CAPM & Efficient Frontier
How diversification reduces risk and what the market pays for
If a portfolio holds ten assets instead of one, its risk isn't just the average of the ten risks. It depends on how those assets move relative to each other. That relationship is the core of modern portfolio theory.
The Efficient Frontier shows every possible combination of assets, plotting each portfolio's expected return against its risk. The frontier itself is the set of portfolios that offer the highest return for each level of risk — it's not possible to achieve higher return without accepting more risk.
The Capital Asset Pricing Model (CAPM) takes this further: it says the expected return of any asset depends on just one thing — its sensitivity to market movements, measured by beta.
Key concepts
Beta (β)
How much an asset moves relative to the market. β = 1 means it moves with the market. β > 1 means it's more volatile. β < 1 means less volatile.
Sharpe Ratio
Return above the risk-free rate per unit of risk. Higher is better. The “optimal” portfolio maximizes this ratio.
Efficient Frontier
The upper boundary of all possible portfolios. Any portfolio below the frontier can be improved — more return for the same risk, or less risk for the same return.
CAPM Formula
E(R) = Rf + β × (Rm − Rf). Expected return = risk-free rate + beta times the market risk premium.
Educational content only — not investment advice, recommendations, or a suggestion to act. Past performance is not indicative of future results. Your decisions are your own. Full disclaimer.
See it in action
What to notice:
- The cloud shape — portfolios cluster in a bullet pattern. The upper-left edge is the efficient frontier
- Individual assets (diamonds) usually sit below the frontier — diversification improves the risk/return trade-off
- The Max Sharpe portfolio (star) is where the line from the risk-free rate is tangent to the frontier
- Click Re-run — the frontier shape stays similar even with different random portfolios
When it works, when it doesn't
The insight that holds
Diversification reduces risk. This is mathematical, not opinion. As long as assets aren't perfectly correlated, combining them reduces portfolio volatility below the weighted average.
The limitation
CAPM assumes rational markets, stable correlations, and a single risk factor (beta). In reality, correlations spike during crises, multiple factors drive returns, and the “market portfolio” is impossible to observe precisely.
Your turn
Look at the Max Sharpe portfolio weights. Would you be comfortable with that allocation? The “optimal” portfolio is a mathematical construct — an actual allocation would also depend on the investor's time horizon, risk tolerance, and liquidity needs.
The lesson from the efficient frontier isn't to blindly follow the math — it's that diversification is the only free lunch in investing. You can reduce risk without reducing expected return, simply by combining assets that don't move in lockstep.
Reflect in your JournalWhat you've learned
- -The efficient frontier shows the best possible risk/return trade-offs — you can’t get more return without more risk once you’re on it.
- -Diversification reduces portfolio risk below the weighted average of individual risks — as long as assets aren’t perfectly correlated.
- -Beta measures sensitivity to the market. CAPM says expected return = risk-free rate + beta × market risk premium.
- -Alpha is the return above what CAPM predicts. Positive alpha is historically valuable but not guaranteed to persist.
- -Correlations are not stable — they tend to increase during market stress, exactly when diversification is needed most.
Want to test this?
Many experienced investors suggest practicing with a paper money account on a reputable broker before risking real capital. Many brokers offer free simulated trading environments where you can test strategies with real market data and no financial risk.
Paper trading lets you build confidence, understand execution, and see how a strategy behaves in real time — without the emotional weight of real money on the line.
Important
Everything on this platform is educational and didactic in nature. We do not provide investment advice, financial advisory, or recommendations to buy or sell any financial instrument. Past performance is not indicative of future results. All strategies shown are historical simulations for learning purposes only. Always do your own research and consult a qualified financial advisor before making investment decisions.
Educational content · Not investment advice or recommendations
We're educators, not advisors. Your decisions are your own. Disclaimer