What a trade really costs · Ankur Trapasiya

Every backtest in this blog so far has assumed that a trade happens at the closing price for nothing. Real trades do not. This post is the list of what they cost, worked with numbers, and then a test of two trading rules on SPY to show which kind of rule the costs destroy.

the price you actually geta costa loss

The order book: where the price comes from

A stock does not have one price. It has a queue of buyers, each naming the most they will pay (bids), and a queue of sellers, each naming the least they will accept (asks). The best bid and the best ask are the two numbers you see quoted; the gap between them is the spread; the point halfway is the mid.

The toy book in the first panel has a best bid of 99.95 and a best ask of 100.05: a spread of $0.10, a mid of 100.00. Two kinds of order meet it:

Item	Market order	Limit order
You say	“buy 500 now”	“buy 500 at 100.00 or better”
Guarantees	execution	the price, or better
Risk	the price: you take whatever is in the book	it may never fill
A buyer trades at	the ask	its own limit, when a seller comes down to it

A buyer who wants it now pays the ask. A seller who wants it now gets the bid. The spread is what the people on the other side, the market makers, are paid for being there. Buy and immediately sell 100 shares at the quotes and you have lost the spread: $0.10 a share, 0.10% of the price. That is the price of immediacy.

Spreads are compared as a share of the price, not in dollars:

Stock	Price	Spread	Relative spread
A	$20	$0.04	0.20%
B	$200	$0.20	$\key{0.10\%}$ : the “wider” spread is the cheaper one

Walking the book: big orders pay more

The best ask has only 300 shares behind it in the toy book. Buy more than that and the order walks up to the next price level, and the next. The average price paid rises with the size of the order:

Market buy	Fills	Average price	Above the best ask
300 shares	all at 100.05	100.050	0
800	300 at 100.05, 500 at 100.10	100.081	0.03%
1,800	plus 1,000 at 100.20	100.147	0.10%
3,800	plus 2,000 at 100.35	100.254	0.20%
7,800	plus 4,000 at 100.60	$\key{100.431}$	$\risk{0.38\%}$

That rise is market impact: your own order moving the price against you. It is why a large order is split into pieces over the day (a schedule such as a fixed share of each hour’s volume), and why a strategy has a capacity: past some size, the impact eats the edge. A working rule of thumb is to keep an order under about 1% of the stock’s average daily volume. An order for a million shares in a stock that trades two million a day is half the day’s volume, and the book will know.

Two more words for the same family. Slippage is the gap between the price you decided on and the price you got; decide at 40.00, fill at 40.12, 10,000 shares, and the slippage is $1,200. Implementation shortfall is the paper profit minus the real profit, slippage and commissions included.

Short selling pays to borrow

To sell a stock you do not own, you borrow the shares, sell them, and buy them back later to return them. Profit is the fall in price, minus two things most people forget: the lender charges a borrow fee, and any dividend paid while you are short is owed to the lender.

Case	Working	Result
Short 1,000 at 50, cover at 42	8 × 1,000	$8,000 gross
Gain $1,000, dividend owed $200, borrow fee $150	1,000 − 350	$650 net

The maximum gain is the price falling to zero. The maximum loss has no limit, and the lender can recall the shares at the worst moment, which is what a short squeeze is.

A cost model a simulator can apply

A simulator cannot see the order book, so it charges a model instead. The common one has two parts: a fixed commission per order, and an impact that moves the fill price against you by a fraction of the trade. With a $10 commission and 0.5% impact:

Order	Price you get	Cash
Buy 1,000 at 100	100 × 1.005 = $\key{100.50}$	−100,500 − 10 = −$100,510
Sell 1,000 at 100	100 × 0.995 = $\key{99.50}$	+99,500 − 10 = +$99,490
Round trip, price unchanged		$\bad{-\usd 1{,}020}$ , about 1%

The percentage is what matters. A rule that trades every day pays that round trip about 250 times a year. A rule that trades once a quarter pays it four times.

Two rules on SPY, with and without costs

Two simple rules, five years of SPY, both holding either SPY or cash, both charged the same cost per position change:

20/100 crossover: hold SPY while the 20-day average price is above the 100-day average. It changed position 13 times in five years.
Yesterday-up rule: hold SPY the day after an up day, cash the day after a down day. It changed position 633 times.

Cost per position change	20/100 crossover	Yesterday-up rule
none	+42.5%	+14.5%
0.1%	+40.7%	$\bad{-39.2\%}$
0.5%	+33.6%	$\bad{-95.2\%}$
1.0%	+25.1%	−99.8%

Buy and hold made +106.2% over the same five years, so neither rule is good. The point is the difference between them. The slow rule gives up nine points to a half-percent cost; the busy rule, which had a small positive return on paper, is wiped out by a tenth of a percent. Costs decide the ranking of strategies, not just their level. The third panel of the chart draws both, with and without the half-percent cost.

The arithmetic behind it is turnover times cost:

Daily turnover	Cost per dollar traded	Cost a day	Cost a year
40% of the book	0.10%	0.040%	$\risk{10.1\%}$
10%	0.10%	0.010%	2.5%
40%	0.05%	0.020%	5.0%

A strategy that turns over 40% of its book every day at a tenth of a percent needs a 10%-a-year edge just to pay for itself. Decide on net returns, never on the signal alone: an expected edge of 0.01% a trade against a cost of 0.02% is a rule not to trade.

Traps

Trap	Truth
A buyer trades at the bid	At the ask
A smaller dollar spread is more liquid	Compare the relative spread
A limit order guarantees a fill	It guarantees the price, not the fill
The whole order fills at the best ask	Only the shares shown there
Zero commission means zero cost	Spread and impact remain
A short seller keeps the dividend	Pays it to the lender
Faster execution is always cheaper	It trades timing risk for impact

The code

import numpy as np
import pandas as pd

def walk(asks, qty):                          # asks: [(price, shares), ...] best first
    left, cost = qty, 0.0
    for price, size in asks:
        take = min(size, left); cost += take * price; left -= take
        if left == 0:
            return cost / qty                 # average fill price
    return None                               # the book was not deep enough

def fill(price, qty, side, commission=10.0, impact=0.005):
    sign = 1 if side == "buy" else -1
    px = price * (1 + sign * impact)          # impact moves the price against you
    return -sign * qty * px - commission      # cash change

prices = pd.read_csv("prices.csv", index_col="date", parse_dates=True)["SPY"]
r = prices.pct_change().dropna()
pos = (prices.rolling(20).mean() > prices.rolling(100).mean()).astype(float).shift(1).reindex(r.index).fillna(0)
trades = pos.diff().abs().fillna(0)
net = pos * r - trades * 0.005                # 0.5% per position change
total = (1 + net).prod() - 1                  # +33.6%

Summary

Idea	Formula or rule	Remember it as
Spread, mid	ask − bid; (ask + bid)/2	a buyer pays the ask
Relative spread	spread ÷ mid	compare in percent
Walking the book	average of the prices taken	big orders pay more
Impact model	price × (1 ± impact)	plus a commission per order
Short profit	fall in price − dividend − borrow fee	the lender is paid
Cost a year	turnover × cost × 252	busy rules pay the most

References

U.S. Securities and Exchange Commission, Investor.gov: Types of orders, the plain definitions of market and limit orders
U.S. Securities and Exchange Commission, Investor Bulletin: An introduction to short sales
Philip J. Romero and Tucker Balch, What Hedge Funds Really Do: An Introduction to Portfolio Management (Business Expert Press, 2014), chapter 4: the order book, market makers and walking the book
Ernest P. Chan, Quantitative Trading: How to Build Your Own Algorithmic Trading Business (2nd ed., Wiley, 2021), chapters 2 and 5: transaction costs as half the spread plus commission, and keeping orders under 1% of daily volume