CAPM Calculator

What CAPM does

The Capital Asset Pricing Model, universally shortened to CAPM, does one profound thing: it puts a price on risk. Given how risky an investment is, it tells you what return that investment ought to offer to make the risk worth taking. It is the bridge between risk and reward, and it is one of the cornerstones of modern finance.

The logic runs on a simple, fair idea. An investor parting with money deserves to be compensated, and CAPM says they deserve compensation for exactly two things, which the next section unpacks. This calculator works with the four quantities in the model, and it is flexible: you can solve for the expected return, or, if you already know the return, work backwards to any of the other three.

The two things investors get paid for

Why should an investment pay you anything at all? CAPM answers with two distinct reasons, and seeing them separately is the key to the whole model.

The first is simply the passage of time. Even with no risk whatsoever, money today is worth more than money later, so any investor deserves a baseline return just for tying their money up. The second is risk. If an investment might lose money, an investor needs the prospect of extra return to be tempted into it, over and above that risk-free baseline, and the riskier it is, the bigger that extra reward must be. CAPM takes these two ideas, the reward for waiting and the reward for risk-taking, and builds them into a single required return. Everything in the formula is one of those two things, or the ingredient that sizes them.

The three ingredients

The model needs three inputs, and each maps neatly onto the logic above.

The risk-free rate is the return you could earn with essentially no risk, usually taken from government bonds. It is the reward for waiting, the baseline every investment starts from. The expected market return is what the market as a whole is expected to deliver, and the gap between it and the risk-free rate, the market's return minus the risk-free rate, is the market risk premium: the extra reward the market pays for bearing market risk. Finally, beta measures how much of that market risk your particular asset carries. A beta of 1 carries exactly the market's risk; a higher beta carries more, a lower one less. Beta is the dial that scales the market's risk premium up or down to fit your specific investment, and it is the figure our beta calculator is built to estimate.

The formula, read as a sentence

Put the ingredients together and CAPM reads: expected return equals the risk-free rate, plus beta multiplied by the market risk premium. In symbols, E(Ri) = Rf + βi × (E(Rm) − Rf). But it is clearer as a sentence than as symbols.

Start with the baseline reward for waiting, the risk-free rate. Then add a reward for risk, which is the market's risk premium scaled by how much market risk your asset carries. That second term, beta times the market risk premium, is the whole of the risk compensation, and it is worth naming: it is your asset's own risk premium. A high-beta stock earns a large risk premium on top of the baseline; a low-beta stock earns a small one. The elegance is that the entire required return collapses into just those two parts, the reward for time and the reward for risk, with beta deciding how much of the second you are owed.

A worked example

Say the risk-free rate is 4%, the market is expected to return 10%, and your stock has a beta of 1.5.

First find the market risk premium: 10% minus 4% is 6%, the extra the market pays for its risk. Your stock carries 1.5 times the market's risk, so its own risk premium is 1.5 times 6%, which is 9%. Add that to the 4% baseline and the expected return CAPM demands is 13%. In other words, given how much market risk this stock carries, an investor should require a 13% return to hold it. If the stock looks likely to return more than 13%, it is attractively priced for its risk; if less, it is not paying you enough for the risk you would be taking. That is the judgement CAPM exists to inform. You can drop your own beta, perhaps the one from our beta calculator, straight into this to get a figure tailored to your stock.

Solving for any piece

Because the four quantities are bound together by one equation, knowing any three pins down the fourth, and this calculator lets you solve for whichever one you are missing. That opens up some genuinely useful questions beyond the standard one.

You can work out the beta implied by a stock's expected return: given what the market and the risk-free asset offer, and the return you expect from a stock, what level of risk does that expectation imply? Or you can back out the market return that a given set of figures assumes. In our example, the pieces fit together in every direction: a 13% return with a 4% risk-free rate and a 10% market return implies a beta of exactly 1.5, and the same figures rearranged confirm the 10% market return and the 4% risk-free rate. Being able to turn the model around like this makes it a tool for interrogating assumptions, not just producing a single number.

Why only market risk is priced

There is a striking implication tucked inside CAPM worth drawing out: the only risk it pays you for is market risk. Notice that beta, which measures market risk alone, is the sole risk term in the formula. A stock's own company-specific risk appears nowhere.

That is deliberate, and it follows from diversification. Company-specific risk can be spread away by holding many stocks, so the model assumes a rational investor has already done that and is left holding only market risk. Since that private risk can be avoided for free, the market does not reward you for bearing it. What this means in practice is quietly powerful: two stocks with the same beta command the same required return, even if one is far more volatile on its own, because their extra volatility is the diversifiable kind that earns no premium. CAPM prices the risk you cannot escape, and ignores the risk you should have diversified away.

Using it, and its limits

CAPM's main job in practice is to produce the return shareholders require from a company, its cost of equity, which then feeds into company valuations and into the weighted average cost of capital used to judge investments. It also serves as a hurdle: compare an investment's expected return against the return CAPM says its risk deserves, and you have a clean test of whether it is worth it.

For all its usefulness, it is a model, and models simplify. CAPM leans on assumptions that reality only partly honours, that markets are efficient, that investors hold the market portfolio, that beta is stable, and real-world returns do not follow it perfectly; scholars have found patterns it misses, which is why extensions to the model exist. On top of that, the inputs are estimates: beta is measured with error, and the expected market return is a forecast, not a fact. None of this makes CAPM useless, far from it, but it does mean the number it produces is a well-reasoned estimate to inform judgement, not a precise truth to follow blindly. To carry the cost of equity it yields into the fuller cost of capital, our WACC calculator is the next step, and the beta calculator supplies the risk input this model runs on.

Questions people ask

What is the Capital Asset Pricing Model?

CAPM is a model that estimates the return an investment should offer given its risk. It says expected return equals the risk-free rate plus beta times the market risk premium, compensating investors for the time value of money and for the market risk they take on.

What inputs does CAPM need?

Three: the risk-free rate, usually from government bonds; the expected market return; and the asset's beta, which measures its market risk. The market return minus the risk-free rate gives the market risk premium, which beta then scales for the specific asset.

How do I calculate expected return with CAPM?

Subtract the risk-free rate from the market return to get the market risk premium, multiply that by beta, and add the risk-free rate back. With a 4% risk-free rate, a 10% market return, and a beta of 1.5, the expected return is 4% plus 1.5 times 6%, which is 13%.

Why doesn't CAPM account for company-specific risk?

Because company-specific risk can be diversified away by holding many stocks, so the market does not reward investors for bearing it. CAPM prices only market risk, measured by beta, which is the risk that cannot be removed through diversification.

References

The Capital Asset Pricing Model, its decomposition into the risk-free rate and a beta-scaled market risk premium, and its use in estimating the cost of equity follow Wall Street Prep and standard corporate finance, as set out by Brealey, Myers, and Allen below.

1. Wall Street Prep. Capital Asset Pricing Model (CAPM). wallstreetprep.com
2. Brealey, R. A., Myers, S. C., and Allen, F. Principles of Corporate Finance (risk and the cost of capital). McGraw-Hill.