Portfolio Construction: Why 20 Great Ideas Can Still Make a Bad Portfolio

The investment committee approved 20 names this year, and every thesis held up under questioning. The book still trails its benchmark by a wide margin. The post-mortem finds that half the positions were the same bet on falling interest rates.

A portfolio of 20 strong ideas can underperform because the positions share the same risks. When holdings are correlated, sized only by conviction, or tilted toward the same factors, 20 names behave like a handful of bets. Portfolio construction decides how much of each idea’s edge reaches the portfolio.

This guide shows you how to calculate how many independent bets your book actually holds, how to build risk contribution in Excel, and where the process usually breaks inside an investment team.

Why Can 20 Great Ideas Still Make a Bad Portfolio?

A portfolio of 20 great ideas fails when the ideas share the same underlying risks. Four mechanisms cause this: hidden concentration, correlation between positions, sizing driven only by conviction, and common factor exposures. Each idea can be right on its own while the portfolio still carries one large, unintended bet.

The CFA Institute’s Level III curriculum treats position sizing as a core building block of portfolio construction. Sizing has to account for both risk and active weight. Stock selection sets the potential, and construction decides how much of it shows up in returns.

Mechanism	What it looks like	What it costs
Hidden concentration	17 of 20 names depend on the same spending cycle	One macro shift hits most of the book at once
Correlation	Different companies, same price behavior	Fewer independent bets than positions
Conviction-only sizing	The favorite idea is also the most volatile	One position drives most of the portfolio’s risk
Factor exposure	The book leans heavily into growth, momentum, or long duration	A factor reversal overrides stock-level theses

The common thread is that each idea is judged by itself. The portfolio question is what an idea adds to everything you already own.

How Many Independent Bets Do 20 Stocks Really Give You?

The number of independent bets in a portfolio falls quickly as the average correlation between holdings rises. Take 20 equally weighted stocks with an average pairwise correlation of 0.2. That portfolio behaves like about 4 independent bets, not 20. At a correlation of 0.4, it behaves like about 2.

The math in one formula

For N equally weighted stocks with the same volatility σ and the same average correlation ρ, portfolio volatility is:

σp = σ × √(1/N + (1 − 1/N) × ρ)

The approximate number of independent bets is:

Independent bets ≈ N / (1 + (N − 1) × ρ)

Both formulas assume identical volatilities and correlations. Real portfolios are messier, but the direction of the result holds.

Worked example (illustrative): 20 stocks, 5% weight each, 30% annual volatility per stock.

Average correlation (ρ)	Portfolio volatility	Independent bets
0.0	6.7%	20.0
0.2	14.7%	4.2
0.4	19.7%	2.3
0.6	23.6%	1.6

Moving from a correlation of 0.0 to 0.2 more than doubles portfolio volatility. Most of the diversification benefit is gone before correlations look high.

Why this caps your edge

The fundamental law of active management, developed by Richard Grinold and Ronald Kahn, states that the information ratio equals the information coefficient times the square root of breadth. Breadth is the number of independent decisions, not the number of positions.

Take a team whose skill per decision stays the same. With 20 truly independent bets, √20 ≈ 4.5. With 4.2 effective bets, √4.2 ≈ 2.0. Correlation cuts the expected information ratio by more than half, with no change in research quality.

The same pattern shows up at index level. The ten largest stocks reached a record 40.7% of the S&P 500 in 2025, compared with 18% to 23% between 1990 and 2015. By the end of 2024, the S&P 500 held about 46 effective stocks, measured as the inverse of the Herfindahl-Hirschman Index. That was the lowest level in 55 years.

Why Diversification Fails When You Need It Most

Diversification measured in calm markets overstates protection in a sell-off. Research on international equity markets found that correlations rise in bear markets but not in bull markets. A portfolio that looks diversified on trailing data can behave like one concentrated position during a drawdown.

Correlation depends on the market regime

François Longin and Bruno Solnik studied five major equity markets from 1958 to 1996. Their Journal of Finance paper found that correlation is tied to the market trend, not to volatility as such. Correlation increases in bear markets, which is exactly when diversification is supposed to work.

Crowding: when different funds are one trade

What the evidence shows: August 2007
In the week of August 6, 2007, quantitative long/short equity funds suffered large losses with almost no movement in broad markets. Amir Khandani and Andrew Lo traced the losses to a market-wide deleveraging of similarly built portfolios. The unwinds began in financial stocks, long book-to-market and short earnings momentum. Funds with different models turned out to hold the same trade.

Factor reversals

Momentum shows how fast a factor bet can turn. From March to May 2009, the past-loser decile of US stocks rose 163%, while the past-winner decile gained only 8%, according to Kent Daniel and Tobias Moskowitz. A book full of recent winners lost ground even where the company theses were intact.

Warning: Use stressed correlations, not trailing averages. Rerun your portfolio volatility with correlations from a drawdown period, or add a fixed stress uplift. If the result breaks your risk budget, the book is more concentrated than it looks.

Equal Weight Is Not Equal Risk: How to Calculate Risk Contribution in Excel

Risk contribution measures how much each position adds to total portfolio volatility. It equals the position’s weight times its marginal contribution to portfolio risk. In a correlated portfolio, a position with 25% of the capital can carry well over 25% of the risk. Risk contribution shows where the risk actually sits.

Worked example (illustrative): four stocks at 25% each.

Stock	Weight	Volatility
A	25%	20%
B	25%	25%
C	25%	35%
D	25%	45%

Stocks C and D form a technology cluster with a correlation of 0.7. All other pairs have a correlation of 0.2.

Step 1: Build the covariance matrix. With historical returns, use =COVARIANCE.S(returns_i, returns_j) for each pair. With assumed inputs, use covariance = σi × σj × ρij. For C and D, that is 0.35 × 0.45 × 0.7 = 0.11025.

Step 2: Calculate portfolio variance. With weights in a column range w and the matrix in Cov:

=MMULT(TRANSPOSE(w),MMULT(Cov,w))

In this example, portfolio variance is 0.0508 and portfolio volatility is 22.5%. In Microsoft 365, MMULT works as a dynamic array formula. In older versions, enter it as an array formula with Ctrl+Shift+Enter.

Step 3: Calculate each position’s marginal contribution. =MMULT(Cov,w) returns one value per stock.

Step 4: Calculate the percentage risk contribution. Multiply each weight by its marginal value and divide by portfolio variance:

=w*MMULT(Cov,w)/PortVar

Stock	Capital weight	Share of portfolio risk
A	25%	10.1%
B	25%	13.9%
C	25%	32.5%
D	25%	43.5%

Equal capital produced very unequal risk. C and D hold half the capital but carry 76% of the portfolio’s risk. A PM who trims D to fund a new idea in the same cluster has changed the label, not the risk.

Where Should Position Limits Come From?

Position limits for an equity portfolio come from three sources: the mandate, regulation, and the risk budget. No single cap such as “5% per stock” fits every portfolio. Rules of thumb in blogs and AI answers range from 3% to 10% because they ignore the mandate behind the limit.

The regulatory floor

The 1940 Act in one sentence
A US fund registered as “diversified” under Section 5(b)(1) of the Investment Company Act of 1940 may not, for 75% of its total assets, hold more than 5% of its assets in one issuer or more than 10% of that issuer’s voting securities.

The SEC staff report on diversified funds also describes the tax test for regulated investment companies (RICs). Section 851(b)(3) of the Internal Revenue Code caps a single issuer at 25% of total assets. Separate accounts and private funds follow their own mandate terms.

A risk budget, not a capital budget

Risk budgeting allocates the portfolio’s total risk appetite across positions, sectors, and factors. In practice, that means setting limits on clusters, not only on single names. A cap of 5% per stock does nothing if five stocks in one cluster carry 40% of the risk. Define the cluster first, then cap the cluster’s share of portfolio risk.

Why rules of thumb conflict

A 6% cap can be prudent in a 30-stock long-only fund and reckless in a levered long/short book. The right number depends on the benchmark, tracking-error target, liquidity, and the fund’s legal structure. Write the reasoning behind each limit down, so the limit can be defended in front of the investment committee.

Where the Portfolio Construction Process Breaks Inside an Investment Team

The portfolio construction process usually breaks at the handoff from analyst to portfolio manager. Analyst pitches evaluate the idea itself: thesis, valuation, catalyst, and downside. They rarely show what the idea adds to the existing book. The PM then has to work out correlation, exposure, and sizing on the fly.

Three fields every pitch should carry

In our assessment, a pitch template needs three portfolio fields next to the valuation:

1. Incremental exposure: which sector, theme, or factor exposure the position adds or duplicates.
2. Correlation to the book: the correlation to existing holdings, and to the largest cluster in particular.
3. Bear-case loss in portfolio terms: the downside at the proposed weight, stated as a percentage of the portfolio, not of the position.

A bear case of –40% on a 5% position costs the portfolio 2%. Stated that way, the committee discusses sizing, not only the story. A clear structure for a model memo makes these fields routine.

One shared exposure map

Each analyst sees their own sector. Someone has to own the view across all of them. An exposure map lists the economic drivers (rates, AI capex, consumer spending, credit cycle) and the holdings tied to each. One person maintains it, and the committee reviews it before every sizing decision.

Risk system output nobody reads

Commercial risk models such as Barra or Axioma produce factor exposures and risk contributions. The output only helps if the team can read it and act on it. A weekly report that nobody questions does not stop a cluster from growing. Teams that build the calculation once in Excel tend to understand the system output better, because they know what goes into it. If your team needs a shared standard here, see how we set up training for investment and finance teams, and how a structured model review process catches errors before they reach the committee.

Checklist for the next investment committee

• Each pitch states incremental exposure, correlation to the book, and bear-case loss in portfolio %
• The exposure map is current and has a named owner
• Risk contribution per position and per cluster is calculated
• Volatility is also shown with stressed correlations
• Every limit points to the mandate or the risk budget

When Concentration Is a Choice, Not a Mistake

Concentration is not a construction error when it is deliberate, measured, and within the mandate. Some strategies hold few names on purpose and accept higher volatility in exchange for higher expected active return. The problem is unintended concentration: risk the team did not choose and does not see.

Three cases call for a different standard:

• Concentrated funds by design: A 12-stock fund with a disclosed mandate is not under-diversified. It needs clear limits on clusters and liquidity instead.
• Small books: In a small sleeve, trading costs and monitoring time can outweigh the gain from additional names.
• Index-relative mandates: With a tight tracking-error target, the benchmark sets most of the exposure, and the key question becomes active risk.

The often-quoted number of positions also needs context. Meir Statman found that a well-diversified portfolio of randomly chosen stocks needs at least 30 stocks for a borrowing investor and 40 for a lending investor. That result assumes random selection. Hand-picked portfolios often have higher correlations, so the count says little without the correlation behind it.

How to Measure Whether Your Team’s Portfolio Construction Improved

A head of research can track portfolio construction with four measurable metrics: the effective number of stocks, the risk share of the largest cluster, the share of pitches with complete portfolio fields, and the sizing contribution versus an equal-weight version of the book. Together they show whether the process changes decisions.

Metric	How to calculate	What to watch
Effective number of stocks	1 / sum of squared weights (inverse HHI)	Trend over time, compared with the position count
Largest cluster’s risk share	Sum of risk contributions of the cluster	Stays within the risk budget
Pitches with portfolio fields	Pitches with all three fields / all pitches	Close to 100% after rollout
Sizing contribution	Actual return minus return of the same book at equal weight	Positive over several years

The inverse HHI only measures how capital is spread. It ignores correlation, so use it alongside risk contribution. On sizing, vendor data from Novus shows that the average hedge fund manager outperformed an equal-weighted version of their own portfolio by 0.38% per year. Managers who underperformed their equal-weight version lost an average of 1.56% per year. These figures come from a data vendor and are not an independent study.

FAQ

How many stocks do you need for a diversified portfolio?
It depends on correlation. Statman’s 1987 study found at least 30 to 40 randomly chosen stocks. Twenty correlated stocks can still behave like four independent bets.

Does a commercial risk model replace this analysis?
No. A risk model produces the numbers. The team still has to turn them into sizing decisions and limits, and that requires understanding how the numbers are built.

Should analysts or PMs own position sizing?
The PM decides the size. Analysts should deliver the inputs: incremental exposure, correlation to the book, and bear-case loss in portfolio terms.

What is the difference between active share and tracking error?
Active share measures how far the portfolio’s weights differ from the benchmark’s. Tracking error measures how far the returns differ. Two portfolios with the same active share can have very different tracking error, depending on correlation.

Is the HHI enough to measure concentration?
No. The Herfindahl-Hirschman Index measures only how weights are spread. It treats two highly correlated stocks as two separate positions, so pair it with risk contribution.

Conclusion

The quality of your ideas sets the potential. Portfolio construction decides how much of it reaches the portfolio.

Start with three steps, in this order:

1. Calculate the independent bets in your current book, using actual or stressed correlations.
2. Build risk contribution per position and per cluster in Excel.
3. Add the three portfolio fields to every pitch template before the next committee meeting.

Sources

1. CFA Institute: Active Equity Investing: Portfolio Construction (2026 Curriculum)
2. AnalystPrep: The Fundamental Law of Active Portfolio Management
3. RBC Wealth Management: The “Great Narrowing”: S&P 500 Concentration
4. Bridgeway Capital Management: How Many Stocks Are Effectively in the S&P 500?
5. Longin, F., and Solnik, B. (2001): Extreme Correlation of International Equity Markets, Journal of Finance 56(2)
6. Khandani, A. E., and Lo, A. W. (2011): What Happened to the Quants in August 2007?, Journal of Financial Markets 14(1)
7. Daniel, K., and Moskowitz, T. J. (2016): Momentum Crashes, Journal of Financial Economics 122(2)
8. U.S. Securities and Exchange Commission: Staff Report on the Threshold Limits Applicable to Diversified Funds
9. Statman, M. (1987): How Many Stocks Make a Diversified Portfolio?, Journal of Financial and Quantitative Analysis 22(3)
10. Microsoft Support: MMULT function
11. Novus: The Skill of Prediction: Hedge Fund Position Sizing
12. Featured image: AI-generated illustration created for this article. It does not show real people or a real company model.