---
title: "1.2.1 Stocks: splits, dividends and corporate actions"
description: "What a share is, why its raw price jumps on a split or an ex-date, how rights issues work and how an index is weighted."
url: "https://pythonparatrading.com/en/python-trading-course/level-1/stocks-splits-dividends-corporate-actions/"
lang: "en"
image: "https://pythonparatrading.com/og/en/python-trading-course/level-1/stocks-splits-dividends-corporate-actions.png"
---
# 1.2.1 · Stocks: splits, dividends and corporate actions
> The price of a stock does not change only because the market has an opinion: it also changes because the company pays out cash, multiplies its shares or issues new ones. This lesson explains the economics of each corporate action, measures it on eight years of unadjusted NOVA prices and ends with the three ways of weighting an index.
- Course: [Level 1: Financial data, markets and analysis](https://pythonparatrading.com/en/python-trading-course/level-1/)
- Module: 1.2 · Asset classes
- Duration: 60 min
- Prerequisites: [1.1.1 · Market participants and trading venues](https://pythonparatrading.com/en/python-trading-course/level-1/market-participants-and-trading-venues/), [0.5.3 · Selection, filtering, groupby, merge, pivot, resample and moving windows](https://pythonparatrading.com/en/python-trading-course/level-0/pandas-groupby-merge-resample-rolling/)
## By the end of this lesson
- Explain what rights a share gives and how price, number of shares and market capitalization relate.
- Recognize in an unadjusted price series the jump of a split and the drop of an ex-dividend date, and know which of the two is visible to the naked eye.
- Order the dates of a dividend (declaration, ex, record and payment) and know which date decides who receives it.
- Calculate the theoretical price after a rights issue and the theoretical value of the right.
- Calculate the weights of a price-weighted, a capitalization-weighted and an equal-weighted index, and adjust the divisor after a split.
## What a share is
A share is a proportional part of a company's capital. It gives two kinds of rights: **economic** (a part of the
profits that are distributed, in the form of dividends, and of the assets if the company is wound up) and **voting**
(voting at the general meeting). Many companies also grant a **pre-emptive subscription right**: when they issue new
shares, current shareholders can buy them first, in proportion to what they already hold.
Three quantities are best not confused:
- **Price**: what is paid for one share in the market.
- **Shares outstanding**: how many have been issued (minus those the company itself holds as treasury stock).
- **Market capitalization**: price × shares outstanding. It is what the whole company is worth to the market. Indexes
usually use the **free-float** capitalization: only the shares that actually trade, without those of controlling
shareholders.
The price of a share, on its own, does not say whether a company is large or expensive: a 1,600 USD share can belong
to a smaller company than an 18 USD one with many more shares. This idea comes back at the end of the lesson, with
indexes.
**Corporate actions** are the company's decisions that change the number of shares, the price or both. Each one has
different economics and a different footprint in the data:
| Event | Shares | Price | Value for the shareholder |
|---|---|---|---|
| N-for-1 split | × N | ÷ N | Unchanged |
| 1-for-N reverse split | ÷ N | × N | Unchanged |
| Cash dividend | Unchanged | Falls by the amount on the ex-date | Unchanged: receives the cash |
| Stock dividend (*scrip*) | Rises | Falls proportionally | Unchanged if the rights are not sold |
| Rights issue below market | Rises | Falls to the theoretical price | Unchanged if they exercise or sell the rights |
| Issue without rights (placement) | Rises | May fall | Diluted |
| Share buyback | Falls | No mechanical adjustment | Unchanged for those who do not sell |
| Spin-off | Receives shares of the subsidiary | Falls by the subsidiary's value | Unchanged: the sum of the two |
| Merger or takeover bid | Exchanged or paid out | Converges to the offer price | Depends on the premium |
| Delisting | Disappears | Last traded price | Whatever is left (lesson 1.4.4) |
The right-hand column says “unchanged” in almost every row. That is the central idea: most corporate actions **change
the unit of measurement, not the value**. But the raw price does change, and a trading system that reads raw prices
sees moves that do not exist. The way to correct it, adjusted prices, is lesson 1.4.3; here the point is to understand
why they jump.
## The split: the price changes and the value does not
In a 4-for-1 split, each old share becomes four new ones. The price is divided by four, the market capitalization
does not change. Companies do it mostly so that the share has a “manageable” price: at 240 USD per share, a lot of
100 costs 24,000 USD.
The header figure is NOVA's **unadjusted** weekly close since 2018. On August 23, 2021 the series breaks in two. The
daily data shows it without smoothing:
```python
import pandas as pd
d = pd.read_csv("nova_diario_sin_ajustar.csv", parse_dates=["fecha"],
index_col="fecha")
d.loc["2021-08-18":"2021-08-25"]
```
```output
apertura maximo minimo cierre volumen
fecha
2021-08-18 241.43 247.29 233.13 245.16 1747289
2021-08-19 239.60 251.84 238.19 241.05 2471611
2021-08-20 238.75 240.55 227.85 240.00 2203366
2021-08-23 60.28 60.41 58.11 59.55 13427377
2021-08-24 59.63 60.11 57.33 59.55 13974110
2021-08-25 59.17 62.40 58.71 60.18 6931159
```
On Friday, August 20 NOVA closes at 240.00 USD; on Monday the 23rd it opens at 60.28. It is the effective day of the
split (the split's ex-date): the new shares are already trading. Volume in shares goes from about 2 million to more
than 13 million. None of this is news about the company. A return calculation that does not know about it reads it
like this:
```python
r = d["cierre"].pct_change()
print(r.nsmallest(3).round(4))
antes = d.loc["2021-05-24":"2021-08-20", "volumen"].mean()
despues = d.loc["2021-08-23":"2021-11-19", "volumen"].mean()
print(f"Average volume: {antes:,.0f} before, {despues:,.0f} after"
f" (x{despues / antes:.2f})")
```
```output
fecha
2021-08-23 -0.7519
2021-06-02 -0.1221
2025-03-26 -0.1210
Name: cierre, dtype: float64
Average volume: 3,331,806 before, 11,516,047 after (x3.46)
```
The worst session in NOVA's history, according to this calculation, is −75.19%: the day of the split. The next two,
of about −12%, are real moves. A backtest on this series would buy “the dip”, trigger a stop or produce an absurd
volatility for 2021. Average volume over the following three months is 3.46 times that of the previous three: almost
the split factor of 4, because each new share is a quarter of the old one. A liquidity filter based on shares traded
thinks NOVA has become four times more liquid; in dollars traded (price × volume), almost nothing has changed.
Checking that the value does not change needs the number of shares, which is not in the data. With an assumed figure
of 100 million shares before the split:
```python
acciones = pd.Series(100e6, index=d.index)
acciones.loc["2021-08-23":] *= 4 # 4-for-1 split
cap = d["cierre"] * acciones / 1e9
cap.loc["2021-08-19":"2021-08-24"].round(2)
```
```output
fecha
2021-08-19 24.10
2021-08-20 24.00
2021-08-23 23.82
2021-08-24 23.82
dtype: float64
```
24.00 billion on Friday and 23.82 on Monday: a change of −0.75%, which is what the market moved that day. The
practical rule for the data is twofold: returns are calculated on adjusted prices (lesson 1.4.3) and volumes are
compared in dollars or adjusted by the same factor.
The reverse split is the opposite: 1 new share for every N old ones. It is usually done by a company whose price has
fallen a lot. In the data, the raw price is multiplied from one day to the next: it is not a rally, and it almost
always comes after a long decline.
## Dividends: four dates and a drop
A cash dividend takes cash out of the company and hands it to the shareholders. The company is worth less by exactly
what it pays, and the price discounts it. The calendar has four dates:
```mermaid
flowchart LR
A[Declaration] --> E[Ex-date]
E --> R[Record]
R --> P[Payment]
```
- **Declaration date**: the general meeting or the board approves the amount and the dates.
- **Record date**: whoever is listed as a shareholder in the records that day receives the dividend.
- **Ex-dividend date**: the first session in which the share trades **without** the right to the dividend. Whoever
buys on that day or later no longer receives it; whoever sells on that day still receives it.
- **Payment date**: the cash reaches the account.
The ex-date depends on settlement. To appear on the register the purchase has to have settled; with T+1 settlement
(the US, since May 2024), a purchase made on the record date no longer arrives in time. That is why, according to the
SEC, the ex-date is set **on the record date** (or the previous business day if the record date is not one). With
T+2 settlement, as in the EU, the same reasoning gives one business day before the record date. For a very large
dividend, 25% of the price or more, the US rule is different: the ex-date is deferred to the business day after the
payment.
`nova_eventos.csv` lists NOVA's 34 events: 32 quarterly dividends, one special dividend and the split. Amounts before
the split are per old share:
```python
ev = pd.read_csv("nova_eventos.csv",
parse_dates=["fecha_ex", "fecha_pago"])
print(ev["tipo"].value_counts())
ev.iloc[13:17]
```
```output
tipo
dividendo 32
split 1
dividendo_extraordinario 1
Name: count, dtype: int64
fecha_ex tipo ratio importe fecha_pago
13 2021-05-10 dividendo NaN 0.60 2021-06-01
14 2021-08-10 dividendo NaN 0.60 2021-08-31
15 2021-08-23 split 4.0 NaN 2021-08-20
16 2021-11-10 dividendo NaN 0.15 2021-12-01
```
The dividend goes from 0.60 USD to 0.15 USD right after the split. It is not a cut: 0.60 / 4 = 0.15. Whoever had one
share and received 0.60 now has four and receives 4 × 0.15. A “dividend growth” analysis that does not adjust for the
split would see a 75% cut.
At the open of the ex-date, the price should, in theory, fall by the amount of the dividend. This can be checked by
comparing the gap between the previous close and the open with the drop the dividend explains:
```python
d["cierre_ant"] = d["cierre"].shift()
div = ev[ev["tipo"] != "split"].merge(
d[["apertura", "cierre_ant"]], left_on="fecha_ex",
right_index=True)
div["esperado_pct"] = -100 * div["importe"] / div["cierre_ant"]
div["hueco_pct"] = 100 * (div["apertura"] / div["cierre_ant"] - 1)
cols = ["fecha_ex", "tipo", "importe", "esperado_pct", "hueco_pct"]
div[cols].iloc[23:27].round({"esperado_pct": 2, "hueco_pct": 2})
```
```output
fecha_ex tipo importe esperado_pct hueco_pct
24 2023-11-10 dividendo 0.17 -0.44 -0.95
25 2023-12-14 dividendo_extraordinario 1.50 -3.51 -3.20
26 2024-02-12 dividendo 0.18 -0.37 -0.68
27 2024-05-10 dividendo 0.18 -0.31 0.17
```
The special dividend of December 14, 2023, 1.50 USD on a close of 42.75, explains a 3.51% drop, and the open falls
3.20%: it is visible to the naked eye. The surrounding quarterly dividends explain drops of between 0.31% and 0.44%,
and the observed gaps are −0.95%, −0.68% and +0.17%: the dividend is there, but it is covered up by everything else
that happened that night. On May 10, 2024 the stock even opened above the previous close.
*Fig. — Expected dividend drop against the observed opening gap on each NOVA ex-date, 2018–2025.* Scatter of 33 ex-dividend dates. Horizontal axis: the drop the dividend explains (between −0.17% and −0.44% for the 32 quarterly ones); vertical axis: the gap between the previous close and the open (between −2.35% and +1.25%). The quarterly ones form a narrow column with a wide vertical spread, far from the diagonal; the USD 1.50 special dividend, highlighted, lies almost on it: −3.51% expected and −3.20% observed.
The figure plots the two quantities against each other on the 33 ex-dates. If the gap were only the dividend, all the
points would lie on the diagonal. The special dividend is almost on it; the quarterly ones form a column that is
narrow (they all explain between −0.17% and −0.44%) and very tall. How much noise is there in a normal night?
```python
ordinarios = div[div["tipo"] == "dividendo"]
print(ordinarios[["esperado_pct", "hueco_pct"]].mean().round(2))
print("Positive gaps on ex-date:",
(ordinarios["hueco_pct"] > 0).sum(), "of", len(ordinarios))
hueco = 100 * (d["apertura"] / d["cierre_ant"] - 1)
sin_evento = hueco.drop(ev["fecha_ex"])
print(f"Standard deviation of the gap without events: "
f"{sin_evento.std():.2f} %")
```
```output
esperado_pct -0.29
hueco_pct -0.55
dtype: float64
Positive gaps on ex-date: 9 of 32
Standard deviation of the gap without events: 0.97 %
```
On average, the quarterly dividends explain −0.29% and the observed gap is −0.55%: the sign and the order of magnitude
match, but on 9 of the 32 ex-dates the stock opened **above** the previous close. The standard deviation of the gap on
a night without events is 0.97%, three times the dividend drop. Not being visible does not mean it does not matter: it
is money the shareholder receives and the price series does not capture.
```python
div["rpd"] = div["importe"] / div["cierre_ant"]
anual = 100 * div.groupby(div["fecha_ex"].dt.year)["rpd"].sum()
anual.round(2)
```
```output
fecha_ex
2018 0.85
2019 1.08
2020 1.13
2021 1.11
2022 1.13
2023 4.98
2024 1.30
2025 1.33
Name: rpd, dtype: float64
```
A little over 1% a year, and almost 5% in 2023 because of the special dividend. Over eight years, a strategy that
measures its return with prices only misses nine or ten points that the investor did receive. It is the difference
between a price index and a total return index (lesson 1.2.2), and the reason for dividend-adjusted prices (lesson
1.4.3).
## Capital increases and subscription rights
A capital increase issues new shares to raise money. If the new shares are sold below the market price, the old
shareholders lose value unless they have the right to buy them in proportion. That is the **pre-emptive subscription
right**: each old share receives one right, and a fixed number of rights subscribes one new share at the issue price.
With $N$ old shares for every $n$ new ones, market price $P$ and issue price $E$, the theoretical price after the
issue (*TERP*, *theoretical ex-rights price*) is the weighted average of what the company is worth plus the new money:
$$
P_{\text{ex}} = \frac{N \cdot P + n \cdot E}{N + n},
\qquad
D = P - P_{\text{ex}} = \frac{n\,(P - E)}{N + n}
$$
where $D$ is the theoretical value of one right (one per old share). On the day the rights are detached from the
shares, the share trades “ex-rights” and its price falls, in theory, to $P_{\text{ex}}$; the rights trade separately
during the subscription period.
```python
def ampliacion(P, E, N, n):
"""Theoretical ex-rights price and theoretical value of one right."""
p_ex = (N * P + n * E) / (N + n)
return p_ex, P - p_ex
p_ex, derecho = ampliacion(P=60.0, E=40.0, N=4, n=1)
print(f"Theoretical price: {p_ex:.2f} right: {derecho:.2f}")
tengo = 400
print("Before:", tengo * 60.0)
print("Exercises (pays 100 x 40):", (tengo + 100) * p_ex - 100 * 40)
print("Sells the rights:", tengo * p_ex + tengo * derecho)
print("Does nothing:", tengo * p_ex)
```
```output
Theoretical price: 56.00 right: 4.00
Before: 24000.0
Exercises (pays 100 x 40): 24000.0
Sells the rights: 24000.0
Does nothing: 22400.0
```
With one new share for every four at 40 USD on a price of 60, the theoretical price is 56 USD and each right is worth
4 USD. Whoever exercises or sells the rights keeps their 24,000 USD; whoever does nothing and lets them lapse loses
1,600 USD, 6.7%. In practice the market does not hit the theoretical price exactly, but this is the order of
magnitude.
```mermaid
flowchart TB
A[Rights issue] --> D[Receives rights]
D --> X[Exercises]
D --> V[Sells rights]
D --> N[Does nothing]
X --> I[Value intact]
V --> I
N --> L[Loses the right]
```
In the data, a rights issue is a drop in the price on the ex-rights date that providers adjust with a factor
$P_{\text{ex}} / P$, just like a dividend. Two other variants are common in Spain:
- **Stock dividend or *scrip*** (“flexible dividend”): the company grants free allotment rights; the shareholder
chooses between receiving new shares or selling the rights (to the company itself at a fixed price or in the
market). For the data it resembles a bonus issue: more shares and an adjusted price.
- **Accelerated placement without rights**: the company sells new shares to institutional investors within a few
hours, at a discount. There is no right to compensate, so the shareholder who does not take part is diluted. In the
data it appears as a real drop, not as an adjustment.
## Buybacks, spin-offs, mergers and delistings
- **Buyback**: the company buys its own shares in the market. It is another way of returning money: shares outstanding
fall and earnings per share rise. There is no price adjustment, because there is no day on which the value changes
all at once. For fundamental analysis it does matter: the number of shares changes from one quarter to the next
(lesson 1.5.1).
- **Spin-off**: the company distributes shares of a subsidiary. The parent's price falls by what the subsidiary is
worth, and the shareholder receives new shares. A provider that does not adjust for it shows a drop the shareholder
did not suffer.
- **Merger or takeover bid**: the price of the acquired company converges to the offer price and stops trading. If the
deal is a share exchange, the shareholder ends up holding shares of the acquirer.
- **Delisting**: the share stops trading, because of a merger, a bankruptcy or a decision of the company itself. If
the data only has the companies listed today, all those that left are missing, and they are precisely the ones that
ended badly: survivorship bias (lesson 1.4.4).
- **Ticker change**: the ticker changes and the company is the same. A database indexed by ticker splits it into two
unrelated series.
## Indexes: how a basket is weighted
An index summarizes the price of a basket of stocks in one number. What changes from one to another is how much each
stock weighs. The three basic weightings are:
- **Price-weighted**: the index is the sum of the prices divided by a divisor. A 1,600 USD share weighs a hundred
times more than a 16 USD one, whatever the size of the company. The Dow Jones Industrial Average works this way,
according to its methodology.
- **Capitalization-weighted**: each stock weighs as much as its market capitalization, usually free-float. It is the
weighting of most S&P Dow Jones Indices indexes and, among others, of the S&P 500 and the IBEX 35.[^1]
- **Equal-weighted**: they all weigh the same and the index is rebalanced periodically. It gives more weight to the
small ones than capitalization weighting does.
The course universe data (lesson 1.4.4) says which stocks were members of a fictitious 40-stock index each day. On
June 2, 2025:
```python
miembros = pd.read_csv("universo_miembros.csv",
parse_dates=["alta", "baja"])
dia = pd.Timestamp("2025-06-02")
vivos = miembros[(miembros["alta"] <= dia)
& (miembros["baja"].isna() | (miembros["baja"] > dia))]
print(len(vivos), "members on", dia.date())
precios = pd.read_parquet("universo_precios.parquet")
p = precios[precios["fecha"] == dia].set_index("ticker")["cierre"]
p[vivos["ticker"]].describe().round(2)
```
```output
40 members on 2025-06-02
count 40.00
mean 229.40
std 302.12
min 17.70
25% 51.24
50% 108.38
75% 309.10
max 1607.97
Name: cierre, dtype: float64
```
The 40 members trade between about 18 USD and about 1,600 USD. To compare weightings five are enough, with an assumed
number of shares outstanding (the data does not include it). The closes in `universo_precios.parquet` are adjusted;
for a single date close to the end of the series, that does not change the example.
```python
acciones = pd.Series({"ZXQZ": 50, "ZXLZ": 300, "ZXGM": 900,
"ZXAD": 2500, "ZXHW": 6000}) # millions
cesta = pd.DataFrame({"precio": p[acciones.index],
"acciones_m": acciones})
cesta["cap_m"] = cesta["precio"] * cesta["acciones_m"]
pesos = pd.DataFrame({
"precio": cesta["precio"] / cesta["precio"].sum(),
"capitalizacion": cesta["cap_m"] / cesta["cap_m"].sum(),
"igual": 1 / len(cesta),
})
print(cesta.round(2))
(100 * pesos).round(1)
```
```output
precio acciones_m cap_m
ZXQZ 1607.97 50 80398.5
ZXLZ 921.91 300 276573.0
ZXGM 171.20 900 154080.0
ZXAD 36.58 2500 91450.0
ZXHW 17.70 6000 106200.0
precio capitalizacion igual
ZXQZ 58.4 11.3 20.0
ZXLZ 33.5 39.0 20.0
ZXGM 6.2 21.7 20.0
ZXAD 1.3 12.9 20.0
ZXHW 0.6 15.0 20.0
```
*Fig. — Weight of five stocks in an index depending on the weighting: by price, by market capitalisation or equally.* Three panels of horizontal bars with the weight of five stocks of the course universe on 2 June 2025. Price-weighted, the highest-priced one (ZXQZ, USD 1,607.97) weighs 58.4%, highlighted, and the two cheapest 1.3% and 0.6%. Cap-weighted, with an assumed share count, ZXLZ weighs 39.0%, ZXGM 21.7%, ZXHW 15.0%, ZXAD 12.9% and ZXQZ 11.3%. Equal-weighted, 20% each.
By price, ZXQZ is 58.4% of the index: its share is the most expensive, but with 50 million shares it is the smallest
company of the five (80,398 million in market capitalization). By capitalization it weighs 11.3%, and the largest is
ZXLZ, with 39.0%. The equal-weighted index gives 20% to each one. Three indexes with the same five stocks can have
very different returns: the price-weighted one is, in practice, a bet on ZXQZ.
The divisor of a price-weighted index is what makes it continuous. If ZXQZ did a 10-for-1 split, its price would go
from 1,607.97 to 160.80 and the index would fall because of an event that does not change the value of anything. The
provider recalculates the divisor so that the level is the same just before and just after:
```python
divisor = 5.0
nivel = cesta["precio"].sum() / divisor
print(f"Index: {nivel:.2f}")
tras = cesta["precio"].copy()
tras["ZXQZ"] /= 10 # 10-for-1 split
print(f"Without adjusting the divisor: {tras.sum() / divisor:.2f}")
nuevo = tras.sum() / nivel
print(f"New divisor: {nuevo:.4f}, index {tras.sum() / nuevo:.2f}")
peso = 100 * tras["ZXQZ"] / tras.sum()
print(f"ZXQZ weight after the split: {peso:.1f} %")
```
```output
Index: 551.07
Without adjusting the divisor: 261.64
New divisor: 2.3739, index 551.07
ZXQZ weight after the split: 12.3 %
```
Without an adjustment, the index would go from 551.07 to 261.64, a fictitious −52.5%. With the new divisor (2.3739),
the level stays at 551.07. But ZXQZ's weight falls from 58.4% to 12.3% without the company having changed: that is
the oddity of price weighting. In a capitalization-weighted index, the same split changes nothing, because price ×
shares stays the same.
Capitalization-weighted indexes also have a divisor, and they adjust it for other events: additions and removals of
members, share issues, large buybacks or changes in the free float. In all of them, the rule is the same: the index
level only changes because of prices, never because of mechanics.
## What this changes in your data
- **Unadjusted prices to trade, adjusted prices to measure.** The price at which an order was executed is the raw
one; the return of a position is measured with the adjusted one (lesson 1.4.3). Mixing them gives −75% returns or
stops that trigger on their own.
- **Volume is adjusted too.** After a split, volume in shares is multiplied; in dollars, it is not.
- **The date that counts is the ex-date.** The dividend adjustment is applied on the ex-date; using the payment date
shifts it.
- **Dividends are return.** A little over 1% a year in NOVA, invisible on the chart, real in the account. A short
strategy pays them.
- **The index is not the sum of its companies.** Before comparing a strategy with an index, you have to know how it
weights and whether it is a price or a total return index.
- **Events are stored separately.** An events table (`fecha_ex`, type, ratio, amount) makes it possible to redo any
adjustment; an already adjusted series cannot be undone.
## Exercises
1. Leaving out the split, which are NOVA's three largest opening gaps (in absolute value)? Do they coincide with any
ex-dividend date?
**Solution.**
```python
grandes = hueco.drop(pd.Timestamp("2021-08-23")).abs().nlargest(3)
print(hueco[grandes.index].round(2))
print("Is any of them an ex-date?",
grandes.index.isin(ev["fecha_ex"]).any())
```
```output
fecha
2018-04-27 13.49
2021-07-23 -9.39
2019-04-26 -7.55
dtype: float64
Is any of them an ex-date? False
```
None of them coincides with a dividend. NOVA's large gaps come on the day after an earnings release (after the close
on the fourth Thursday of January, April, July and October, according to the data README). A 13% gap is not explained
by any corporate action: it is new information. Telling a “mechanical” gap (split, dividend) from an informative one
is the first step of any data cleaning (lesson 1.4.2).
2. Calculate the weight of each index member on June 2, 2025 if the index were price-weighted. What weight does the
largest have? And how much would it have in an equal-weighted one?
**Solution.**
```python
p40 = p[vivos["ticker"]]
peso_precio = 100 * p40 / p40.sum()
print(peso_precio.nlargest(3).round(2))
print(f"Equal-weighted: {100 / len(p40):.2f} % each")
```
```output
ticker
ZXQZ 17.52
ZXLZ 10.05
ZXZE 7.80
Name: cierre, dtype: float64
Equal-weighted: 2.50 % each
```
ZXQZ, with the highest price, would weigh 17.52% in a price-weighted 40-stock index: seven times the 2.50% an
equal-weighted one would give it. The three most expensive add up to more than a third of the index. That is why
price-weighted indexes are a historical oddity today.
3. A Spanish company announces a dividend and a record date on Thursday. With T+2 settlement, what is the last day to
buy with the right to receive it? If instead of buying you want to sell and still receive the dividend, what is the
first day you can sell?
**Solution.**
With T+2, a purchase on Tuesday settles on Thursday and appears on the register: Tuesday is the last day with the
right (*last trading date*) and Wednesday is the ex-date, one business day before the record date. Whoever wants to
sell and keep the dividend can do so from Wednesday, the ex-date: on that day the share already sells “without” the
dividend, which is still theirs. The reasoning is the same as in the US, with one more day of settlement (lesson
1.1.5).
[^1]: According to the S&P Dow Jones Indices index mathematics methodology (in the resources), most of its equity
indexes are weighted by free-float market capitalization; chapter 358 of the CME rulebook describes the S&P 500 as a
value-weighted composite index, and the MEFF factsheet for the IBEX 35 future describes the IBEX 35 as “a
capitalization-weighted index”.
## Self-assessment
1. NOVA does a 4-for-1 split. An investor had 100 shares at 240 USD. What do they have the next day, not counting market moves?
- A. 100 shares at 60 USD: they have lost 75%
- B. 400 shares at 240 USD: they have quadrupled their investment
- C. 400 shares at 60 USD: the same as before
- D. 100 shares at 240 USD and 300 rights
*Answer C: 400 shares at 60 USD: the same as before.* A split multiplies the number of shares and divides the price by the same factor. The value of the position (100 × 240 = 400 × 60 = 24,000 USD) and the company's market capitalization do not change. Only the unit of measurement changes.
2. In the US, with T+1 settlement, a company sets the record date of a dividend on Monday, March 16. What is the last day you have to buy to receive it?
- A. Monday the 16th itself
- B. Friday the 13th
- C. Tuesday the 17th
- D. The payment date
*Answer B: Friday the 13th.* With T+1, the ex-date coincides with the record date (Monday the 16th). Whoever buys on the 16th or later no longer receives it; whoever buys on Friday the 13th settles on Monday the 16th and appears on the register.
3. Why are NOVA's quarterly dividends barely distinguishable in the opening gap of their ex-date?
- A. Because dividends are paid later and do not affect the price
- B. Because the provider has already adjusted the prices
- C. Because dividends only affect the close, not the open
- D. Because the drop they explain (0.3% on average) is small compared with the normal noise of a night (standard deviation of 0.97%)
*Answer D: Because the drop they explain (0.3% on average) is small compared with the normal noise of a night (standard deviation of 0.97%).* The price falls by the dividend, but it also moves because of everything else. A 0.3% drop is buried in noise three times larger; the special dividend of 1.50 USD (3.5%) does show. Not being visible to the naked eye does not mean it does not matter: added up, it is a little over 1% a year.
4. A stock trades at 60 USD and the company raises capital: 1 new share for every 4 old ones at 40 USD. What is the theoretical value of each right?
- A. 4 USD
- B. 20 USD
- C. 5 USD
- D. 0 USD: the rights are worthless
*Answer A: 4 USD.* The theoretical price after the issue is (4 × 60 + 1 × 40) / 5 = 56 USD, and each old share carries a right worth 60 − 56 = 4 USD. Whoever does nothing and lets the rights lapse loses those 4 USD per share.
5. In a price-weighted index, one of its stocks does a 10-for-1 split. What does the index provider do?
- A. Nothing: the index falls and recovers on its own
- B. Multiplies that stock's price by 10 forever
- C. Removes the stock from the index
- D. Changes the divisor so that the index is worth the same just before and just after the split
*Answer D: Changes the divisor so that the index is worth the same just before and just after the split.* Without an adjustment, the index would fall because of an event that does not change the value of anything. The divisor is recalculated so that the level is continuous. The side effect is that, from then on, that stock weighs much less in the index.
## Key points
- Market capitalization = price × shares outstanding. A split changes both factors and leaves the product unchanged; a dividend takes cash out of the company and lowers the price by its amount.
- In unadjusted NOVA prices, the 2021 split is a −75% jump and volume is multiplied by four; a return calculation that does not know about it sees the worst session in its history.
- The ex-date decides who receives a dividend. In the US, with T+1, the ex-date coincides with the record date; the price drop comes at the open of the ex-date.
- Ordinary dividends get lost in the noise of a night, but added up they are a little over 1% a year in NOVA: a price-only series understates the return.
- A rights issue lowers the market price to the theoretical price; the right compensates the shareholder who sells or exercises it.
- A price-weighted index gives more weight to the stock with the highest price, not to the largest company. After a split, the divisor is adjusted and that stock's weight collapses.
## Resources
### Research
- [Big Data Management 3 - Building a Datalake on the Nasdaq with ArcticDB.](https://pythonparatrading.com/en/big-data-with-arcticdb/) · Research-0021 · 5 min
### Documentation
- [Investor.gov (SEC): ex-dividend dates, record dates and stock dividends](https://www.investor.gov/introduction-investing/investing-basics/glossary/ex-dividend-dates-when-are-you-entitled-stock-and) · investor.gov
- [S&P Dow Jones Indices: Dow Jones Averages methodology (price-weighted index and divisor)](https://www.spglobal.com/spdji/en/documents/methodologies/methodology-dj-averages.pdf) · spglobal.com
- [S&P Dow Jones Indices: Index Mathematics Methodology (capitalization weighting, equal weighting and others)](https://www.spglobal.com/spdji/en/documents/methodologies/methodology-index-math.pdf) · spglobal.com
### Data
- [Level 1 data: unadjusted NOVA daily prices (CSV)](https://pythonparatrading.com/curso/datos/nivel-1/nova_diario_sin_ajustar.csv) · Download · nova_diario_sin_ajustar.csv
- [Level 1 data: NOVA corporate actions (CSV)](https://pythonparatrading.com/curso/datos/nivel-1/nova_eventos.csv) · Download · nova_eventos.csv
Previous lesson: [1.1.5 · Costs, settlement, leverage and margin](https://pythonparatrading.com/en/python-trading-course/level-1/trading-costs-settlement-leverage-and-margin/)
Next lesson: [1.2.2 · ETFs: replication, tracking error, leveraged ETFs and UCITS](https://pythonparatrading.com/en/python-trading-course/level-1/etfs-replication-tracking-error-ucits/)