What’s the difference between “Market Return” and “Risk Premium” input modes?

In “Market Return,” you provide the market’s expected total return and the tool derives the premium as (market return − risk-free rate). In “Risk Premium,” you provide the premium itself. Both modes use the same formula: expected return = risk-free rate + beta × premium.

Can you show a quick example?

Yes. With risk-free rate = 2%, market return = 8%, and beta = 1, the premium is 6%, so expected return = 2% + 1 × 6% = 8%.

How are unusual inputs handled (e.g., beta = 0, negative beta, or premium)?

Beta is treated as a real number: beta = 0 yields expected return = risk-free rate; beta < 0 inverts exposure so the premium subtracts from the risk-free rate; a negative premium (bearish expectations) reduces expected return. No caps or floors are applied; the result can be below the risk-free rate.

How are units, rounding, and display managed?

Inputs/outputs are percentages (e.g., enter 2 for 2%). Internally, calculations use decimal fractions (0.02) and results are rounded with round-half-even (“banker’s rounding”). Display precision is applied only at the end; intermediate steps keep full precision.

CAPM Calculator - Expected Return

Q: How are units, rounding, and display managed?

Inputs/outputs are percentages (e.g., enter 2 for 2%). Internally, calculations use decimal fractions (0.02) and results are rounded with round-half-even (“banker’s rounding”). Display precision is applied only at the end; intermediate steps keep full precision.

CAPM Calculator (Capital Asset Pricing Model)

Estimate the expected return on equity using CAPM: Re = Rf + Beta × (Rm – Rf). Enter either the market return (Rm) or the market risk premium directly.

Input Mode

Provide expected market return (Rm) and risk-free rate (Rf). Premium is computed as Rm – Rf.

Risk-free Rate (Rf)

Equity Beta (β)

Expected Market Return (Rm)

Market Risk Premium (Rm – Rf)

Results

Expected Return (Re) %
Risk-free Rate (Rf) %
Market Risk Premium (Rm – Rf) %
Risk Premium Contribution (β × Premium) %

Formula

Re = Rf + β × (Rm − Rf)
Equivalent form
Re = Rf + β × Premium

Where Rf = risk-free rate, Rm = expected market return, Premium = equity risk premium (Rm − Rf), β = asset beta.

Inputs

Risk-free rate (Rf)
Beta (β)
Choose one:
- Expected market return (Rm), or
- Equity risk premium (Premium = Rm − Rf)

Outputs

Expected return (Re)
Risk-free rate (Rf)
Market risk premium (Rm − Rf) or entered Premium
Risk premium contribution: β × Premium
Visual return breakdown

CAPM Calculator — Inputs & Output Guide
Field	What it is / How to use	Where to get it	Typical range*	Impact on result
Risk-free rate (Rf)	Yield on a default-free bond in the same currency and time horizon as your expected return (usually 10-year government bond).	Central bank / Treasury site, investing data portals.	Developed markets ~1–6% (historically 0–8%).	+1% to Rf → +1% to expected return, one-for-one.
Beta (β)	Sensitivity of the asset to the market (use levered beta for equity). If unsure, use sector beta as a proxy.	Finance sites (Yahoo/Reuters), company filings, your regression.	Most stocks ~0.5–1.8 (can be <0 or >2).	Higher β amplifies the market risk premium effect.
Market return (Rm)	Expected broad-market total return (price + dividends). Use forward estimate or long-run average.	Equity risk premium studies, index providers, your model.	Often ~6–10%/year (US long-run).	Increases expected return via (Rm − Rf).
Market risk premium (MRP)	Shortcut input if you don’t have Rm: MRP = (Rm − Rf). Use one of: either Rm or MRP, not both.	Damodaran/ERP reports, house view.	Developed markets ~3–7%.	Bigger MRP → higher expected return.
Currency & period	Match currency and compounding across Rf, Rm/MRP, and output (e.g., all annual, same currency).	Your calculator settings.	Annual, local currency (common).	Mismatches distort results; keep consistent.
(Optional) Adjustment	Size/liquidity/country add-on or alpha. Keep 0 for “pure” CAPM.	Analyst judgment / policy.	−2% to +2% (typical).	Shifts result directly, +/− the add-on.
Expected return (Re)	Output: required equity return. Plain-text formula: Re = Rf + β × (Rm − Rf) or Re = Rf + β × MRP.	Calculated by the tool.	Varies by inputs.	Use as cost of equity (feed into WACC if needed).
*Ranges are indicative, not guarantees. Keep inputs consistent: same currency, same horizon, same compounding basis.

How to Use the CAPM Calculator

Follow these steps to calculate expected return (Re) with market return or directly with the market risk premium.

Choose the input mode
Select Market Return if you have the expected market return (Rm) and the risk-free rate (Rf). Choose Risk Premium if you already know the market risk premium (Rm − Rf). Don’t mix modes—enter values only for the fields shown for your selection.
Enter the risk-free rate (Rf)
Type the current government bond yield (e.g., a 3–10 year Treasury) that matches your return horizon. Enter as a percent number, e.g., 2.5 for 2.5%. Keep period consistency (annual Rf with annual Rm/premium). Avoid entering 0.025 or using commas—use 2.5, not 2,5.
Set the equity beta (β)
Input the stock or portfolio beta (unitless), typically found on broker research pages or finance sites. Use a plain number like 1.2; values below 0 or far above 2 may indicate a niche or data issue. Don’t paste a percentage—beta is not a %.
Enter expected market return (Rm) or premium
If in Market Return mode, type the market’s expected annual return (e.g., 8). If in Risk Premium mode, type the market risk premium directly (e.g., 5.5). Ensure the figure is in percent terms and aligned with Rf’s period; don’t mix arithmetic means with monthly inputs.
Review results and breakdown
The calculator shows Expected Return (Re), Risk-free Rate (Rf), Market Risk Premium (Rm − Rf), and β × Premium. Use Show decimals if you need more precision for reporting or rounding checks. Compare Re to your hurdle rate or WACC inputs when using CalcMastery in budgeting or valuation.

Tip: Enter percentages as plain numbers (e.g., 7.5, not 0.075) and keep all rates on the same time basis (annual with annual).

Frequently Asked Questions

It computes an asset’s expected return using the Capital Asset Pricing Model: expected return = risk-free rate + beta × (market return − risk-free rate). You can enter either the market return or the market risk premium directly.
In “Market Return,” you provide the market’s expected total return and the tool derives the premium as (market return − risk-free rate). In “Risk Premium,” you provide the premium itself. Both modes use the same formula: expected return = risk-free rate + beta × premium.
Yes. With risk-free rate = 2%, market return = 8%, and beta = 1, the premium is 6%, so expected return = 2% + 1 × 6% = 8%.
Beta is treated as a real number: beta = 0 yields expected return = risk-free rate; beta < 0 inverts exposure so the premium subtracts from the risk-free rate; a negative premium (bearish expectations) reduces expected return. No caps or floors are applied; the result can be below the risk-free rate.
Inputs/outputs are percentages (e.g., enter 2 for 2%). Internally, calculations use decimal fractions (0.02) and results are rounded with round-half-even (“banker’s rounding”). Display precision is applied only at the end; intermediate steps keep full precision.

Methodology & Sources

The tool evaluates the single-factor CAPM in plain text form: expected return = risk-free rate + beta × (market return − risk-free rate). In “Risk Premium” mode, the provided premium replaces the parenthetical term. All rates are interpreted as annual percentage rates; internally they are converted to decimal fractions for computation and converted back to percentages for display. Rounding follows NIST SP 811 round-half-even and occurs only on the final displayed values to avoid compounding rounding error. Beta is dimensionless and may be any real value; no constraints are imposed, so negative or zero beta and negative premiums are computed as entered. If any required input is missing or non-numeric, no result is produced.

Bibliography

William F. Sharpe (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk — Wiley for the American Finance Association https://doi.org/10.1111%2Fj.1540-6261.1964.tb02865.x
Accessed 2025-10-20
John Lintner (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets — The MIT Press https://doi.org/10.2307%2F1924119
Accessed 2025-10-20
Jan Mossin (1966). Equilibrium in a Capital Asset Market — Wiley for the Econometric Society https://doi.org/10.2307%2F1910098
Accessed 2025-10-20
Barry N. Taylor; Ambler Thompson (2019). NIST Guide to the SI (Special Publication 811) — Rounding and Number Presentation — National Institute of Standards and Technology (NIST) https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-1-introduction
Accessed 2025-10-20

CAPM Calculator (Capital Asset Pricing Model)

Results

Formula

Inputs

Outputs

How to Use the CAPM Calculator

Choose the input mode

Enter the risk-free rate (Rf)

Set the equity beta (β)

Enter expected market return (Rm) or premium

Review results and breakdown

Frequently Asked Questions

Methodology & Sources

Bibliography

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