would add up to 2*3.38= 6.76% and 2*1.36= 2.72%. For an assumed zero-investment portfolio with 4 buy and sell transactions (sell reference portfolio, buy anomaly portfolio, sell anomaly portfolio, buy back reference portfolio) an estimate of accumulated trading costs could be 2*3.38 (buy sell portfolio 1) + 2*1.40 (buy sell value-weighted portfolio) for a total of 9.56%.
Schultz (1983) estimated the bid-ask spread and commission rate for NYSE and AMEX stocks for the the years 1962 through 1979. His period average turnaround trading cost estimate for the small firm portfolio is 11.4% (range of 4.9% to 22.4% over time), due to the smaller AMEX stocks in the portfolio.
Bhardwaj and Brooks (1992 Table II) provide estimates of quoted bid-ask spreads (1982-1986, NYSE-AMEX stocks) and commission costs from a prominent discount broker. Results are provided for 5 different price range groups.
Estimated round-trip trading costs range from 20.4% for small price stocks to 2.3% for large price stocks.
Bessembinder (2003 Table 2) provides quoted bid-ask spreads for a sample of capitalization-matched 300 NYSE and 300 NASDAQ stocks during July-December 1998. The focus here is on the difference between exchange trading systems (ignoring the many smaller and low price stocks on NASDAQ). The results are:
Eleswarapu (1997) provides estimates of bid-ask spreads for NASDAQ stocks over the period 1973-1990. The results for 7 spread-ranked subgroups are
Clearly, the bid-ask spread component of trading costs can rise to very high levels for the smallest and least liquid stocks. A bid-ask spread of 30% or higher would definitely eliminate all hope for after-trading-cost profits of any of the popular anomaly trading strategies.
Jones (2002) provides an annual time-series of estimated trading costs (bid-ask spreads and commission costs) for the stocks in the Dow Jones Index. One-way trading costs for these largest of stocks were approx. 1% until 1975 and have consistently declined over the years since, until approx. 0.2% in 2000.
There are several other estimates of trading costs in the literature. For example, one could argue that many stock market trades are actually executed against transaction prices within the quoted bid-ask spreads: these effective bid-ask spreads (taking into account "price improvement") are smaller than quoted bid-ask spreads.
Knez and Ready (1996) estimate effective spreads for NYSE stocks. Allowing for different order sizes and firm sizes the results are:
Again we find that trading costs are relatively low and constant for larger stocks. For smaller stocks and larger order sizes, trading costs can become substantial.
Taxes
Profits from financial market investments are subject to government taxes. The important question with respect to profitable trading strategies is whether some strategies are subject to different (higher) tax rates.
In the United States, frequent trading strategies face the difference between (higher) ordinary income tax rates and (lower) capital gains tax rates applied to investments with long(er)-term holding periods (ranging from 6 months to 18 months). For most of the historical period the maximum capital gains tax rate was less than 50% of the ordinary tax rate (for an historical review of US income and capital gains tax rates, see Siegel 1998, Chapter 8). In order for a frequent trading strategy to generate economic profits, the after-tax return on the normal buy-hold portfolio (1-t) r would have to be less than the after-tax return on the frequent trading portfolio (1-t') r' (with t<t'). If we assume tax rate t = 0.5 t', long-term capital gains tax rate t = 30% and ordinary buy-hold return r = 7% we find that the before-tax return r' on the anomaly portfolio would have to be at least 12.25%, or at least 5.25% higher than the normal buy-hold portfolio.
Some countries have special securities transactions taxes. For example, the United Kingdom imposes a stamp duty tax of 0.5% on the transaction value of stock market transactions. Unavoidable round-trip (buy and sell) transaction costs of any frequent trading strategy therefore are 2*0.5= 1%. Using the 4-time transactions view, stamp duty tax costs would of course be 2%. Since 1997, registered financial intermediaries trading at any UK-recognized exchange have been exempt from stamp duty.
Market impact of trading
Exploiting a market anomaly would imply that speculators and arbitrageurs add new transactions (buy or sell orders) to the market system. In dealer markets only limited size transactions can be effectuated against the dealers' pre-determined bid and ask quotes. Larger orders will always be subject to renegotiation of the price and of course in practice dealers will adjust prices in an adverse direction for the desired trade (see the micro marketstructure literature on the topic of bid-ask prices). In auction markets the market impact of new orders is even more direct. A large buy order will mean that the transaction will be effectuated by walking along the supply curve in the limit order book, hitting successively more of the available limit orders with successively higher limit order prices. The larger the desired trade, the larger will be the adverse price impact, depending on market liquidity. On the other hand, the smaller the desired trade, the less will be the economic relevance of the trading profit. How much adverse effect any given transaction from a trading strategy will have on the actual transaction price is uncertain. Various estimates exist, but will depend on the empirical methodology.