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A bedrock principle of all investing is that returns are directly proportional to risk. In other words, the more risk you take on, the higher returns you hope to earn. The capital asset pricing model (CAPM) helps investors understand the returns they can expect given the level of risk they assume.

## Understanding the Capital Asset Pricing Model

The CAPM was conceived in the early 1960s by William Sharpe, an economist and academic. He took up the question of how risk—more specifically, risk that could not be diversified away—influenced returns. His research led to the capital asset pricing model, which he introduced in his 1970 book, “Portfolio Theory and Capital Markets.”

Sharpe was looking at diversification, more specifically which risks can be dealt with by diversification and which cannot. In the CAPM framework, he identified two types of risk:

**Systemic Risk.**Also called market risk, this is general risk from developments impacting the entire economy and all investment assets. It is influenced by factors such as interest rates, inflation, recessions and geopolitical events like war. Systemic risk applies to the market as a whole, which means that all assets are impacted in similar ways.**Unsystemic Risk.**Also known as specific risk, these are risks that are unique to each asset. Individual stocks face risks from adverse developments at companies that may not impact any other peer firms, for instance. These risks are not correlated across different assets, unlike systemic risk.

Specific risk can be reduced by diversification, or investing in a basket of different assets—a concept that’s at the heart of modern portfolio theory (MPT). But systemic risk is a tougher nut to crack since it impacts all investment assets in a similar way.

The capital asset pricing model concentrates on measuring systemic risk and its impact on the value of an asset. CAPM helps factor in systemic risks to estimate the fair value of an asset and understand the relationship between risk and expected returns.

## Key Terms for the Capital Asset Pricing Model

Before looking at the CAPM equation and how to use the result to assess the fair market value of an asset, it’s important to understand the elements that go into the capital asset pricing model.

**Expected return.**The output of the capital asset pricing model is expected return. It is a well-grounded estimate of the returns an investor can expect over the life of an investment.**Risk-free rate.**The rate of return an investor would expect from an asset that bears no risk. U.S. Treasury securities are commonly used to represent the risk-free rate since they are backed by the full faith and credit of the U.S. government, which has never defaulted on a payment. Different Treasury maturities are used, depending on an investor’s timeline.**Beta.**A measure of volatility relative to the overall market. A stock with a beta of 1.0 exhibits the same level of volatility as the market—typically represented as the returns on the S&P 500—while a beta of less than 1.0 indicates a stock is less volatile than the market. Similarly, a beta greater than 1.0 indicates a stock is more volatile than the market.**Market risk premium.**The additional return beyond the risk-free rate that investors require to hold a risky market portfolio instead of simply holding risk-free assets, like Treasuries. The more volatile the market or asset class, the higher the market risk premium would be.

## What Is the CAPM Formula?

The CAPM formula describes the expected return for investing in a security that’s equal to the risk-free return plus a risk premium.

In the formula, the risk premium—a rate of return that’s greater than the risk-free rate—represents an investor’s compensation for taking on systemic risk that can’t be diversified away.

**ER = RFR + [Beta x (MR – RFR)]**

**ER = RFR + [Beta x (MR – RFR)]**

**ER:**Expected return on a given asset**RFR:**Risk-free rate, or the return on a Treasury security**MR:**Market return, or return on a comparable market index

In the CAPM formula, the risk premium—also referred to as the market risk premium—is calculated in the * (MR – RFR)* component.

Estimates of market return vary according to asset class. An investor can use their own expectations of market return or base the return on historical data from an index, most commonly the S&P 500 for stocks.

### CAPM Example

Let’s use the CAPM formula above to calculate the expected return (* ER*) of a stock over one year.

- A comparable risk-free rate (
) comes from the current yield on the one-year treasury bill. As mid February 2022, the one-year treasury was yielding 1.05%, so we’ll use that.**RFR** - Next, we’ll take the average return of the S&P 500 as our market return (
). According to Morningstar, the total return of the S&P 500 over the past 12 months is approximately 11%.**MR** - The stock in question has a
of 1.5, meaning that the stock is 1.5 times as volatile as the S&P 500.**beta**

**ER = 1.05 + [1.5 x (11 – 1.05)]**

**ER = 1.05 + [1.5 x (11 – 1.05)]**

Factoring these figures gives us an expected return of 16%. The market risk premium is (11 – 1.05) or approximately 10%.

The expected return can also be used as a discount rate to determine the present value of future cash flows from the stock. The future cash flows must be estimated. If the stock price is $75 and the present value of future cash flows using the 16% rate is $75, the stock is fairly valued. If the present value is greater than $75, the stock is cheap.

## Why Is the CAPM Important?

The CAPM plays a key role in financial modeling and asset valuation. When a financial analyst values a stock, they use the weighted average cost of capital (WACC) to find the net present value (NPV) of future cash flows.

The WACC equation uses the expected value calculated from the CAPM as the cost of equity. The company value is divided by the number of shares outstanding to arrive at the fair value of the stock.

An investment decision is made based on the current price relative to fair value. If the current price is lower than the fair value, it’s a buy. If it’s higher than the fair value, it’s a sell.

## Advantages and Disadvantages of the CAPM

The principal criticisms of the CAPM center around the ambiguity of the data that goes into the formula.

Take the risk-free rate, for example. Over an analyst’s chosen investment time horizon, the risk-free rate can fluctuate, sometimes considerably—just look at the yields on treasuries in any unsettled market environment. A higher risk-free rate would increase the cost of capital while a lower rate would reduce it—either would significantly impact the outcome of a CAPM calculation.

Beta can also be troublesome as a measure of volatility. Beta is calculated using a regression of historical stock returns. However, historical stock returns don’t follow a normal distribution. Upward and downward price movements are not equally risky, which makes some observers wonder if it’s a completely accurate measure of risk.

Finally, the market risk premium is based on a theoretical value. The choice of that value is subjective. Even using a historical average from a major index is imperfect as there is no guarantee that the market will perform similarly.

The CAPM remains widely used despite its reliance on a variety of assumptions. Used as a tool combined with other methods of evaluating securities, it can play an integral role in helping investment professionals make informed investment decisions.

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