The CAPM calculator above applies the capital asset pricing model: required return equals the risk-free rate plus beta multiplied by the equity risk premium. It accepts either an expected market return or a premium directly, breaks the answer into its risk-free and risk-bearing components, and shows what discounting at that rate does to a sum of money over a horizon you set. Every rate is an input, because every one of them changes and none of them can honestly be baked into a web page.
Arb Digital publishes free finance calculators that name the model they use and state what it assumes. CAPM deserves that treatment more than most, because it is simultaneously the most widely taught model in finance and one of the most heavily criticised. A page that returns a cost of equity without saying what stands behind it is not being helpful.
What This CAPM Calculator Does
The model was developed independently by William Sharpe, John Lintner and Jan Mossin in the mid-1960s, building on Harry Markowitz's portfolio theory, and Sharpe and Markowitz shared the 1990 Nobel Memorial Prize in Economic Sciences largely for it. Its claim is narrow and precise: in equilibrium, the only risk an investor is compensated for is the part that cannot be diversified away, and beta measures exactly that part.
You enter three things. The risk-free rate is the return on an asset assumed to carry no default risk, usually a government bond of a term matching the horizon of the decision. Beta is the sensitivity of the asset's returns to the market's, obtained by regression — a beta of 1.2 means the asset historically moved 20 per cent more than the index in both directions. The equity risk premium is the extra return the market as a whole is assumed to offer over the risk-free rate.
The tool multiplies beta by the premium, adds the risk-free rate, and reports the result. It then shows the two components separately, because seeing how much of a required return is simply the bond yield and how much is compensation for risk changes how the number reads. The last box discounts 100 units of currency over your chosen horizon at that rate, which is the operation the cost of equity actually exists to perform.
This page sits next to the beta calculator, which produces the beta input from return data, and the WACC calculator, which blends the cost of equity this page gives with a cost of debt to get a whole-company discount rate. The boundary is clean: beta in, required return out, and that required return is one of the two ingredients WACC needs.
How to Use It
- Take the risk-free rate from a current government bond quote. Match the term roughly to the horizon of your analysis. A ten-year valuation conventionally uses a ten-year yield rather than an overnight rate.
- Source beta deliberately. Published betas differ depending on the index, the period and the return frequency used in the regression. Note which one you took and why, because the choice moves the answer.
- Decide whether you hold a market return or a premium. Switch the selector to match. Entering a premium into a field the tool is treating as a market return will understate the answer badly.
- Leave the additional premium at zero unless you can justify it. Size and country adjustments are common in practice but are not part of the published model, and they are an easy place to smuggle in a desired answer.
- Test the sensitivity before you rely on the figure. Move the premium by a percentage point and watch the required return move by beta times that amount. That range is the honest output, not the single number.
The Formula and a Worked Example
The model is E(R) = Rf + β(E(Rm) − Rf), where Rf is the risk-free rate, β is the asset's beta and the bracketed term is the equity risk premium. Plotted with beta on the horizontal axis, it is a straight line called the security market line, with intercept Rf and slope equal to the premium.
Work the defaults through. With a risk-free rate of 4.2 per cent and an expected market return of 9 per cent, the equity risk premium is 9 − 4.2 = 4.8 per cent. A beta of 1.2 scales that to 1.2 × 4.8 = 5.76 per cent of risk compensation. Adding back the risk-free rate gives a required return of 9.96 per cent. Discounting 100 units over ten years at 9.96 per cent gives about 38.69, so a payment of 100 a decade out is worth under 39 today at this rate.
Two edge cases are worth understanding. A beta of zero returns the risk-free rate exactly, because the model says uncorrelated risk earns no premium. A negative beta returns less than the risk-free rate, which looks wrong until you see the logic: an asset that reliably rises when the market falls is valuable as insurance, so investors accept a lower expected return to hold it. MIT's open courseware for Finance Theory I covers the derivation and the security market line in full, with lecture slides on both portfolio theory and CAPM.
The Assumptions the Model Rests On
CAPM is an equilibrium model, and equilibrium models buy their tidiness with assumptions. These are the ones that matter, and none of them holds exactly.
A single source of risk. The model says one factor — co-movement with the market — explains the whole risk premium. Decades of research have found other characteristics that appear to carry premia as well, which is why multi-factor models exist at all. If those effects are real, a single-beta figure is incomplete by construction.
A stable beta. Beta is estimated from past returns and then used as though it describes the future. It is not stable. A company that changes its leverage, its business mix or its size can see beta move substantially, and the estimate itself carries a standard error that is rarely quoted alongside it.
Investors can borrow and lend at the risk-free rate, hold the same expectations, face no taxes or transaction costs, and trade a market portfolio that in principle includes every asset in existence. In practice the market portfolio is proxied by a stock index, which leaves out property, private business, human capital and much else — a substitution known to be imperfect since Roll pointed it out in 1977.
Volatility stands in for risk. Beta measures co-movement in prices, so it treats an upward surprise the same as a downward one and says nothing about the chance of permanent loss. The SEC's investor education page on risk lists business risk, inflation risk, interest rate risk and liquidity risk as separate categories, and a single beta collapses all of them into one number or ignores them entirely.
Why the Inputs Dominate the Output
The arithmetic here is trivial. The difficulty is entirely in the three numbers, and the spread of defensible values for each is wide enough that two careful analysts can produce required returns several percentage points apart for the same company without either of them doing anything improper.
The equity risk premium is the worst offender. Historical estimates depend on the country, the period, the index and whether an arithmetic or geometric average is used, and forward-looking estimates depend on a model of their own. Published figures commonly sit anywhere between about 3 and 7 per cent. At a beta of 1.2, that range alone moves the required return by nearly five percentage points.
Beta adds its own spread. The same stock can carry noticeably different published betas depending on whether the regression used weekly or monthly returns, two years of history or five, and which index served as the market. Some providers apply a shrinkage adjustment toward one; others do not.
The practical response is not to hunt for the correct value, because there isn't one. It is to compute a range, state the inputs alongside the output every time the figure is quoted, and see whether the decision the number feeds actually changes across that range. If it does, the model is not settling the question. If you are using the result inside a valuation, the NPV calculator and the present value calculator will show you directly how sensitive the answer is to the discount rate.
What the Number Is Actually For
Required return has two everyday uses, and they are different enough to be worth separating. In corporate finance it is the cost of equity: the return shareholders are assumed to demand, which becomes the equity leg of a weighted average cost of capital and then the discount rate in a valuation. Combined with a cost of debt from the cost of debt calculator, it feeds straight into WACC.
In portfolio analysis it is a benchmark. The difference between an asset's realised return and its CAPM required return is Jensen's alpha, a measure of performance relative to the risk taken. That is a description of what already happened, computed after the fact, and it is a statement about a past period rather than a claim about a future one.
What the number is not is a forecast. CAPM does not say the asset will return 9.96 per cent. It says that under a specific set of assumptions, an investor bearing that much non-diversifiable risk would require that much to hold it. Whether the asset delivers it depends on events the model does not attempt to describe. Risk-adjusted performance measured a different way is available in the Sharpe ratio calculator, which uses total volatility rather than beta.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering a market return where a premium belongs — the two differ by the whole risk-free rate, and mixing them up understates the required return substantially.
- Quoting the output without its inputs — a required return means nothing on its own. The premium and beta behind it have to travel with it, or the figure cannot be checked.
- Treating beta as a fixed property — it is a regression estimate with a standard error, and it shifts with leverage, business mix and the period sampled.
- Reading the result as an expected return — it is what the model requires given the assumptions, not a prediction of what the asset will deliver.
- Adding size or country premia without saying so — those adjustments sit outside the published model and are the easiest place for a desired answer to enter unnoticed.
Related Free Tools From Arb Digital
Produce the beta input with the beta calculator, then blend this cost of equity into a full discount rate with the WACC calculator and the cost of debt calculator. For probability-weighted rather than model-based returns there is the expected return calculator, and for risk-adjusted performance the Sharpe ratio calculator. Discounting work is handled by the NPV calculator and the present value calculator, while realised outcomes are measured by the stock return calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Required return equals the risk-free rate plus beta multiplied by the equity risk premium, where the premium is the expected market return minus the risk-free rate. Plotted against beta it forms the security market line.
In corporate finance the two terms are used for the same number. CAPM is the most common way of estimating a cost of equity, and that figure then becomes the equity leg of a weighted average cost of capital.
Conventionally a government bond yield with a term close to the horizon of the analysis. It is a market figure that moves daily, so it has to be taken from a current quote rather than from memory or from a stored value on any web page.
Because an asset that tends to rise when the market falls reduces the risk of a portfolio. The model says investors will accept a lower expected return for that hedging property, so the required return falls below the risk-free rate.
There is no single accepted value. Estimates vary with the country, the historical period, the index and the averaging method, and published figures commonly span several percentage points. The honest approach is to compute a range rather than to defend one number.
That it uses a single factor when other characteristics appear to carry premia, that beta is unstable and estimated with error, that the true market portfolio cannot be observed, and that volatility is a poor stand-in for the risk of permanent loss.
No. It states what return the model requires for the level of non-diversifiable risk the inputs describe. Realised returns depend on events the model makes no attempt to forecast.
The beta calculator measures an asset's sensitivity to an index from return data and stops there. This page takes that beta as an input and converts it into a required return by combining it with a risk-free rate and a market premium.
This tool is provided for information and education only and is not investment advice, a recommendation, a valuation, or a price target. It computes one published model whose assumptions are widely disputed, and its output is driven almost entirely by inputs you choose. Speak to a licensed financial adviser before making any investment decision.
