Costs, settlement, leverage and margin.

What a trade costs

The cost of a trade is the difference between what the system would have earned in a frictionless world and what it actually earns. Part of it shows up on the broker statement; most of it does not.

The reference for all the implicit costs is the decision price: the midpoint at the moment the system decides to trade. The difference between that price and what ends up being paid, plus the explicit costs, is called implementation shortfall. Measuring it in basis points (hundredths of a percentage point) makes it possible to add costs of different nature and to compare assets with very different prices.

Effective spread and realized spread

The quoted spread (lesson 1.1.3) is what it costs to cross the book if the order fits in the first level. The effective spread measures what was actually paid on each trade, against the prevailing midpoint just before it:

where $P$ is the trade price, $M_t$ the prevailing midpoint and $D = +1$ if the aggressor buys and $-1$ if it sells. The factor 2 makes it comparable with the quoted spread, which is a round trip. The realized spread uses instead the midpoint a few seconds or minutes later, $M_{t+\Delta}$:

The realized spread is what whoever provided the liquidity keeps if they unwind their position at the midpoint of that moment. If the price moves in the aggressor's direction, the liquidity provider loses part of the spread, or all of it: that is adverse selection, and the difference between the two spreads is the price impact of the trade.

To calculate them, each trade has to be joined with the quote prevailing before it, with allow_exact_matches=False, as in lesson 1.1.1, and with the quote prevailing at $t+\Delta$:

import numpy as np
import pandas as pd

op = pd.read_parquet("nova_operaciones.parquet")
cot = pd.read_parquet("nova_cotizaciones.parquet")
cot["medio"] = (cot["bid"] + cot["ask"]) / 2
medios = cot[["ts", "medio"]]

reg = op[op["condicion"] == "regular"].copy()
reg = pd.merge_asof(reg, medios, on="ts", allow_exact_matches=False)
reg["D"] = np.where(reg["agresor"] == "compra", 1, -1)

def medio_en(ts):
    """Prevailing midpoint at each instant of `ts` (last change <= ts)."""
    m = pd.merge_asof(pd.DataFrame({"ts": ts}), medios, on="ts")
    return m["medio"].to_numpy()

reg["ef_pb"] = (2e4 * reg["D"] * (reg["precio"] - reg["medio"])
                / reg["medio"])
cols = ["ts", "precio", "agresor", "centro", "medio", "ef_pb"]
reg[cols].head(3).round({"ef_pb": 3})

                                ts  precio agresor     centro  medio  ef_pb
0 2025-06-02 13:30:00.301051+00:00   53.34   venta  PRINCIPAL  53.35  3.749
1 2025-06-02 13:30:00.301052+00:00   53.34   venta  PRINCIPAL  53.35  3.749
2 2025-06-02 13:30:00.407366+00:00   53.34   venta  PRINCIPAL  53.35  3.749

def media_pond(g, col):
    return np.average(g[col], weights=g["tamano"])

por_centro = reg.groupby("centro").apply(
    lambda g: pd.Series({"efectiva_pb": media_pond(g, "ef_pb"),
                         "operaciones": len(g)}))
por_centro.round(3)

                efectiva_pb  operaciones
centro
INTERNALIZADOR        1.054       3914.0
MTF_A                 2.039       9640.0
MTF_B                 2.078       7230.0
OSCURO                0.000       4380.0
PRINCIPAL             2.074      25774.0

The three lit venues charge on average between 2.04 and 2.08 basis points of effective spread, somewhat more than the typical one-tick quoted spread (1.9 basis points, lesson 1.1.3) because some orders sweep more than one level. The dark venue, which crosses at the midpoint, has a zero effective spread: neither buyer nor seller pays spread. The internalizer, which often improves on the book price (lesson 1.1.1), charges half as much as the visible books. For a client, that is the economic argument for both.

Now the realized spread, at several horizons, for the trades on the lit venues:

lit = reg[reg["centro"].isin(["PRINCIPAL", "MTF_A", "MTF_B"])].copy()
filas = {}
for h in ("1s", "10s", "1min", "5min"):
    m_desp = medio_en(lit["ts"] + pd.Timedelta(h))
    real = 2e4 * lit["D"] * (lit["precio"] - m_desp) / lit["medio"]
    ef = media_pond(lit, "ef_pb")
    rr = np.average(real, weights=lit["tamano"])
    filas[h] = {"efectiva": ef, "realizada": rr, "impacto": ef - rr}
pd.DataFrame(filas).T.round(2)

      efectiva  realizada  impacto
1s        2.07       1.68     0.38
10s       2.07       0.27     1.80
1min      2.07      -6.95     9.02
5min      2.07     -14.47    16.54

At one second, the liquidity provider keeps 1.68 of the 2.07 basis points of spread. At ten seconds, almost nothing. At one minute and at five, the realized spread is negative: the price has followed the aggressor so far that whoever gave it liquidity loses money if they hold the position. In the simulated NOVA session, the aggressive order flow is what moves the price, and that is paid for in the spread of whoever provides liquidity. In real data the shape is usually the same (the realized spread falls with the horizon), although the figures depend on the stock and the day.

The impact curve

The average effective spread is about small orders. For a large order, what matters is how much of the book it has to walk through. With the 2,340 L2 snapshots of the session, a market buy of each size can be simulated on each snapshot and its average cost measured against the prevailing midpoint:

l2 = pd.read_parquet("nova_libro_l2.parquet")
tamanos = [100, 500, 1_000, 2_000, 5_000,
           10_000, 20_000, 30_000, 50_000]

def coste_pb(foto, n):
    a = foto[foto["lado"] == "ask"].sort_values("precio")
    b = foto[foto["lado"] == "bid"]
    medio = (a["precio"].iloc[0] + b["precio"].max()) / 2
    if a["tamano"].sum() < n:
        return np.nan                     # the visible book is not deep enough
    resto, gasto = n, 0.0
    for p, q in zip(a["precio"], a["tamano"]):
        t = min(resto, q)
        gasto, resto = gasto + t * p, resto - t
        if resto == 0:
            break
    return 1e4 * (gasto / n - medio) / medio

costes = {n: [] for n in tamanos}
for _, foto in l2.groupby("ts"):
    for n in tamanos:
        costes[n].append(coste_pb(foto, n))
curva = pd.DataFrame({n: pd.Series(v) for n, v in costes.items()}).T
pd.DataFrame({"coste_medio_pb": curva.mean(axis=1),
              "mediana_pb": curva.median(axis=1),
              "sin_liquidez_pct": 100 * curva.isna().mean(axis=1)}
             ).round(2)

       coste_medio_pb  mediana_pb  sin_liquidez_pct
100              0.98        0.94              0.00
500              1.04        0.94              0.00
1000             1.10        0.94              0.00
2000             1.22        0.94              0.00
5000             1.55        0.95              0.00
10000            2.02        1.68              0.17
20000            2.82        2.40              1.20
30000            3.57        3.02              5.64
50000            5.33        4.81             48.46

Up to 2,000 shares, the cost barely exceeds half the spread: a little over one basis point. From 5,000 on, the order usually goes past the first level and the cost accelerates: 2.0 basis points with 10,000 shares, 3.6 with 30,000. With 50,000 the average is 5.3, and in almost half of the snapshots the visible book does not even have that many shares for sale across ten levels. That is why large orders are split into pieces and spread over time (the TWAP and VWAP algorithms of lesson 1.1.4) or sent to a dark venue (lesson 1.1.1).

Two caveats. The curve is optimistic: it assumes the book does not react while the order walks through it, and in reality liquidity providers pull orders as soon as they see a large one. And it is one-sided: if the position is unwound later, the cost is paid again.

One order, all its costs

The header figure is the cost waterfall of a specific order. At 15:00:00 New York time a system decides to buy 20,000 NOVA shares, with the midpoint at 52.745. The market order reaches the book ten seconds later. The system pays an assumed commission of 0.005 USD per share and finances half of the purchase on margin for five days at an assumed 6% annual rate (360-day basis). The broker figures are hypothetical; the book figures are those of the L2 snapshot.

def foto_en(ts):
    return l2[l2["ts"] == ts]

def precio_medio_compra(foto, n):
    a = foto[foto["lado"] == "ask"].sort_values("precio")
    resto, gasto = n, 0.0
    for p, q in zip(a["precio"], a["tamano"]):
        t = min(resto, q)
        gasto, resto = gasto + t * p, resto - t
        if resto == 0:
            break
    return gasto / n

def mejores(foto):
    return (foto.loc[foto["lado"] == "bid", "precio"].max(),
            foto.loc[foto["lado"] == "ask", "precio"].min())

n = 20_000
decision = sum(mejores(foto_en("2025-06-02 19:00:00+00:00"))) / 2
f10 = foto_en("2025-06-02 19:00:10+00:00")
bid10, ask10 = mejores(f10)
medio10 = (bid10 + ask10) / 2
pagado = precio_medio_compra(f10, n)

pb = lambda x: 1e4 * x / decision
cascada = pd.Series({
    "retraso": pb(medio10 - decision),
    "media_horquilla": pb(ask10 - medio10),
    "impacto": pb(pagado - ask10),
    "comision": pb(0.005),
    "financiacion": 1e4 * 0.5 * 0.06 * 5 / 360,
})
print(f"decision {decision:.3f} · paid {pagado:.4f}")
print(f"notional {n * pagado:,.0f} USD")
cascada["total"] = cascada.sum()
cascada.round(2)

decision 52.745 · paid 52.7693
notional 1,055,386 USD
retraso            1.90
media_horquilla    0.95
impacto            1.76
comision           0.95
financiacion       4.17
total              9.72
dtype: float64

In ten seconds the midpoint rises by one cent, from 52.745 to 52.755: 1.90 basis points of delay paid before touching the book (in that snapshot the first level was heavily loaded on the bid side, and lesson 1.1.3 showed that this anticipates the rise). Then half the spread, 0.95, and the impact of walking the book beyond the best ask, 1.76. The assumed commission adds 0.95. Execution costs add up to 5.56 basis points, about 590 USD on 1.06 million. And the financing of five days on margin adds 4.17 more basis points: the largest cost in the waterfall is the one that does not appear in the execution.

Settlement: T+1 in the US, T+2 in Europe

After the trade, the delivery of the securities against cash happens a few business days later: settlement (lesson 1.1.1). Until then, buyer and seller have a commitment, not the securities or the money.

flowchart LR
  T[T: trading] --> C[T: clearing]
  C -->|settlement| L1[T+1: US]
  C -->|settlement| L2[T+2: EU]

• The US settles stocks on T+1, the next business day, since May 28, 2024, the compliance date of the rules the SEC approved in February 202311Note 1 · SEC, press release 2023-29, “SEC Finalizes Rules to Reduce Risks in Clearance and Settlement”, February 15, 2023: “The compliance date for the final rules is May 28, 2024”..
• The European Union settles on T+2 the trades in transferable securities executed on trading venues. Regulation (EU) 2025/2075 of October 8, 2025, which amends the central securities depositories regulation (CSDR), moves them to T+1 from October 11, 202722Note 2 · AMF, “Transition to T+1 settlement of transactions” (updated on April 23, 2026). The text of the regulation on EUR-Lex could not be read automatically when this lesson was prepared..

Business days are counted with a calendar, not by adding calendar days:

import exchange_calendars as xcals

nyse = xcals.get_calendar("XNYS")
bme = xcals.get_calendar("XMAD")

for cal, n_dias, fechas in ((nyse, 1, ["2025-07-03", "2025-11-26",
                                       "2025-12-31"]),
                            (bme, 2, ["2025-04-16", "2025-12-23"])):
    for f in fechas:
        liq = cal.session_offset(f, n_dias)
        print(f"{cal.name}  trade {f} ({pd.Timestamp(f):%a})"
              f"  ->  T+{n_dias} {liq.date()} ({liq:%a})")

XNYS  trade 2025-07-03 (Thu)  ->  T+1 2025-07-07 (Mon)
XNYS  trade 2025-11-26 (Wed)  ->  T+1 2025-11-28 (Fri)
XNYS  trade 2025-12-31 (Wed)  ->  T+1 2026-01-02 (Fri)
XMAD  trade 2025-04-16 (Wed)  ->  T+2 2025-04-22 (Tue)
XMAD  trade 2025-12-23 (Tue)  ->  T+2 2025-12-29 (Mon)

July 3, 2025 settles on Monday the 7th, because the NYSE is closed on the 4th; November 26, on Friday the 28th, skipping Thanksgiving. In Madrid, a sale on Wednesday, April 16, 2025 settles on Tuesday the 22nd, because Good Friday and Easter Monday are not business days. The exchange calendar is an approximation: the one that rules is that of the depository and the payment system, which may differ from the exchange's on some day of the year (lesson 1.1.2).

For a system, settlement matters in three places. In a cash account, the proceeds of a sale cannot be used to buy something else until it settles (or the broker advances them under conditions). Dividends are collected by whoever is listed as holder on the record date, so the ex-date depends on the settlement cycle (lesson 1.2.1). And in a margin account, it is the broker who puts up the missing cash when the purchase settles, and from then on charges interest on it.

Margin and leverage

A margin account makes it possible to buy with money lent by the broker, with the securities as collateral. Leverage is exposure divided by own equity: with 50,000 USD of your own and 50,000 borrowed, a 100,000 position has leverage 2. A 10% drop in the price becomes a 20% drop in equity.

In the US there are two minimum rules for stocks bought on margin:

• Initial margin (Regulation T). The broker can lend up to 50% of the purchase price: the client puts up at least half33Note 3 · 12 CFR 220.12 (Regulation T): “50 percent of the current market value of the security” for margin equity securities..
• Maintenance margin (FINRA Rule 4210). Account equity must be at least 25% of the market value of the long securities44Note 4 · FINRA Rule 4210 (c)(1): “25 percent of the current market value of all margin securities … ‘long’ in the account”. FINRA notes that the broker can liquidate the account at any time to cover a deficiency.. If it falls below, there is a margin call: post collateral or sell.

flowchart TB
  P[The price falls] --> E{Below 25%?}
  E -- no --> S[Position stays open]
  E -- yes --> M[Margin call]
  M --> A[Deposit cash]
  M --> V[Sell position]

With a loan $L$ per share and price $P$, equity per share is $P - L$. The call is triggered when equity falls to the maintenance margin $m$ of the value:

If the purchase was made at $P_0$ with the maximum Reg T loan, $L = (1 - m_i)\,P_0$ with $m_i = 0.5$, and this gives

def precio_llamada(p0, m_inicial=0.50, m_mant=0.25):
    prestamo = (1 - m_inicial) * p0
    return prestamo / (1 - m_mant)

p0 = op.loc[op["condicion"] == "subasta_cierre", "precio"].iloc[0]
acciones = 1_000
pstar = precio_llamada(p0)
print(f"purchase of {acciones} shares at {p0} USD")
print(f"loan: {(1 - 0.5) * p0 * acciones:,.0f} USD")
print(f"margin call at {pstar:.2f} USD ({pstar / p0 - 1:.1%})")
for mm in (0.30, 0.35, 0.40):
    print(f"  {mm:.0%} maintenance: call at "
          f"{precio_llamada(p0, m_mant=mm):.2f}")

purchase of 1000 shares at 53.12 USD
loan: 26,560 USD
margin call at 35.41 USD (-33.3%)
  30% maintenance: call at 37.94
  35% maintenance: call at 40.86
  40% maintenance: call at 44.27

With the NOVA close of June 2, 2025, 53.12 USD, the call is triggered at 35.41: a drop of one third. It looks far away, but with stricter requirements it gets closer: with a 40% maintenance, which a broker can impose on volatile stocks, the call comes with a 16.7% drop. The figure plots account equity against the price and the required maintenance: they cross at the call.

Three things the calculation does not say. The broker can sell without notice and at whatever price there is, including a gap like the one in lesson 1.1.4: the call does not guarantee an exit at $P^{*}$. The broker's requirements can be higher than the legal minimums, and change with volatility. And the loan costs interest every day, which is subtracted from equity and brings the call closer. Leveraged products for retail investors in the EU (CFDs, with ESMA leverage limits) are covered in lessons 1.2.4 and 1.2.7; futures margins, which work differently, in 1.2.3.

prestamo = (1 - 0.5) * p0 * acciones
for dias in (5, 30, 365):
    interes = prestamo * 0.06 * dias / 360     # assumed rate, 360-day basis
    print(f"{dias:>3} days: {interes:8.2f} USD · "
          f"{1e4 * interes / (p0 * acciones):6.1f} bp of the position")

  5 days:    22.13 USD ·    4.2 bp of the position
 30 days:   132.80 USD ·   25.0 bp of the position
365 days:  1615.73 USD ·  304.2 bp of the position

A year on margin at a 6% rate on half the position costs 3.04% of the position, 6.08% of own equity. It is a return hurdle the strategy has to clear before earning anything from the leverage.

Exercises

1. Calculate the volume-weighted average effective spread of the trades on the lit venues in the first half hour of the session (13:30 to 14:00 UTC) and in the rest of the day. Is it more expensive to trade at the start of the session?

apertura = lit["ts"] < "2025-06-02 14:00:00+00:00"
for nombre, g in (("first half hour", lit[apertura]),
                  ("rest of the day", lit[~apertura])):
    print(f"{nombre:<19} {media_pond(g, 'ef_pb'):.3f} bp"
          f" · {len(g)} trades")

first half hour     2.065 bp · 6090 trades
rest of the day     2.067 bp · 36554 trades

2. Repeat the cost waterfall with an order of 5,000 shares and another of 40,000. Which component changes most?

for n in (5_000, 40_000):
    pagado = precio_medio_compra(f10, n)
    print(n, "shares · impact",
          round(1e4 * (pagado - ask10) / decision, 2), "bp")

5000 shares · impact 0.0 bp
40000 shares · impact 3.08 bp

3. An account with 30,000 USD of its own buys 1,000 NOVA shares at 53.12 with the rest borrowed. What leverage does it have? At what price is the margin call triggered with the 25% maintenance? Does it meet the Reg T initial margin?