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The capital asset pricing model (CAPM) is a financial model used to determine a security’s expected return considering its associated risk. Developed in the 1960s, CAPM has become an essential tool in analyzing and managing investments, as it provides investors with a quantitative way to measure the expected return and risk of a given asset. Here’s how CAPM is used, the formula for CAPM, its limitations and more.

## How CAPM works

Financial analysts use CAPM to estimate the fair value of a stock by considering factors such as the stock’s volatility (beta), the risk-free interest rate and the equity risk premium – the premium demanded by investors to own a volatile asset such as a stock. CAPM is a theoretical representation of how financial markets behave and can estimate a company’s cost of equity capital, which is the return investors demand from the stock.

### CAPM formula

Here’s the CAPM formula:

#### ER = RFR + [ Beta * ( MR – RFR ) ]

##### Key
• ER: Expected return on a specific asset
• RFR: Risk-free rate, typically the return on a Treasury security
• Beta: The volatility of the investment
• MR: The return on a comparable market index

To put it in plain terms, the return that investors expect from an asset is what they can get with no risk (such as a Treasury bond) plus the extra return they demand for the risk of investing in a stock. This extra return is what’s called the equity risk premium [Beta * (MR – RFR)]. As in the formula above, the equity risk premium depends on the returns of other available investments (such as the S&P 500) and the volatility of the asset in question.

A recap of how the equation models the way investors respond to the various factors is outlined below.

• Investors demand a higher return from an asset when the risk-free rate – the overall level of interest rates – is high. If interest rates are lower, then investors demand a lower return on the stock.
• Investors demand a higher return when the stock or other asset has higher volatility. If the asset’s volatility is lower, investors accept a lower return, given the perceived safety.
• Investors demand a higher return from an asset if other similar assets (or the market as a whole) are trading with higher expected returns. If similar assets are trading with lower expected returns, investors accept a lower return on the stock.

In sum, the CAPM formula takes into account an investor’s willingness to take on additional risk, given the state of interest rates and the expected return of alternative investments.

### How CAPM is used

Investors can use the CAPM equation in a variety of ways to make better-informed decisions when evaluating investment opportunities. For example, the most common use is to determine if a stock’s current value is in alignment with its expected return. This helps investors determine if the stock is overvalued or undervalued. Investors also use the CAPM equation in combination with modern portfolio theory (MPT) to analyze the expected return and risk of a portfolio. Through CAPM, investors can identify which assets are more attractive for their portfolios and adjust their asset allocation accordingly.

### Assumptions and limitations of the CAPM model

CAPM is criticized for its many unrealistic assumptions, and investors must understand the assumptions underlying the CAPM to accurately understand and interpret the results.

CAPM assumes that investors are looking to maximize their return and that they can evaluate expected return and risk. It also assumes that investors have access to risk-free borrowing and lending. Furthermore, it assumes that all assets can be divided and sold consistently at the market price and there are no taxes or transaction costs. CAPM, which is derived from modern portfolio theory, also assumes that markets are efficient and that prices accurately reflect all available information. These assumptions mean that all investors have access to the same information about an asset, and as such, all investments are carried out on a level playing field. Additionally, it assumes that investors are rational, risk-averse and always make the best decision based on the information they have.

Also critical to CAPM is the assumption that a stock’s risk is the same as its volatility. This assumption effectively disregards the key fact that an investment is based on the fundamental performance of the underlying business and, instead, conflates risk with stock price fluctuations. Given that CAPM is built upon some dubious assumptions, investors should consider whether those assumptions are valid in a given situation. If any of the assumptions are not consistently met, the results of the model may not be reliable.

## History of CAPM

In the 1950s Harry Markowitz, creator of modern portfolio theory, established the groundwork for the capital asset pricing model. Building off his work, CAPM was developed by William Sharpe, Jack Treynor, John Lintner and Jan Mossin in the early 1960s. For his work on developing the CAPM, Sharpe was awarded the 1990 Nobel Prize in Economic Sciences.

## CAPM and the efficient frontier

CAPM can be used to model a range of the highest possible returns for a given level of risk. The line of these best risk-adjusted returns is called the efficient frontier, and this approach was also developed by Markowitz as part of modern portfolio theory.

The efficient frontier can be depicted by graphing a portfolio’s expected returns on the Y axis and its risk on the X axis. By plotting the return of a security against its risk (beta), investors can use the efficient frontier to determine if a security is undervalued or overvalued in relation to the market. If the security plots above the line, it’s undervalued; if below, it’s overvalued.

## Bottom line

The capital asset pricing model can be a useful tool for understanding the relationship between risk and return in the stock market. While it is not without flaws, CAPM has been used for decades and is still an important tool for financial planners and investors, though users should understand its key limitations.

Editorial Disclaimer: All investors are advised to conduct their own independent research into investment strategies before making an investment decision. In addition, investors are advised that past investment product performance is no guarantee of future price appreciation.