Interactive Tool
The trouble with picking stocks
Findings from real stock-level data that together make the case against hand-picking a few names. Adding stocks cuts risk, but only down to a floor you can't diversify away. More startling: most individual stocks actually underperform Treasury bills over their lifetimes, while a tiny handful create essentially all the market's wealth — miss those, and you miss everything. And even for a single stock, a "fair price" is slipperier than it looks: nudge one assumption and the value lurches.
Real stocks are positively correlated (typically 0.1–0.4), so they can't diversify to zero, only down to the market floor.
With 10 stocks you've removed 90% of the diversifiable risk (in variance terms). But you can never beat the 13.4% floor. That leftover is systematic risk, the same thing CAPM's beta prices.
Risk falls. Expected return doesn't.
This is the whole argument in one picture. The green risk curve falls steeply; the purple expected-return line sits flat, because a basket of stocks earns the average of what its stocks earn no matter how many it holds. So everything the green line sheds was risk nobody was paying you to carry. Most of it goes early — 20–30 stocks captures the bulk — and past that the curve flattens onto the floor you can't remove.
Expected return is the average outcome. Your typical one actually improves as you diversify, because a smoother ride loses less to volatility drag. Return 11.8%/yr, US stocks 1928–2025 (Aswath Damodaran, Historical Returns on Stocks, Bonds and Bills (NYU Stern).). Dots are the actual risk curve; hit “Real US stocks” to snap the model onto them. Calculated from CRSP data, © Center for Research in Security Prices, LLC, via WRDS.
Each thin line is one stock's noisy ups and downs; the bold line is your equal-weight portfolio. Add stocks and watch it steady, but never go flat. Method: the dotted reference curve is the real risk-vs-count relationship measured directly from individual US stocks (CRSP); the animated lines are a live illustrative draw around it.
How many stocks is enough?
Holding one stock is a gamble on one company; holding many averages the company-specific luck away. But the benefit fades fast: most of the diversification is captured in the first few dozen names, and no amount of adding removes the market risk they all share. You hit a floor: the undiversifiable risk you're actually paid to bear.
Why owning them all beats picking a few
Here's the catch that floor hides. Stock returns are wildly skewed: across decades, most stocks lose to T-bills, and a small percentage account for the entire equity risk premium. That makes stock-picking a game of trying to catch a few needles in a giant haystack, and missing them is the common case. Owning the whole haystack guarantees you hold the winners. It's the deepest argument for a broad index fund.
Prices, fair value, and the speculation end
The "What's a fair price?" tab shows why even careful valuation is fragile — a one-point change in assumed growth or the discount rate moves a DCF's "right answer" by double digits, which is why prices leap on small news and two honest analysts can sit far apart. And the options tab prices the purest form of speculation: drag the strike, expiry, and volatility until intrinsic value and time value finally click — and notice that an option's fair price already charges you for every hope it embodies. Educational only, not financial advice.
Sources & further reading
How this tool was made
Two halves. The diversification curve and the lifetime-return distribution behind “why a few win” are computed from real CRSP US common-stock records and shipped as aggregate tables. The fair-price and options tabs use no market data at all: they are a textbook two-stage DCF and the Black–Scholes formula, evaluated live on assumptions you choose.
Research
- Markowitz, H. (1952). “Portfolio Selection.” The Journal of Finance 7(1): 77–91. The founding paper of modern portfolio theory.
- Evans, J. L., & Archer, S. H. (1968). “Diversification and the Reduction of Dispersion: An Empirical Analysis.” The Journal of Finance 23(5): 761–767.
- Elton, E. J., & Gruber, M. J. (1977). “Risk Reduction and Portfolio Size: An Analytical Solution.” The Journal of Business 50(4): 415–437.
- Statman, M. (1987). “How Many Stocks Make a Diversified Portfolio?” Journal of Financial and Quantitative Analysis 22(3): 353–363.
- Bessembinder, H. (2018). “Do Stocks Outperform Treasury Bills?” Journal of Financial Economics 129(3): 440–457.
- Bessembinder, H., Chen, T.-F., Choi, G., & Wei, K.-C. J. (2023). “Long-Term Shareholder Returns: Evidence from 64,000 Global Stocks.” Financial Analysts Journal 79(3): 33–63.
- Black, F., & Scholes, M. (1973). “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81(3): 637–654. The Black–Scholes option-pricing formula.
- Merton, R. C. (1973). “Theory of Rational Option Pricing.” The Bell Journal of Economics and Management Science 4(1): 141–183.
Data
- CRSP US Stock Database, Center for Research in Security Prices, LLC, via WRDS. Source: CRSP®, Center for Research in Security Prices, Booth School of Business, The University of Chicago. Used with permission. All rights reserved. Accessed through WRDS under an academic subscription; only aggregate, non-identifiable statistics are published here — never a per-security series.
- Historical Returns on Stocks, Bonds, Bills & Real Estate — United States, Aswath Damodaran, NYU Stern School of Business. Annual series from 1928 (histretSP.xls), published by the author without stated usage terms; used with attribution.
Educational use only, not financial advice. Every figure traces back to the sources above or to the inputs you set — the full method and the source code are public.