CAPM Expected Return Calculator
CAPM expected return from risk free rate, beta, and market premium.
What it does
The capital asset pricing model answers a plain question: what return should risky stock promise when safe bonds pay something known? Investors demand the safe rate plus a premium for market risk, scaled by how much of that risk the stock carries. Beta is the scaling dial.
The tool above runs E(R) = Rf + beta x (Rm - Rf) the moment you type. Enter the risk free rate, beta, and expected market return. It returns the expected return plus both premiums. Defaults of 3, 1.2, and 9 print 10.2%, so the page opens solved.
Beta reads as behavior, not quality. A beta of 1.2 means the stock typically moves 20 percent more than the market in either direction, so it must promise 7.2 against a 6 market premium. A beta of zero, like a T bill, promises only the risk free rate, and a negative beta promises less, acting as insurance.
The model rests on strong assumptions: investors diversify fully, share one horizon and beliefs, and borrow at the risk free rate. Real markets add size, value, and momentum effects that beta misses, which is why researchers call CAPM a starting lens rather than a pricing machine.
Use the table to feel beta from defensive to aggressive, then run your stock. The expected number feeds directly into dividend discount and DCF models as the cost of equity.
How to use
- Enter the risk free rate for your horizon.
- Enter the stock beta from a data source or regression.
- Enter the expected market return.
- Read expected return first, then both premiums.
- Compare with your required return before buying.
- Reuse the expected return as a DCF discount rate.
Formula
- Rf
- Risk free rate in percent, often Treasury yield.
- Beta
- Stock sensitivity to the market: 1 moves with it, above 1 amplifies.
- Rm
- Expected market portfolio return in percent.
Rf is the risk free rate and Rm the expected market return. The market premium (Rm - Rf) prices one unit of market risk; beta scales it to the asset. The page assumes investors diversify, so only systematic risk earns a premium.
Worked example
Example: beta 1.2 stock in a 9% market
Risk free rate 3%, stock beta 1.2, expected market return 9%. Find the CAPM expected return.
- Market premium: 9 - 3 = 6%.
- Scale by beta: 1.2 x 6 = 7.2%.
- Add the risk free rate: 3 + 7.2 = 10.2%.
- The tool prints expected 10.2%, risk premium 7.2%, market premium 6%.
- A beta above 1 lifts the premium; a beta of 1 would print exactly 9%.
- Use 10.2% as the discount rate for this stock in a DCF.
Reference table
| Beta | Risk premium | Expected |
|---|---|---|
| -0.5 (insurance-like) | -3% | -1% |
| 0 (cash-like) | 0% | 3% |
| 1 (market-like) | 6% | 9% |
| 1.2 (worked case) | 7.2% | 10.2% |
Limits
- Single factor only; size and value effects ignored.
- Beta drifts with debt levels, cycles, and estimation windows.
- Needs an honest market expectation, which nobody observes.
- Average outcome, not a yearly promise.
Common mistakes
- Mixing nominal cash flows with a real risk free rate.
- Using a 1 year beta for a 10 year valuation.
- Forgetting the market premium sign in down markets.
- Treating expected return as guaranteed return.
- Comparing betas across different market indexes.
Try it yourself
Quick checks. Answers sit tucked under each question.
Beta -0.5 with Rf 2% and market 8%?
Premium 8 - 2 = 6%. Scaled: -0.5 x 6 = -3%. Expected 2 - 3 = -1%.
Beta 0 with Rf 4% and market 10%?
Beta zero kills the premium: expected equals Rf at 4%.
Beta 1 with Rf 3% and market 9%?
Premium 9 - 3 = 6%. Beta 1 takes all of it: 3 + 6 = 9%.
Questions
What is the market risk premium?
The market price of risk: how much extra return one unit of market risk demands. Beta scales it to the stock.
Which risk free rate should I use?
Often the 10 year Treasury yield for long horizons or the T bill for short ones. Match the currency and horizon to the cash flows.
How is beta estimated?
Regression of the stock returns on market returns, usually 2 to 5 years of monthly data. Data providers publish it; the page takes it as a given.
Can expected return go below the risk free rate?
A negative beta asset zigs when the market zags, like some gold positions at times. CAPM then demands less than the risk free rate, even negative.
Why do tests say beta is not enough?
Size, value, profitability, and momentum explain returns beta misses. CAPM stays the classroom start, multifactor models do the pricing work.
Does 10.2% mean the stock gains that yearly?
No. Expected return is an average over many paths; single year results swing far around it. Judge over cycles, not quarters.
Sources
- CFA Institute: portfolio risk and return, CAPM and SML
- Columbia University: CAPM lecture notes (Sigman)