Capital Asset Pricing Model (CAPM
### Modern Portfolio Theory (Sharpe, Lintner, Mossin): The Power of CAPM Developed by Nobel laureate William Sharpe, the **Capital Asset Pricing Model (CAPM)** describes the mathematical.
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📐 Formula
💡 Practical Example
For example, evaluating an aggressive tech stock with a 1.25 Beta against a 4.25% 10-Year Treasury yield and a 9.50% expected S&P 500 return (5.25% ERP) that delivered a 12.00% actual return: \(E(R) = 4.25\% + 1.25 \times (9.50 - 4.25)\% = \mathbf{10.81\%}\). The manager generated Jensen's Alpha of \ above the SML with a 6.20% Treynor Ratio.
📖 About Capital Asset Pricing Model (CAPM
Modern Portfolio Theory (Sharpe, Lintner, Mossin): The Power of CAPM
Developed by Nobel laureate William Sharpe, the Capital Asset Pricing Model (CAPM) describes the mathematical relationship between systematic risk and expected asset return:
- Systematic Risk (β): Risk that cannot be diversified away (inflation, interest rates, macroeconomic recessions). Investors are only compensated for taking on systematic risk.
- Unsystematic (Idiosyncratic) Risk: Company-specific risk (lawsuits, executive changes) that can be completely eliminated through proper portfolio diversification.
How to Use This Calculator
Enter your Risk-Free Rate (R_f in % - 10-Yr US Treasury Yield) (e.g. 4.25), Asset Equity Beta (β - Systematic Volatility Risk) (e.g. 1.25 (1.0 = Market Volatility)), Expected Market Benchmark Return (R_m in % - S&P 500) (e.g. 9.50), and Actual / Target Portfolio Return (% / year) [for Alpha] (e.g. 12.00). Results update instantly as you type — no submit button or page reload required. Adjust any value to compare scenarios side by side.
The Formula
Capital Asset Pricing Model (CAPM) & Modern Portfolio Theory equations: Market Risk Premium (ERP) = R_m - R_f Expected Return: E(R_i) = R_f + β_i × (R_m - R_f)'s Alpha (α) = R_actual - E(R_i) Ratio = R_actual - R_fβ_i Market Line (SML): Plots required return against systematic beta risk β
Worked Example
For example, evaluating an aggressive tech stock with a 1.25 Beta against a 4.25% 10-Year Treasury yield and a 9.50% expected S&P 500 return (5.25% ERP) that delivered a 12.00% actual return: E(R) = 4.25\% + 1.25 × (9.50 - 4.25)\% = 10.81\%. The manager generated Jensen's Alpha of \ above the SML with a 6.20% Treynor Ratio.
Understanding Your Result
A CAPM-derived cost of equity represents the minimum return investors require to hold the asset given its systematic (market) risk. Beta above 1.0 means the stock amplifies market moves; below 1.0 means it dampens them. WACC is the blended cost of capital used to discount cash flows in DCF valuation — higher WACC lowers present value of future cash flows. For most stable public companies, WACC ranges from 6–10%; for high-growth or distressed companies, 12–20%.
💡 Financial Planning: Expert Principles & Risk Awareness
- All calculations assume fixed rates and idealized conditions. Real-world results vary due to market volatility, inflation, fees, and taxes.
- The Consumer Financial Protection Bureau (CFPB) recommends consulting a certified financial planner (CFP) for decisions involving significant sums.
- Run at least three scenarios: optimistic, pessimistic, and most-likely — to understand the full range of potential outcomes before committing.
- Inflation averages 2–3% annually in the US (Federal Reserve target). Long-term projections that ignore inflation significantly overstate future purchasing power.
- Tax treatment varies widely by account type (IRA, 401k, brokerage), jurisdiction, and income level. Verify tax implications with a CPA before acting.
- Compound interest works for you in savings/investments and against you in debt. The difference of even 1% in rate, sustained over decades, is enormous.
- Emergency funds (3–6 months of expenses) should be established before optimizing for returns — financial security precedes financial growth.
- Financial projections older than 12 months should be recalculated. Interest rates, tax brackets, and market conditions shift materially year to year.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.