# CAPM Calculator

This CAPM calculator will tell you the expected return on asset, risk premium, and market risk premium given a risk-free rate, expected return on the market, and beta coefficient.

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Asset moves in same direction as market.
The expected return on the asset is 6.90%.

6.90% Expected return on the asset

4.40% Risk premium of the asset

8.00% Expected return of the market

5.50% Risk premium of the market

Show calculations

## Using this calculator

### Risk-free rate

The risk-free rate is usually the rate of a government bond, such as a 30-year Treasury Bill.

### Expected return on the market

This is usually the historical return of a market benchmarket such as the S&P 500.

Benchmark Historical return Time period of return
S&P 500 7.96% 1957 to 2018
S&P 500 5.90% 1999 to 2019
Dow Jones Industrial Average 5.42% 1896 to 2018
Dow Jones Industrial Average 7.03% 1999 to 2019
Russell 2000 7.70% 1999 to 2019
MSCI EAFE 4.00% 1999 to 2019

### Beta

Beta is the level of the asset return's sensitivity compared to the market. For example:

Beta Movement
Beta <= −1 Asset moves in opposite direction as the market. Movement is greater than market.
−1 < Beta < 0 Asset moves in opposite direction as the market.
Beta = 0 No correlation between asset and market.
0 < Beta < 1 Asset moves in same direction as market.
Beta = 1 Asset and market are perfectly correlated. Both both in the same direction by the same amount.
Beta > 1 Asset moves in same direction as market. Movement is greater than market.

## What is CAPM?

The capital asset pricing model, or CAPM, calculates the exposure of an asset to market risk. The model was developed in the mid-1960s by William Sharpe, John Lintner, and Jan Mossin.

CAPM is a model that describes the relationship between the risk premium of an individual asset and the risk premium of the market. The risk premium of an individual asset is equal to the risk premium of the market, adjusted by the beta of the asset.

The purpose of CAPM is to understand whether an asset is fairly priced relative to its beta and the market premium.

$E(r_i) = r_f + \beta_i \times (E(r_m)-r_f)$

$E(r_i)$ is the expected return on asset $i$

$r_f$ is the risk-free rate

$\beta_i$ is the beta coefficient

$E(r_m)$ is the expected return on the market

CAPM can also be represented as:

$E(r_i) - r_f = \beta_i(E(r_m) - r_f)$

$E(r_i) - r_f$ is considered to be the risk premium of the asset

$E(r_m) - r_f$ is considered to be the market premium

Let’s go through each of the inputs into the CAPM equation.

## CAPM components

### Expected return on asset

The expected return on the asset is what CAPM calculates. This is what an investor expects to earn on the asset over time.

### Risk-free rate

The risk-free rate is the rate you would receive on an asset that has no risk. This is typically the yield on a long-term government bond, where the asset is based. For a U.S. stock, this could be the yield on the 10-year Treasury Bill.

### Expected return on the market

The expected return on the market is the return of a market benchmark, such as the S&P 500, Russell 2000, Dow Jones Industrial Average, or another benchmark that encompasses most of the market.

Investors generally use the historical rate of return for the S&P 500, which was 8% between 1957 and 2018.

### Beta

An asset’s beta measures the risk involved with investing in the asset relative to the market risk and the risk-free rate.

Beta reflects the sensitivity of the asset to the market risk. A beta of 1 signifies that the asset has the same risk as the market. When the market goes up a little, the asset goes up a little. When the market goes down a lot, the asset goes down a lot. The two are perfectly correlated.

A beta of 0 means the asset and the market are not at all correlated. The two move independently of each other.

A positive beta means the asset and the market move in the same direction, while a negative beta means the two move in opposite directions.