Model explainer — theory, significance, and formulas.
Each model's background and principle in plain language, so newcomers to finance can follow along, followed in each section by how DIVA Quantizer implements it and how to use it.
Capital Asset Pricing Model (CAPM)
Where does your portfolio stand against the whole market?
CAPM holds that only risk that moves with the market is rewarded with expected return. On that basis, DIVA shows how sensitive your portfolio is to the market, how much of its risk is rewarded risk, and whether any return the market does not explain is left over.
The market does not pay for risk you can diversify away.
Risks like one company’s poor results shrink when you mix many assets. Risks that shake the whole market, like a recession, stay no matter how many holdings you add.
CAPM’s conclusion is simple. The market pays nothing for risk anyone can avoid by diversifying, so expected return is set only by how exposed you are to market risk you cannot avoid. The size of that exposure is market beta (β).
So two portfolios with the same beta have the same CAPM expected return. Whichever swings more has simply taken on more unrewarded risk.
DIVA shows market sensitivity and total risk together.
At the top of the result page, volatility, expected return and Sharpe show total risk and performance, and market beta and alpha show how you relate to the benchmark market.
“Expected return” here is the past average monthly return, annualized. It is a different number from the forward required return the CAPM formula gives.
The example portfolio’s market beta is 0.84. Over the analysis window, when the market’s excess return moved 1pp, it moved 0.84pp on average — the same amount of market risk as 84% in a market ETF and 16% in cash.
Markowitz’s tangency point becomes the market portfolio.
In the Markowitz explainer you saw the tangency point, where a line from the risk-free rate touches the efficient frontier: the mix with the most excess return per unit of risk.
Sharpe started from this: if every investor runs that calculation on the same information, everyone buys the same tangency portfolio. That portfolio then becomes the market portfolio, every risky asset held at its market-cap weight. The line from the risk-free rate through the market portfolio is the capital market line (CML), the best risk–return mix anyone can build.
Points on the line differ only in how much is in the market portfolio versus cash. The stretch to the right of the market portfolio assumes you borrow at the risk-free rate to invest more in the market.
DIVA widens the yardstick from your holdings to the whole market.
The curve on the Markowitz screen bounds the mixes you can build from your holdings. The curve on the CAPM screen bounds the mixes you can build from the whole market.
For the US market, DIVA draws it from Kenneth R. French’s 12 industries; for the Korean market, from every KRX stock sorted by DIVA into the same 12 industries. If you hold both, the two markets’ 24 industries are blended by your Korea–US weights. Each industry’s expected return uses the CAPM equilibrium value instead of its past average, so the curve touches the capital market line exactly at the market portfolio. Covariances between industries use a shrinkage estimate (Ledoit–Wolf), so noise from a short window does not exaggerate the curve.
The blue curve is the whole market’s efficient frontier and the dashed line is the capital market line. A portfolio point above the line shows green, below it red. At the same volatility, the example portfolio sits 4.55pp a year below the line.
The portfolio point uses the full window of the key metrics, while the curve and line use the months that overlap with market data, so the windows can differ slightly. Korean and mixed KR–US markets have no industry data, so only the line is drawn.
Beta, market share and alpha answer different questions.
Market beta answers how sensitive you were to the market; market share (R²) answers how much of your swings the market explains. With a similar beta, more swings unrelated to the market mean a lower market share.
Alpha (α) is the return left after taking out what market beta earns (Jensen, 1968). If you beat the market only by taking more market risk, alpha is close to zero. Alpha is an estimate, so whether it can be told apart from zero comes before its sign.
DIVA shows how risk is made up and where alpha came from.
The Risk split divides total risk into a market share and a stock-specific share. The specific share holds not only company news but also factors one market cannot explain, such as industries and interest rates. Beta contribution uses each holding’s (weight × market beta) to show which holdings raise your market sensitivity, and By holding compares beta, alpha and market share across holdings.
In the example, the market share is 72.6% and the specific share 27.4%. Building the same beta of 0.84 from a market ETF and cash alone would have meant volatility of just 13.3%, the market part. That gap is the unrewarded risk from 01. Part of the example’s specific share comes from moves outside the stock market, such as TLT (see 06).
The two shares split variance, so they add up to 100%; the two volatilities below do not simply add up.
| Holding | Weight | Market beta | Beta contrib. | Alpha (yr) | p-value | Market share (R²) |
|---|---|---|---|---|---|---|
TLT | 30.0% | 0.46 | 0.14 | −16.29% | 0.002 | 27% |
AAPL | 25.0% | 1.03 | 0.26 | +4.83% | 0.545 | 44% |
SPY | 25.0% | 0.97 | 0.24 | +1.02% | 0.192 | 99% |
MSFT | 20.0% | 1.00 | 0.20 | +3.30% | 0.710 | 37% |
The example’s alpha is −2.76% a year, with a p-value of 0.43. With 70 months of data and this much stock-specific swing, alpha would need to exceed ±7% a year to stand out from chance, so these numbers give too little evidence to judge. That does not make it zero. Portfolio alpha is the sum of each holding’s (weight × alpha), and most of this −2.76% came from TLT (−4.89pp).
Turning a theory of expected return into a regression on past data.
CAPM writes expected return as the risk-free return plus a reward for market risk.
With real data, beta and alpha are estimated by regressing each month’s excess return. The intercept α is Jensen’s alpha, and the coefficients minimize the sum of squared residuals ε (least squares).
The risk split uses this relation from the same regression.
How DIVA sets each term
- Rp
- Months in the last 6 years where all holdings and market data exist (min. 12 months). Your entered amounts set the weights on monthly holding returns.
- RM
- US = Kenneth R. French value-weighted stock market return · Korea = KRX market return computed by DIVA, delisted stocks included.
- KR–US mix
- One benchmark that blends both markets’ returns and the regression risk-free rate by your Korea–US weights.
- Rf,t
- The regression uses the monthly risk-free return from the market data source.
- Rf
- The capital market line and Sharpe use the site-wide current 13-week US T-bill rate (^IRX) (4.03% in the example).
- β · α
- Portfolio excess return is regressed on the same month’s market excess return. Alpha is marked significant when its p-value is below 0.05.
- Annualized
- Monthly mean return and alpha ×12, monthly volatility ×√12.
- Example window
- Key metrics 72 months; the CAPM regression uses the 70 months that overlap with market data (2020-11 to 2026-08).
Moments when CAPM helps
- 01Gauge how far you would fall in a market drop
Market shock scenarios multiply a market move by your beta; in the example, a −10% market means about −8.4%. The shaded band is ± one stock-specific volatility; if the swings are evenly spread, about two times in three you land inside it.
- 02You hold many names yet move just like the market
If the market share is high, adding names leaves your market exposure unchanged. To cut it, lower the market beta itself.
- 03Wonder whether beating the market was skill
Alpha and its significance strip out what market risk earns before you judge.
What to change after reading the result is in the CAPM guide. For weight efficiency within your holdings, see Markowitz; for size, value, profitability and investment factors beyond the market, see Fama–French.
One market cannot explain every move.
CAPM is an equilibrium model that assumes every investor shares the same expectations and trades without costs. Empirical studies have consistently found that low-beta assets earn more than CAPM predicts and high-beta assets less (Black, Jensen & Scholes, 1972). So low-beta portfolios tend to show a positive CAPM alpha.
Beta and alpha change with the analysis window and the benchmark market, and what one market cannot explain may include other common factors such as size and value.
Read the benchmark and the data window together.
The theory’s market portfolio holds every risky asset, bonds and real estate included, but DIVA uses the stock market in its place (Roll’s 1977 critique). So assets driven by factors outside stocks, such as bonds, show a low beta and a large specific share.
Mixed KR–US portfolios combine returns in their own currencies, so exchange-rate effects are left out, and the past is computed with the weights you enter today, so results can differ from an actual account’s realized performance. This analysis is for education and information, not investment advice.
References
- W. F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” Journal of Finance, 1964 · Market equilibrium, market risk and the capital market line
- M. C. Jensen, “The Performance of Mutual Funds in the Period 1945–1964,” Journal of Finance, 1968 · Risk-adjusted performance and alpha
- F. Black, M. C. Jensen, M. Scholes, “The Capital Asset Pricing Model: Some Empirical Tests,” 1972 · Empirical results for low-beta assets
- R. Roll, “A Critique of the Asset Pricing Theory’s Tests,” Journal of Financial Economics, 1977 · Limits of a market-portfolio proxy
- Kenneth R. French Data Library — Fama/French Factors · US market excess return and risk-free rate
- Kenneth R. French Data Library — 12 Industry Portfolios · The 12 industries behind the market-wide frontier
- Korea 12 industries — DIVA Quantizer calculation (all KRX stocks incl. delisted, DART industry codes) · The 12 industries behind the Korean market frontier
- O. Ledoit, M. Wolf, “Honey, I Shrunk the Sample Covariance Matrix,” Journal of Portfolio Management, 2004 · Shrinkage estimate of industry covariances
Now apply the theory to your own portfolio.
Enter your holdings and amounts to see the CAPM analysis as real numbers.