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Educational content only — not financial, tax, or investment advice. In active development — how it's built and checked

Interactive Tool

How markets price risk

Diversification leaves one risk you can't escape: the market's. The Capital Asset Pricing Model says that's the only risk you're paid for, and prices every asset by a single number: its beta. But decades of data showed beta wasn't the whole story, so Fama and French added more factors. Meet both, in order: one risk, then many.

Pick a view — risk and return, step by step

The big idea

Each dot is a real US asset class, 1928–2025, placed by how much it bounced around (risk) and what it returned. They line up: to earn more, you had to accept more risk. One catch, and it is the whole game — only risk you can't diversify away pays. Every dot here is an entire asset class, so the risk of any single company inside it has already been diversified out. Buying one volatile stock does not put you on this line.

At about 20% volatility, history paid roughly10.7%/yrnominal — on this line, each extra point of volatility added about 0.41 of a point of return

Method: nominal annualized return and volatility of annual returns, Damodaran US data (1928–2025). The line is fit through the core asset ladder; gold is shown but left out of the fit. Educational only, not advice.

More risk you can't diversify away, more reward — the century-long pattern

0%5%10%15%20%0%10%20%30%40%T-bills (cash): 3.4% return, 3% volatilityT-bills (cash)Treasury bonds: 4.8% return, 8% volatilityTreasury bondsCorporate bonds: 6.9% return, 8% volatilityCorporate bondsUS stocks: 11.8% return, 19% volatilityUS stocksSmall-cap value: 17.8% return, 38% volatilitySmall-cap valueGold: 7.4% return, 22% volatilityGoldRisk (volatility) → · return on the vertical axis
Asset classes Risk/return line Off the line (paradox)

From cash at the bottom-left to small-cap value at the top-right, more volatility came with more return. The open marker is where your chosen risk level lands on that line.

Watch it play out: the growth of $1 over a lifetime

$1$10$100$1.0k$10k$100kstartyr 20yr 40yr 60yr 80$12k$77$26Years invested → · growth of $1 (log scale, nominal)
US stocks Treasury bonds T-bills (cash) Inflation

Each line is one hypothetical path drawn at that asset's real long-run volatility — the higher the volatility, the wilder the squiggle. Stocks lurch around and pull far ahead; cash barely moves, and barely grows. Flip to Historical to swap this model for real-return Monte Carlo. Log scale (every gridline is 10×), nominal dollars; the dashed line is inflation — what $1 needed to keep its purchasing power.

The catch: this only holds when you're diversified. These lines are broad, whole-market indices, and CAPM only pays you for the market risk you can't diversify away. Hold a single, undiversified stock and you take on a pile of extra risk that earns nothing on average — most individual stocks have historically trailed even T-bills, with a handful of winners carrying the whole market. This describes the basket, not the ticket. (See Stock-Picking.)

This upward slope is the entire premise of investing — and of this site. Nobody hands you return for free; it's the compensation for holding assets that can fall, sometimes hard. Cash returned 3.4% at almost no risk; small-cap value returned 17.8% but with gut-wrenching 38% swings.

The catch — the low-beta paradox. The line is flatter than you'd guess, and the extra risk isn't always paid for. Gold carries stock-like volatility (22%) for a bond-like return (7.4%), sitting well below the line. And inside the stock market the puzzle is sharper still: the lowest-volatility, lowest-beta stocks have historically delivered better risk-adjusted returns than the wild ones — the opposite of what simple theory predicts. Switch to the CAPM tab and flip on the real US data to see that same line come in too flat. The lesson: risk is necessary for return, but piling on the most volatile bets is not sufficient. Educational only, not advice.

One level up: which region wins is anyone's guess

US · 15% vol11.8%/yr
Developed ex-US · 16% vol7.4%/yr
Emerging · 21% vol10.2%/yr

All three are broad, diversified, CAPM-consistent equity — bearing market risk they should be paid for. Yet since 1990–2026 the US delivered the most return at the least risk ("US exceptionalism"), while developed international lagged despite higher volatility. Realized returns over any one window drift from the clean line, and leadership rotates: the US led the 2010s, international the 2000s, Japan was once a third of the world. You can't call the next winner — which is the whole case for owning them all in proportion. See Home Bias →

Realized nominal annual return & volatility of each region's broad market, 1990–2026. Data: Ken French Data Library.

CAPM: the price of market risk

Once you've diversified away company-specific risk, what's left is exposure to the market itself, captured by beta. CAPM says an asset's fair expected return is just the risk-free rate plus its beta times the market's risk premium. Nothing else should be rewarded. Measure beta from a scatter of returns, and it sets the fair return on the Security Market Line.

Factors: beyond beta

In the data, small stocks, cheap "value" stocks, and profitable, conservative firms all earned more than their beta could explain. Fama and French turned those persistent patterns into extra factors (size, value, profitability, investment), and what CAPM called mysterious "alpha" became exposure you can dial on purpose. The lesson isn't that CAPM was wrong, but that "the market" is one of several kinds of compensated risk. Educational only, not financial advice.

Sources & further reading

How this tool was made

Nothing here is assumed — every plotted figure is estimated from real data: asset-class risk and return from long-run historical series, the security market line from realized betas and returns, and the size, value, profitability, and investment premia from the Fama–French factor library. Your sliders re-run the models against those estimates in the browser. Two honest caveats on the numbers themselves: premia have run materially smaller since their discovery (McLean–Pontiff), and the long series is US-only — the best-performing major market of the century (Dimson–Marsh–Staunton) — so treat historical premia as upper bounds.

Research

  • Treynor, J. L. (1962). “Toward a Theory of Market Value of Risky Assets.” Unpublished manuscript, 1962; published in R. A. Korajczyk (ed.), Asset Pricing and Portfolio Performance, Risk Books, 1999, pp. 15–22.
  • Sharpe, W. F. (1964). “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” The Journal of Finance 19(3): 425–442.
  • Lintner, J. (1965). “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” The Review of Economics and Statistics 47(1): 13–37.
  • Mossin, J. (1966). “Equilibrium in a Capital Asset Market.” Econometrica 34(4): 768–783.
  • Fama, E. F., & MacBeth, J. D. (1973). “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy 81(3): 607–636.
  • Fama, E. F., & French, K. R. (1992). “The Cross-Section of Expected Stock Returns.” The Journal of Finance 47(2): 427–465.
  • Fama, E. F., & French, K. R. (1993). “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33(1): 3–56. The three-factor model.
  • Fama, E. F., & French, K. R. (2015). “A Five-Factor Asset Pricing Model.” Journal of Financial Economics 116(1): 1–22.
  • Jegadeesh, N., & Titman, S. (1993). “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” The Journal of Finance 48(1): 65–91. Documents the momentum effect.
  • Carhart, M. M. (1997). “On Persistence in Mutual Fund Performance.” The Journal of Finance 52(1): 57–82. Adds momentum as a fourth factor.
  • McLean, R. D., & Pontiff, J. (2016). “Does Academic Research Destroy Stock Return Predictability?” The Journal of Finance 71(1): 5–32. Across 97 published predictors, returns run ~26% lower out of sample and ~58% lower after publication — the reason historical factor premia are upper bounds, not entitlements.
  • Dimson, E., Marsh, P., & Staunton, M. (2002). Triumph of the Optimists: 101 Years of Global Investment Returns. Princeton University Press.

Data

  • Kenneth R. French Data Library, Tuck School of Business, Dartmouth College. Data © Eugene F. Fama and Kenneth R. French. The library publishes no formal license; we ship derived series (daily market returns, regional monthly returns, factor summaries) with attribution, not the library's files.
  • AQR Factor & Quality-Minus-Junk / Betting-Against-Beta datasets, AQR Capital Management. Datasets 'Quality Minus Junk: Factors, Monthly' and 'Betting Against Beta: Equity Factors Data, Monthly'. AQR's site terms prohibit reproducing or publishing its content without written consent, so the series are not redistributed: only a handful of long-run annualized summary figures (facts about the factors) are quoted here, with attribution to AQR and to the underlying papers.
  • Liquidity factor (traded), Ľuboš Pástor & Robert F. Stambaugh. The traded liquidity factor (LIQ_V) of Pástor & Stambaugh (2003), monthly from January 1968, from Ľuboš Pástor's Chicago Booth data page. No usage terms are published; we ship its long-run annualized premium only.
  • 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.

Next in the playground → Can You Outsmart the Market? Five bets against the market (predicting it, timing it, deploying into it, hiring active managers, and trusting they're really active) — then the industry's own SEC-filed cash register delivering the same verdict. The whole case for indexing.