📖 常见指数：S&P 500, FTSE, MSCI

Equity Investments

I. Lesson Focus

This lesson examines the construction methodologies, weighting schemes, and practical applications of the world’s most widely used equity benchmarks: the S&P 500, FTSE 100, and the MSCI suite of indices. Candidates must be able to distinguish between price-weighted, equal-weighted, market-capitalization-weighted, and free-float-adjusted market-capitalization-weighted indices, calculate index returns, understand divisor adjustments, and identify which index is the appropriate benchmark in a given scenario.

II. The Problem

A global portfolio manager must select the correct benchmark to evaluate equity performance. Using the S&P 500 to judge a Europe-focused fund, or using the MSCI World (developed markets only) to assess an emerging-market allocation, will produce misleading conclusions. The weighting method, float adjustment, country classification, and rebalancing rules differ substantially across providers. This lesson equips candidates to identify each index’s methodology, compute its return, adjust for corporate actions, and avoid common traps tested on the CFA Level I exam.

III. Fundamental Classification of Equity Indices

Equity indices are statistical measures of market performance. Their construction hinges on two decisions: (1) which stocks to include and (2) how to weight them. The four primary weighting schemes are:

1. Price-Weighted Index
   Each stock’s weight is proportional to its share price.
   Index level = $\frac{\sum P_i}{D}$ where $D$ is the divisor adjusted for splits, rights issues, etc.
   Classic example: Dow Jones Industrial Average. High-priced stocks dominate regardless of economic size — a major limitation.

2. Equal-Weighted Index
   Every constituent receives identical weight and the index is rebalanced periodically. Small-cap stocks receive the same importance as large caps, but turnover and transaction costs are higher.

3. Market-Capitalization Weighted (Value-Weighted)
   Weight of stock $i$ = $\frac{\text{Market Cap}_i}{\text{Total Market Cap of Index}}$.
   Larger companies exert greater influence, reflecting economic reality more closely.

4. Free-Float-Adjusted Market-Capitalization Weighted
   Only shares available to public investors (excluding government holdings, founder stakes, and strategic blocks) are used. This is the dominant methodology today. S&P 500, FTSE, and all MSCI indices employ free-float adjustment.

IV. The S&P 500 Index in Detail

The S&P 500, maintained by S&P Dow Jones Indices, selects 500 leading U.S. companies that together represent approximately 80% of U.S. equity market capitalization. Eligibility criteria include: - Minimum market capitalization (currently around USD 8.2 billion); - Positive earnings over the most recent four consecutive quarters; - Adequate monthly trading volume; - U.S. domicile or primary listing on a major U.S. exchange.

Weighting: Free-float-adjusted market capitalization. As of late 2023 the “Magnificent 7” stocks (Apple, Microsoft, Nvidia, etc.) occasionally exceeded 30% combined weight, illustrating the index’s concentration bias.

Index formula:
$$ \text{S\&P 500} = \frac{\sum (\text{Price}_i \times \text{Free-Float Shares}_i)}{\text{Divisor}} $$

The S&P 500 serves as the primary benchmark for U.S. large-cap equity, underlies the SPY ETF, and is the reference for performance evaluation of most U.S. equity managers.

V. The FTSE Index Family

FTSE Russell, owned by the London Stock Exchange Group, produces the FTSE 100 (largest 100 UK-listed companies) and the broader FTSE All-Share Index.

FTSE 100 characteristics: - Free-float market-cap weighted; - Constituents must be listed on the LSE Main Market; - Quarterly reviews; minimum free-float market cap approximately GBP 2 billion; - Applies foreign-ownership caps and liquidity screens.

The index is heavily concentrated in financials, energy, and consumer staples. In 2023 Shell, AstraZeneca, and HSBC together represented more than 25% of the index.

VI. The MSCI Index Family

MSCI is the leading provider of international equity benchmarks. Flagship indices include: - MSCI World: ~1,500 large- and mid-cap stocks from 23 developed markets, covering ~85% of free-float market cap in developed countries; - MSCI EAFE: Europe, Australasia, and Far East (ex-U.S. and Canada); - MSCI Emerging Markets: 24 emerging-market countries.

Construction process: 1. Country classification (Developed / Emerging / Frontier); 2. Size segmentation (Large / Mid / Small); 3. Free-float adjustment using the Foreign Inclusion Factor (FIF), a value between 0 and 1; 4. Semi-annual and quarterly index reviews.

MSCI’s consistent global methodology makes its indices the de-facto standard for asset allocation, performance benchmarking, and passive investment by sovereign wealth funds and international institutions.

VII. Index Return Calculation and Rebalancing

Indices publish both price-return and total-return versions. Total return assumes dividends are reinvested.

Approximate single-period index return:
$$ R_t = \sum_{i=1}^{n} w_{i,t-1} \times r_{i,t} $$

Corporate actions (splits, spin-offs, additions/deletions) require divisor adjustment to keep the index level continuous.

Worked Cases

Case 1: Price-Weighted vs. Market-Cap Weighted Bias

Three stocks form a simplified index:
Stock A: Price $100, 10 m shares, market cap $1.0 bn
Stock B: Price $50, 40 m shares, market cap $2.0 bn
Stock C: Price $200, 2 m shares, market cap $0.4 bn

Price-weighted (initial divisor = 3.5): Index = (100 + 50 + 200) / 3.5 ≈ 100.
Market-cap weights: A 29.4%, B 58.8%, C 11.8%.

If Stock A rises 20% to $120 while others are unchanged:
- New price-weighted index = (120 + 50 + 200) / 3.5 ≈ 105.71 → +5.71%.
- Market-cap-weighted return = 0.294 × 20% = +5.88%.

The price-weighted index understates the economic importance of the largest company (B). This bias is a classic CFA trap.

Case 2: FTSE 100 Free-Float Adjustment

A UK company has 1 billion shares outstanding. 35% held by a strategic investor and 10% by government; therefore free float = 55%. Share price = £8.
Free-float shares = 550 million.
Free-float market cap = £4.4 billion.

If the FTSE 100’s total free-float market cap is £20 trillion, the company’s weight = 4.4 / 20,000 = 2.2%.
Should the strategic stake fall to 20%, free float rises to 70% and the weight increases materially. This float-adjustment mechanism is used by FTSE, S&P, and MSCI alike.

Case 3: MSCI Foreign Inclusion Factor (FIF) Impact

An A-share has a 3% weight in MSCI China before float adjustment. MSCI initially sets its FIF at 0.20.
Effective index weight = 3% × 0.20 = 0.6%.
After gradual increases to FIF = 0.40, the effective weight doubles to 1.2%, triggering large passive inflows. This explains the capital-flow effects observed when MSCI raised China A-share inclusion factors between 2018 and 2021.

Traps

Key Formulas

• Price-weighted index level = $\frac{\sum P_i}{D}$
• Market-cap weight $w_i = \frac{P_i \times Q_i \times \text{Float Factor}}{\sum (P_j \times Q_j \times \text{Float Factor})}$
• Index return $R_t \approx \sum w_{i,t-1} \times r_{i,t}$
• Total-return index = Price-return index × (1 + dividend reinvestment)
• Divisor adjustment: New $D = $ Old $D \times \frac{\text{Post-adjustment market value}}{\text{Pre-adjustment index level}}$
• Effective weight in MSCI = Free-float market-cap weight × FIF (0 ≤ FIF ≤ 1)

Practice Questions

Q1. The S&P 500 is currently constructed using which weighting method?
A. Price-weighted
B. Equal-weighted
C. Free-float-adjusted market-capitalization weighted
D. Fundamental weighted

Q2. Which of the following is not a factor MSCI considers when constructing its equity indices?
A. Foreign Inclusion Factor (FIF)
B. Free-float percentage
C. Country classification (developed/emerging)
D. Whether the company has been profitable in each of the last four quarters

Q3. A price-weighted index contains three stocks priced at $40, $80, and $120 with a divisor of 4, giving an index level of 60. After the first stock undergoes a 1-for-2 split, what should the new divisor be to keep the index continuous?
A. 2
B. 3
C. 6
D. 8

Q4. The dominant feature of the FTSE 100 index is:
A. Heavy concentration in a few large banks and energy companies
B. Pure equal weighting
C. Inclusion of every company listed in London
D. Price weighting

Q5. The MSCI World index does not include which of the following markets?
A. Japan
B. United Kingdom
C. China
D. Australia

Q6. A company represents 5% of an index’s total market capitalization, but 60% of its shares are held by insiders and cannot be freely traded. Its weight in a free-float-adjusted index is closest to:
A. 5.0%
B. 3.0%
C. 2.0%
D. 0.5%

Q7. Which statement about the S&P 500 is incorrect?
A. It covers approximately 80% of U.S. equity market capitalization
B. Constituents must have positive earnings over the last four quarters
C. It is price-weighted to emphasize high-priced blue-chip stocks
D. It is the primary benchmark for the SPY ETF

Q8. An index’s total free-float market capitalization rises from USD 1,000 billion to USD 1,120 billion with no constituent changes and no dividends paid. The index’s price return is closest to:
A. 10.0%
B. 12.0%
C. 8.5%
D. Cannot be determined

Answers

Takeaways

• S&P 500, FTSE 100, and MSCI indices all employ free-float-adjusted market-capitalization weighting, the industry standard.
• Price-weighted indices systematically overweight high-priced stocks irrespective of economic size.
• MSCI uses the Foreign Inclusion Factor (FIF) to modulate investability of emerging-market stocks.
• Distinguish clearly between price return and total return; total return includes reinvested dividends.
• Corporate actions are neutralized by adjusting the divisor to maintain index continuity.
• The S&P 500 benchmarks U.S. large-caps, FTSE 100 benchmarks the UK, and MSCI World benchmarks global developed markets; they are not interchangeable.