Learn what a market index is and how it's built — Stock-Market notes

What Exactly IS a Market Index?

WHY these properties matter:

Fixed methodology → investors can replicate results
Representative selection → reflects actual market conditions
Regular rebalancing → index stays relevant as companies grow/shrink

How Indices Are Built: The Three Approaches

Figure — Learn what a market index is and how it's built

1. Price-Weighted Index

Formula Price-Weighted Index Formula

$\text{Index Value} = \frac{\sum_{i=1}^{n} P_i}{D}$ Where:

$P_i$ = price of stock $i$
$n$ = number of stocks in index
$D$ = divisor (adjusted for splits, dividends)

DERIVATION FROM FIRST PRINCIPLES: Start with the simplest idea: "average price of my stocks" $\text{Simple Average} = \frac{P_1 + P_2 + ... + P_n}{n}$

Problem: When a stock splits 2-for-1, its price halves but nothing fundamental changed. Your average would suddenly drop!

Solution: Replace $n$ with an adjustable divisor $D$ : $\text{Index} = \frac{\sum P_i}{D}$

HOW the divisor works:

Initially $D = n$ (the count of stocks)
Before split: Stock at $100, $D = 10$ , index $= 950/10 = 95$
After 2:1 split: Stock now $50, adjust $D$ so index stays95 $\frac{900 + 50}{D} = 95 \implies D = 10$ Wait, that's wrong! Let me recalculate: $\frac{\text{sum of remaining9} + 50}{D} = 95$ If the sum of 9 stocks stayed the same (say $850) and one split from $100 to $50: $\frac{850 + 50}{D} = 95 \implies D = \frac{900}{95} \approx 9.47$ The divisor decreases to keep index value continuous.

Worked example Price-Weighted: Dow Jones Industrial Average

Setup: DJIA tracks 30 large US companies. Suppose today:

Apple: $180
Microsoft: $350
UnitedHealth: $520
... (27 more stocks)
Sum of all30 prices = $4,500
Current divisor = 0.152 (adjusted over decades)

Calculation: $\text{DJIA} = \frac{4500}{0.152} = 29,605.26$

WHY this step? Dividing by 0.152 instead of 30 accounts for all historical stock splits and changes. The divisor makes today's value comparable to 1896's inaugural value.

Next day: If Apple rises to $185(+)$5) but Microsoft falls to $345 (-1)$5):

\text{New DJIA} = \frac{4500}{0.152} = 29,605.26 \text{ (unchanged!)}

$\textbf{KEY INSIGHT:} \text{ A } \$1 \text{ move in a } \$500 \text{ stock (0.2\%) = same impact as } \$1 \text{ move in } \$50 \text{ stock (2\%). This is } \textbf{WEIRD} \text{ — expensive stocks dominate, regardless of company size.}$

2. Market-Cap Weighted Index

Formula Market-Cap Weighted Index Formula

$\text{Index Value} = \frac{\sum_{i=1}^{n} (P_i \times Q_i)}{\sum_{i=1}^{n} (P_{i,0} \times Q_{i,0})} \times \text{Base Value}$ Where:

$P_i$ = current price of stock $i$
$Q_i$ = shares outstanding of stock $i$
$P_{i,0}, Q_{i,0}$ = price and shares at base date
Base Value = arbitrary starting point (often 100) DERIVATION: WHAT we want: Bigger companies should have bigger influence. HOW to measure "bigness"? Market capitalization: $\text{Market Cap}_i = P_i \times Q_i$ (Stock price × number of shares = total value of company)

Step 1: Sum all market caps: $\text{Total Market Cap} = \sum_{i=1}^{n} (P_i \times Q_i)$

Step 2: Compare to base date see percentage change: $\text{Ratio} = \frac{\text{Total Cap Today}}{\text{Total Cap at Base Date}} = \frac{\sum P_i Q_i}{\sum P_{i,0} Q_{i,0}}$

Step 3: Multiply by arbitrary base value (e.g., 100) for readable numbers: $\text{Index} = \text{Ratio} \times 100$ WHY this works: If the total market doubles, index doubles. A 10% gain in a $1T company affects the index 10× more than 10% gain in $100B company. This matches economic reality!

Worked example Market-Cap Weighted: S&P 500

Setup: Simplified3-stock example

Company	Price	Shares	Market Cap
Apple	$150	16B	$2,400B
Small Corp	$50	2B	$100B
Tiny Inc	$10	5B	$50B
Base date: Total market cap = $2,000B, Base Value = 100
Today's calculation:
$\text{Total Cap} = 2400 + 100 + 50 = 2,550\text{B}$
$\text{Index} = \frac{2550}{2000} \times 100 = 127.5$
WHY this step? We divide by base-date cap to get a ratio (1.275 = 27.5% growth), then multiply by 100 to return to index scale.
Scenario: Apple rises 10% to $165, others unchanged:
$\text{New Apple Cap} = 165 \times 16 = 2,640\text{B}$
$\text{New Total} = 2640 + 100 + 50 = 2,790\text{B}$
$\text{New Index} = \frac{2790}{2000} \times 100 = 139.5$
Index rose from $127.5 \rightarrow 139.5$ (+9.4%), even though only 1 of 3 stocks moved. WHY? Apple is 94% of the index by weight (2400/2550). Its 10% gain drives the whole index.

3. Equal-Weighted Index

Formula Equal-Weighted Index Formula

$\text{Index Value} = \frac{1}{n} \sum_{i=1}^{n} \left( \frac{P_i}{P_{i,0}} \times 100 \right)$ Or equivalently: $\text{Index Value} = \frac{100}{n} \sum_{i=1}^{n} \frac{P_i}{P_{i,0}}$ DERIVATION:

GOAL: Every company gets equal say, regardless of price or size.

Step 1: Calculate percentage return for each stock: $\text{Return}_i = \frac{P_i - P_{i,0}}{P_{i,0}} = \frac{P_i}{P_{i,0}} - 1$

Step 2: Average all returns: $\text{Avg Return} = \frac{1}{n}\sum \text{Return}_i = \frac{1}{n}\sum \left(\frac{P_i}{P_{i,0}} - 1\right)$

Step 3: Convert to index value (start at 100): $\text{Index} = 100 \times (1 + \text{Avg Return}) = 100 \times \frac{1}{n}\sum \frac{P_i}{P_{i,0}}$

WHY this approach? Each stock contributes $\frac{1}{n}$ to the average. A 10% gain in any stock → index rises by $\frac{10\%}{n}$ , whether the stock is $5 or $500, $10M cap or $1T cap.

Worked example Equal-Weighted Index

Setup: Same 3 stocks, base prices: Apple $100, Small $50, Tiny $10

Today: Apple $150 (+50%), Small $50 (0%), Tiny $12 (+20%)

Calculation: $\text{Index} = \frac{100}{3} \left( \frac{150}{100} + \frac{50}{50} + \frac{12}{10} \right)$ $= \frac{100}{3}(1.5 + 1.0 + 1.2) =frac{100}{3}(3.7) = 123.33$

WHY this step? Each ratio shows how much that stock multiplied. We average the three multipliers (1.5, 1.0, 1.2) and scale to index points.

Compare to market-cap: If Apple had dominated by size, the index might be near 150(tracking Apple's +50%). But equal-weighting gives us $\frac{50 + 0 + 20}{3} = 23.33\%$ average gain → index at 123.33.

Rebalancing necessity: Over time, stocks drift from equal weights. If Apple grows to 60% of portfolio value, you must sell Apple and buy Small/Tiny to return to $\frac{1}{3}$ each. This happens quarterly or annually.

Comparison Table

Method	Example	Advantage	Disadvantage
Price-Weighted	Dow Jones	Simple, historic	High-price stocks dominate (ilogical)
Market-Cap Weighted	S&P 500, Nasdaq	Reflects economic weight	Mega-caps dominate; momentum bias
Equal-Weighted	S&P 500 EW	Diversified, small-cap exposure	High turnover; frequent rebalancing

Index Construction Process

Step-by-step HOW indices are actually built:

Define the universe:
- Geographic (US stocks, Japanese stocks)
- Size (large-cap, small-cap)
- Sector (technology, healthcare)
- WHY? Scope determines what you're measuring.
Set selection criteria:
- Market cap thresholds (e.g., >$10B for large-cap)
- Liquidity requirements (avg daily volume >$5M)
- Listing requirements (exchange, domicile)
- WHY? Ensures stocks are tradable and representative.
Choose weighting scheme:
- Price, market-cap, equal, or factor-based (value, momentum)
- WHY? Determines what drives index movement.
Set base date and base value:
- E.g., S&P 500: 1941-1943 average = 10
- WHY? Provides historical context and scale.
Establish rebalancing rules:
- Frequency (quarterly, annually)
- Reconstitution (add/remove stocks based on criteria)
- Corporate action adjustments (splits, dividends, mergers)
- WHY? Keeps index relevant as markets evolve.
Calculate and publish:
- Real-time calculation during market hours
- Transparency of methodology
- WHY? Investors need timely, trustworthy data.

Worked example Real Index Construction: Nifty 50

Selection criteria:

50 companies from ~1,600 on NSE
Must be traded on National Stock Exchange
Impact cost<0.5% for portfolio size of₹10 crores
Listed for at least 6 months (IPOs wait)
Average free-float market cap rank in top 120

Weighting: Free-float market cap $\text{Free-float Cap} = \text{Price} \times \text{Shares publicly tradable}$ (Excludes promoter holdings, government stakes, locked-in shares) WHY free-float? Reflects shares actually available to investors. If promoter owns 70%, only 30% matters for public market impact. Base: Nov 3, 1995 = 1,000 Rebalancing: Semi-annually (end of January and July) Calculation: $\text{Nifty} = \frac{\sum (\text{Free-float Cap})_{\text{today}}}{\sum (\text{Free-float Cap})_{\text{base}}} \times 1000$

Why Indices Matter for Investors

Benchmarking: "Did my portfolio beat the Nifty 50?"
- If you earned 12% but Nifty rose 18%, you underperformed despite positive returns.
Passive investing: Index funds replicate index composition
- Buy the entire S&P 500 with one fund
- Lower fees than active management
Market sentiment: Quick gauge of investor mood
- "Tech sector index fell 3%" → sector-wide selloff
Derivatives: Options and futures trade on indices
- Nifty futures let you bet on/hedge overall market moves
Academic research: Performance studies, risk models
- "What's the correlation between Indian and US markets?" → compare Nifty and S&P 500

Recall Feynman Technique: Explain to a 12-year-old

Imagine you and your friends start a lemonade-stand-watching club. You want to know: "Are lemonade stands doing well in our neighborhood?"

You could check every single stand every day, but that's too much work. So you pick10 popular stands and create a "Lemonade Index."

Method 1 (Price-Weighted): Add up the price of one cup from each stand. If the total is $15\text{ today and }$16 tomorrow, lemonade got 6.7% more expensive! But weird thing: if one stand charges $5/\text{cup and another }$1/cup, the expensive stand has more influence even if it's a tiny operation.

Method 2 (Market-Cap): You count how many cups each stand sells per day AND the price. Big stand (1000 cups × $2) = $2000/day. Tiny stand (10 cups × $1) = $10/day. Now you add the total money all stands make. This way, big operations matter more, which makes sense!

Method 3 (Equal-Weight): You treat each stand equally. If Stand A doubles in price (+100%) and Stand B halves (-50%), your index says lemonade is up 25% on average, even though Stand A might be 100× bigger.

The "Lemonade Index" becomes your scoreboard. When it rises, lemonade business is good! Investors do the same thing with stocks—they pick a basket and watch its average. Different baskets = different stories about how "the market" is doing.

Connections

What shares represent → Shares are the building blocks of indices
Ownership percentage → Market cap = price × shares (used in cap-weighted indices)
Index funds → Funds that replicate index composition
Portfolio diversification → Indices provide instant diversification
Beta → Measures stock movement relative to index
Stock splits → Why indices need divisor adjustments

#flashcards/stock-market

What is a market index? :: A numerical representation of the value of a selected group of stocks, calculated using a specific formula, serving as a benchmark for market/sector performance.

In a price-weighted index, what gets adjusted to handle stock splits?

The divisor (denominator) is adjusted downward to keep the index value continuous despite the price halving from the split.

Formula for price-weighted index :: Index = (Sum of all stock prices) / Divisor, where divisor accounts for splits and changes

Which stocks dominate a price-weighted index?

High-priced stocks dominate regardless of company size, because each stock contributes its price directly to the sum.

Formula for market-cap weighted index

Index = [Sum(Price × Shares Outstanding) / Sum(Base Price × Base Shares)] × Base Value

What does market capitalization mean?

Market cap = Stock Price × Shares Outstanding; represents the total value of a company in the market.

Which companies dominate a market-cap weighted index?

Large companies (mega-caps) dominate because their market cap is much larger, so their movements have greater impact on the index.

Formula for equal-weighted index

Index = (100/n) × Sum(Current Price / Base Price) for all n stocks

What is the main operational challenge of equal-weighted indices?

Frequent rebalancing required to maintain equal weights as stocks grow at different rates, leading to high turnover and transaction costs.

Why does S&P 500 use free-float market cap instead of total market cap?

Free-float excludes locked-in shares (promoter holdings, strategic stakes), reflecting only shares actually available for public trading.

What does Nifty 50 base value of 1,000 on Nov 3, 1995 mean?

It means the index was set to 1,000 on that date; current value compared to 1,000 shows cumulative percentage growth since then.

Can different indices move in opposite directions on the same day?

Yes, because they track different baskets of stocks. E.g., tech-heavy index can fall while small-cap index rises if sectors move differently.

Why is comparing absolute index levels (18,000 vs 60,000) meaningless?

Index levels depend on arbitrary base values and base dates; only percentage returns from your investment date matter for comparison.

What are the three main index weighting schemes?

Price-weighted (sum of prices), market-cap weighted (weighted by company value), equal-weighted (average of returns).

What is the impact cost criterion in Nifty 50 selection?

Impact cost <0.5% for ₹10 crore portfolio ensures the stock has sufficient liquidity for institutional trading without excessive price impact.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Market index basicallyek scorecard hai jo bata hai kisi group of stocks ka overall performance kaisa chal raha hai. Socho agar tumhe pura stock market track karna ho—thousands of companies! Toh iska solution hai kium ek representative basket chunte hain, jaise S&P 500 mein 500 bade companies hain, aur uska average calculate karte hain. Jab CNBC pe bolte hain "market 2% up hai," actually woh bol rahe hain ki yeh specific basket2% badh gayi.

Teen tarike hain index banana. Price-weighted (jaise Dow Jones) mein sirf stock prices add karte hain—jiska price jyada, uska influence jyada, chahe company choti hi kyu na ho. Yeh thoda weird hai. Market-cap weighted (jaise S&P 500, Nifty 50) mein hum company ka total value dekhte hain

Test yourself — Shares, Ownership & Indices