Capital Asset Pricing Model
Calculate expected returns and understand systematic risk
1. The Risk-Return Trade-off
Why do stocks return more than Treasury bonds? CAPM (Capital Asset Pricing Model) answers this with elegant simplicity: higher risk = higher expected return. Developed by William Sharpe in 1964, CAPM revolutionized how investors price risk and became the foundation of modern portfolio theory.
💡 Core Formula
Beta (β) measures how much a stock moves with the market. Beta = 1 means it moves exactly with the market. Beta > 1 is more volatile (tech stocks). Beta < 1 is less volatile (utilities). The formula tells you the minimum return you should demand for taking on that level of systematic risk.
🧮 Interactive: CAPM Calculator
2. Decoding Beta
📊 Understanding Beta: The Core of CAPM
Beta (β) is the heart of CAPM. It quantifies how much a security moves relative to the overall market. If the S&P 500 rises 10% and your stock rises 15%, your beta is 1.5. If it only rises 5%, your beta is 0.5. Beta separates risk into two categories: systematic (market-wide, unavoidable) and unsystematic (company-specific, diversifiable). CAPM only prices systematic risk because rational investors can eliminate unsystematic risk through diversification.
Systematic vs Unsystematic Risk
Total risk = Systematic risk + Unsystematic risk. Systematic risk affects all securities (recessions, interest rates, inflation, wars). Unsystematic risk affects individual companies (CEO scandal, product failure, lawsuit). Diversification across 20-30 stocks eliminates ~90% of unsystematic risk. What remains is systematic risk, measured by beta.
Why CAPM only prices beta: If you can eliminate unsystematic risk for free (via diversification), the market won't pay you for bearing it. You're only compensated for systematic risk (beta) because it's unavoidable. A stock with high total volatility but low beta (β=0.5) has a lower expected return than a stable stock with high beta (β=1.5).
How Beta is Calculated
Beta measures the covariance between a stock's returns and market returns, divided by the market's variance. It's typically calculated using 3-5 years of monthly or weekly return data. The formula captures how much a stock moves with the market, normalized by how much the market moves with itself.
Interpretation: This stock has β = 1.5, meaning it typically moves 1.5x the market. When the market rises 10%, expect this stock to rise 15%. When the market falls 10%, expect it to fall 15%. The amplification works both ways—higher returns in bull markets, steeper losses in bear markets.
Interpreting Beta Values
Amplifies market movements. More volatile than the market. Typical for growth stocks, tech, small caps, emerging markets. Higher expected returns, but higher risk.
Moves in line with the market. Average systematic risk. Typical for diversified portfolios, blue chips, large-cap blend funds. Expected return = market return.
Dampens market movements. Less volatile than the market. Typical for utilities, consumer staples, bonds, REITs. Lower expected returns, but more stability.
No correlation with market movements. Systematic risk = 0. Expected return = risk-free rate. Examples: T-bills, money market funds, some hedge fund strategies.
Moves opposite to the market. When market falls, these assets rise. Very rare for stocks. Gold sometimes exhibits negative beta during crises (flight to safety). VIX derivatives have negative beta by design.
Historical Beta Examples: Crisis Stress Tests
Beta reveals its true nature during market crashes. High-beta stocks crash harder. Low-beta stocks hold up better. Here's how different beta categories performed during three major crises:
| Asset Type | Beta | 2008 Crisis | 2020 COVID | 2022 Bear |
|---|---|---|---|---|
| Tech Stocks (High Beta) | 1.5-2.0 | -55% | -40% | -35% |
| S&P 500 (Market) | 1.0 | -37% | -34% | -18% |
| Utilities (Low Beta) | 0.4-0.6 | -20% | -15% | -5% |
| Treasury Bonds | 0.1-0.2 | +5% | +8% | -12%* |
| Gold | -0.1 to 0 | +5% | +25% | -1% |
*2022 exception: Bonds fell due to Fed rate hikes (duration risk), not market beta. Shows CAPM's limitation—it doesn't capture interest rate risk for bonds. Data: Peak-to-trough returns during crisis periods. Tech = NASDAQ 100, Market = S&P 500, Utilities = XLU sector.
Beta Limitations & Considerations
Calculated from past returns (3-5 years). Company fundamentals change: Tesla's beta dropped from 2.0 (2018) to 1.3 (2023) as it matured. Past beta ≠ future beta. Use with caution for growth companies.
1-year beta ≠ 5-year beta. Short windows are noisy. Long windows include outdated data. Financial data providers use different lookback periods: Bloomberg (2Y weekly), Yahoo (5Y monthly). Check methodology.
Unlevered beta (asset risk) vs Levered beta (equity risk). Debt amplifies beta: βlevered = βunlevered × [1 + (1-tax rate) × Debt/Equity]. If company takes on more debt, equity beta rises even if business risk is unchanged.
Beta assumes constant correlation with market across all conditions. Reality: correlations spike to 1.0 during crashes (everything falls together). "Diversification fails when you need it most." Downside beta often > upside beta.
📊 Interactive: Beta in Action
🏭 Interactive: Sector Betas
Technology Sector
3. The Security Market Line
📈 The Security Market Line: Risk-Return Relationship
The Security Market Line (SML) is the graphical representation of CAPM. It plots expected return (Y-axis) against beta (X-axis). Every asset should fall on this line in an efficient market. Assets above the line are undervalued (offering excess return for their risk). Assets below are overvalued (insufficient return for their risk). The SML is the tool professional investors use to identify mispriced securities and generate alpha.
SML Equation & Components
Where the line crosses Y-axis (β=0). Typically 10-year Treasury yield (3-4%). The minimum return with zero systematic risk. All assets must offer at least Rf or investors buy Treasuries instead.
The reward per unit of beta. Historical S&P 500 ≈10%, minus Rf ≈3% = 7% premium. Rises during recessions (investors demand more), falls during booms (risk appetite increases).
Systematic risk of asset i. β=1 gives market return. β=2 gives market return + 1× market premium. Beta determines your position along the line.
The return investors should require for holding asset i. Not the actual return (that's realized later), but the fair compensation given the risk. Used for valuation and investment decisions.
Alpha: Measuring Mispricing
Alpha (α) is the difference between a security's actual return and its CAPM-expected return. It measures performance beyond what beta predicts. Positive alpha = outperformance (undervalued). Negative alpha = underperformance (overvalued). Active managers hunt for positive alpha, but most fail—only 20% beat CAPM benchmarks long-term after fees.
Security delivers more return than CAPM predicts. Undervalued— market hasn't fully priced its potential. Buy signal for value investors.
Security performs exactly as CAPM predicts. Fairly valued— no mispricing. Efficient market equilibrium. Index funds target zero alpha.
Security delivers less return than CAPM predicts. Overvalued— market has overpriced it. Sell signal or avoid.
Why alpha is hard to generate: If positive alpha exists, arbitrageurs buy the undervalued asset, driving price up until alpha = 0. Negative alpha triggers selling, driving price down until fair value. Markets are reasonably efficient, so persistent alpha is rare. Transaction costs, taxes, and fees eat most alpha.
Identifying Undervalued vs Overvalued Securities
Plot securities on the SML chart. Those above the line offer excess return (undervalued). Those below offer insufficient return (overvalued). The distance from the line = alpha magnitude. This is how portfolio managers screen thousands of stocks for investment opportunities.
Verdict: BUY. Market underpricing by 4%. Either stock has hidden value (strong fundamentals not yet recognized) or similar risk securities trade at 17%. Opportunity for excess returns.
Verdict: HOLD. Fairly priced. No excess return opportunity. Suitable for passive portfolio allocation, but not a value opportunity. Index fund exposure is just as good.
Verdict: SELL/AVOID. Market overpricing by 4.2%. Taking 1.6x market risk but only getting 11% return—worse than risk-adjusted fair value. Either price will fall, or it's riskier than beta suggests.
Practical application: Compare your portfolio holdings to SML. Sell assets below the line (negative alpha), buy assets above (positive alpha), hold assets on the line. Over time, this rebalancing should generate excess returns if your alpha estimates are correct.
Real-World Alpha Examples
Berkshire returned ~20% annually vs S&P 500's ~10%. Beta ≈0.9 (lower volatility than market). Alpha = 20% - [3% + 0.9×7%] = 20% - 9.3% = +10.7%. Sustained positive alpha for 58 years—statistically impossible without skill.
Magellan returned ~29% annually vs S&P 500's ~16%. Beta ≈1.1 (slightly more volatile). Alpha = 29% - [3% + 1.1×13%] = 29% - 17.3% = +11.7%. Best mutual fund track record in history. $18M fund → $14B under his tenure.
Average fund returned ~7% vs S&P 500's ~8.5%. Beta ≈1.0 (match market exposure). Alpha = 7% - [2% + 1.0×6.5%] = 7% - 8.5% = -1.5%. Negative alpha after fees. Only 20% of funds beat index.
SML vs Efficient Frontier vs CML
Three related but distinct concepts in portfolio theory. Understanding their differences prevents confusion:
📈 Interactive: Security Market Line
💰 Interactive: Is a Stock Fairly Priced?
4. Building Portfolios with CAPM
🎯 Portfolio Beta & Asset Allocation
CAPM isn't just for analyzing individual stocks—it's a powerful tool for building entire portfolios. Portfolio beta equals the weighted average of individual asset betas. This lets you dial risk up or down by adjusting allocations. Want market-level risk? Target β=1.0 (60% stocks, 40% bonds). Want half the volatility? Target β=0.5 (30% stocks, 70% bonds). CAPM makes portfolio construction mathematical and repeatable.
Portfolio Beta Calculation
Portfolio beta is the weighted sum of individual betas. Each asset's weight (% of portfolio value) multiplies its beta. Sum them up. This aggregate beta tells you how your entire portfolio will move relative to the market. It's the foundation for risk budgeting and strategic asset allocation.
Interpretation: This portfolio has 81.5% of the market's systematic risk. When S&P 500 moves 10%, expect this portfolio to move 8.15%. Expected return (using CAPM with Rf=3%, Rm=10%): 3% + 0.815×7% = 8.7%.
Key insight: You control portfolio beta through asset allocation, not by timing the market or picking stocks. Want higher returns? Increase weight of high-beta assets (stocks, growth). Need lower volatility? Increase weight of low-beta assets (bonds, cash, utilities). Beta is your risk dial.
Strategic vs Tactical Asset Allocation
Strategic allocation sets long-term target weights based on risk tolerance and time horizon (buy and hold). Tactical allocation makes short-term bets by deviating from strategic targets (market timing). CAPM supports both, but empirical evidence favors strategic allocation—90% of portfolio returns come from asset allocation policy, not security selection or timing.
Evidence favors strategic: Brinson study (1986, updated 1991) showed 91.5% of portfolio return variation comes from asset allocation policy, 4.6% from security selection, 1.8% from market timing. Message: Set your target beta, stick to it, rebalance mechanically. Don't try to time markets.
Age-Based Portfolio Rules
Traditional rule: Stock allocation = 100 - age. Modern version: 120 - age (accounts for longer lifespans). As you age, reduce beta (shift from stocks to bonds) because your time horizon shrinks and you can't recover from bear markets. CAPM provides the math—younger investors can handle higher beta for higher expected returns.
Rationale: 30-40 year horizon. Can ride out multiple bear markets. High beta captures long-term equity premium.
Rationale: 15-25 year horizon. Balance growth and stability. Can still recover from one major crash.
Rationale: 5-15 year horizon. Preservation > growth. Can't afford 30-50% drawdown before retirement.
Rationale: Living off portfolio. Minimize volatility. 30% stocks hedge inflation over 20-30 year retirement.
Target-date funds automate this: Vanguard Target Retirement 2060 (young investors) has β≈1.0 (90% stocks). Target Retirement 2025 (near retirees) has β≈0.4 (35% stocks). They automatically reduce beta as you age—glide path to lower risk. CAPM in action.
Rebalancing Strategies
Over time, winning assets grow and drift your portfolio beta above target (risk creep). Losing assets shrink and drift it below target. Rebalancing sells winners, buys losers, and restores target beta. It's a disciplined contrarian strategy that enhances returns by buying low and selling high mechanically.
Benefit: Sold stocks near highs ($72K → $64.8K), bought bonds near lows ($40K → $43.2K). If market crashes next year, you're protected. Studies show rebalancing adds 0.3-0.5% annual return over buy-and-hold.
Rebalance on fixed schedule: quarterly, semi-annually, or annually. Simple, disciplined, tax-lot friendly. Most common for 401(k)s and IRAs.
Rebalance only when allocation drifts beyond tolerance (e.g., ±5%). If target is 60/40, trigger at 65/35 or 55/45. More efficient—only trade when necessary.
Use new contributions to rebalance without selling. If stocks are overweight, direct all new money to bonds until balanced. Tax-efficient, no capital gains.
Capital Market Line: Combining Risky & Risk-Free Assets
The Capital Market Line (CML) shows the best possible portfolios: combinations of the market portfolio (β=1.0) and the risk-free asset (β=0). By mixing these two, you can achieve any desired beta. Want β=0.5? Hold 50% market, 50% T-bills. Want β=1.5? Use leverage—borrow at risk-free rate to buy 150% market exposure.
⚠️ Leverage amplifies losses. If market falls 30%, your 2x leveraged portfolio falls 60%. Margin calls can force liquidation at worst times.
📊 Interactive: Portfolio Beta Calculator
🎯 Interactive: Match Your Risk Profile
Recommended Portfolio for Moderate Investor
🔄 Interactive: Asset Type Comparison
5. Key Takeaways
CAPM is the Baseline
CAPM tells you the minimum return you should expect for a given level of systematic risk. If a stock's expected return is below CAPM, it's overpriced. If above, it might be underpriced (positive alpha) or riskier than beta suggests.
Beta Measures Systematic Risk
Beta captures how much a stock moves with the market. β > 1 amplifies market swings (tech stocks). β < 1 dampens them (utilities). β = 0 has no market correlation (gold, T-bills). You can't diversify away beta—it's the risk you're paid to bear.
Hunt for Positive Alpha
Alpha = Actual Return - CAPM Expected Return. Active managers try to generate positive alpha by finding mispriced securities. Most fail—studies show only 20% of active funds beat CAPM benchmarks long-term after fees. Positive alpha is rare and hard to sustain.
Portfolio Beta is Weighted Average
Your portfolio's beta = weighted average of individual betas. 60% stocks (β=1.2) + 40% bonds (β=0.2) = portfolio beta of 0.8. This lets you dial risk up or down. Young investors can handle higher beta. Retirees should target lower beta for stability.
CAPM Has Limitations
CAPM assumes markets are efficient, investors are rational, and beta captures all risk. Reality: markets aren't always efficient, behavioral biases exist, and other factors (size, value, momentum) also drive returns. Use CAPM as a starting point, not gospel.
Match Risk to Goals
Use CAPM to build portfolios that match your timeline and risk tolerance. Need money in 2 years? Target low beta (0.3-0.5). Saving for retirement in 30 years? Higher beta (1.2-1.5) captures long-term growth. CAPM helps you quantify the risk-return trade-off.