Understanding CAPM — The Model That Connects Risk to Return

Career
Written By Ismail Francillon
Understanding CAPM
Finance April 15, 2026 17 min read

Understanding the Capital Asset Pricing Model (CAPM)

Key Takeaways
  • CAPM tells you the expected return of any asset based on its systematic risk
  • The formula is ER = RF + β(ERM − RF) — every variable has an intuitive meaning
  • Beta measures how sensitive an asset is to market movements — it is the only risk that gets compensated
  • The CML plots risk vs return for efficient portfolios, while the SML plots beta vs return for any individual security
  • The Sharpe Ratio measures how much excess return you are generating per unit of risk — it is the slope of the CML

What Is CAPM

The Capital Asset Pricing Model — CAPM — answers one of the most fundamental questions in finance: how much return should I expect from an investment given its risk?

That is the whole thing. CAPM is a pricing model. It takes the risk of an asset, runs it through a formula, and spits out a number — the expected return. If the actual return you observe in the market is higher than what CAPM predicts, the asset might be undervalued. If it is lower, it might be overvalued. That is how investors and analysts use it to make decisions.

But before we get to the formula, we need to understand the type of risk that CAPM actually cares about. Because here is the thing — not all risk is created equal.

Two Types of Risk

Every investment carries risk. But that risk can be broken into two buckets.

Unsystematic risk — also called diversifiable risk or firm-specific risk — is the risk that is unique to a specific company. A CEO gets fired. A factory burns down. A product recall happens. These events affect one company but not the broader market. And here is the key insight: you can eliminate this risk by diversifying. If you hold 30 or 40 stocks across different industries, one company's bad news barely moves your portfolio. The risks cancel each other out.

Systematic risk — also called non-diversifiable risk or market risk — is the risk that affects everything. Recessions. Interest rate changes. Inflation. Geopolitical events. You cannot diversify this away. Even if you hold 1,000 stocks, a recession still hurts your portfolio. This risk is baked into the entire market.

The punchline: Since unsystematic risk can be eliminated through diversification, the market does not compensate you for taking it. CAPM only prices systematic risk — the risk you cannot escape. That is what beta measures.

The Formula

Here it is. The most important equation in asset pricing.

ERi = RF + βi (ERM − RF) Expected Return = Risk-Free Rate + Beta × Market Risk Premium

Let us break each piece down.

ERi — Expected Return of the Asset. This is what you are solving for. It is the return that an investor should demand given the level of risk they are taking on.

RF — Risk-Free Rate. This is the return on an investment with zero risk — typically a government bond like a Canadian T-Bill or a U.S. Treasury. It represents the baseline. Even if you take on no risk at all, you should at least earn this. Think of it as the "guaranteed" return. You park your money, you get RF, and you sleep peacefully at night.

βi — Beta. This is the measure of the asset's sensitivity to market movements. We will go deep on this in the next section, but for now: beta tells you how much the asset's return moves when the market moves. A beta of 1 means the asset moves in lockstep with the market. A beta of 1.5 means the asset is 50% more volatile than the market. A beta of 0.5 means it is half as volatile.

(ERM − RF) — Market Risk Premium. This is the extra return that investors demand for investing in the stock market instead of the risk-free asset. It answers the question: how much more do I earn for taking on market risk? If the market is expected to return 10% and the risk-free rate is 4%, the market risk premium is 6%. That 6% is the compensation for bearing systematic risk.

The intuition: CAPM says your expected return starts at the risk-free rate (the baseline), and then you add a premium that depends on how much systematic risk you are taking (beta × market risk premium). More risk, more expected return. Less risk, less expected return. That is the trade-off.
Worked Example

You are analyzing Stock X. Here is what you know:

Risk-free rate (RF): 4%

Expected market return (ERM): 10%

Beta of Stock X (β): 1.3

Step 1 — Calculate the market risk premium:

ERM − RF = 10% − 4% = 6%

Step 2 — Plug into CAPM:

ER = RF + β(ERM − RF)

ER = 4% + 1.3(6%)

ER = 4% + 7.8%

ER = 11.8%

This means that given Stock X's level of systematic risk (beta of 1.3), an investor should expect to earn 11.8%. If the stock is currently returning 14%, it might be undervalued — you are being compensated more than the model says you should be. If it is returning 9%, it might be overvalued — you are not being compensated enough for the risk.

Test Yourself
A stock has a beta of 0.8. The risk-free rate is 3% and the expected market return is 11%. What is the expected return of this stock according to CAPM?
  • A. 8.8%
  • B. 11.4%
  • C. 9.4%
  • D. 6.4%
Correct: C. ER = 3% + 0.8(11% − 3%) = 3% + 0.8(8%) = 3% + 6.4% = 9.4%. The stock has lower systematic risk than the market (beta under 1), so its expected return is below the market return. That is exactly what CAPM predicts — less risk, less return.

Beta — The Risk That Matters

Beta is the heartbeat of CAPM. It is the single number that captures how much systematic risk an asset carries. And understanding it intuitively — not just mathematically — is critical.

Beta measures how sensitive an asset's return is to the overall market's return. If the market goes up 1%, how much does this stock go up? If the market drops 2%, how much does this stock drop? Beta answers that question.

Here is how to read it:

Beta Value What It Means Example
β = 0 Zero sensitivity to the market. No systematic risk at all. A risk-free asset like a government T-Bill. The market could crash 30% and your T-Bill still pays the same interest.
β = 0.5 Half as volatile as the market. Moves less aggressively. A stable utility company. The market drops 10%, this stock might drop 5%.
β = 1 Moves exactly with the market. Same volatility. An S&P 500 index fund. By definition, the market's beta is 1.
β = 1.5 50% more volatile than the market. Amplifies movements. A high-growth tech stock. The market rises 10%, this stock might rise 15% — but also drops harder.
β < 0 Moves opposite to the market. Negative correlation. Gold or certain hedge fund strategies that profit when markets fall.

Two things that are important to internalize here.

First: the risk-free asset has a beta of 0. This makes intuitive sense. A government bond does not fluctuate with the stock market. It has no systematic risk, and therefore no sensitivity to market movements. That is also why it sits at the y-intercept of every CAPM graph — it is the starting point, the baseline, the place where beta equals zero and your return equals RF.

Second: the market portfolio has a beta of 1. Also intuitive. The market is perfectly correlated with itself. If you ask "how much does the market move when the market moves?" the answer is obviously one-for-one. Beta of the market equals 1. Always.

Why beta matters: CAPM says the only risk you get paid for is systematic risk. Beta is the measure of that risk. A high-beta stock carries more systematic risk, so CAPM assigns it a higher expected return. A low-beta stock carries less, so it gets a lower expected return. The relationship is linear — double the beta, double the risk premium.
Test Yourself
Which of the following statements about beta is correct?
  • A. A stock with a beta of 1 should earn exactly the market return
  • B. A stock with a negative beta has an expected return below the risk-free rate
  • C. The risk-free asset has a beta of zero because it has no sensitivity to market movements
  • D. All of the above
Correct: D. All three are true. A: If β = 1, then ER = RF + 1(ERM − RF) = ERM — exactly the market return. B: If β is negative, the term β(ERM − RF) becomes negative, pulling the expected return below RF. C: The risk-free asset has zero volatility relative to the market, so its beta is zero — it does not contribute any systematic risk.

CML vs SML — Two Lines, Two Stories

This is where most people get confused, so let us be precise. CAPM gives us two important lines that look similar but represent very different things.

But before we get into the differences, here is the thing that makes both of them click: the CML and the SML are just y = mx + b. Seriously. The same linear equation you learned in high school. That is all this is.

Every straight line has an intercept (where it starts on the y-axis) and a slope (how steeply it rises). If you can identify what the intercept is and what the slope is, you understand the entire line. So as we go through each one, keep asking yourself: what is my y, what is my x, what is my intercept, and what is my slope?

The Capital Market Line (CML)

The CML shows the relationship between risk (measured by standard deviation) and expected return for efficient portfolios only.

Here is the setup. Imagine you have two investment options: the risk-free asset (a T-Bill) and the market portfolio (a diversified portfolio sitting on the efficient frontier). The CML is the straight line that connects these two points. Any portfolio that sits on this line is a combination of the risk-free asset and the market portfolio.

At the far left of the line, you are 100% in the risk-free asset — no risk, return equals RF. As you move right along the line, you shift more money into the market portfolio — more risk, more return. At the tangent point, you are 100% in the market portfolio. Beyond that point, you are borrowing at the risk-free rate and investing more than 100% in the market — leveraging up.

CML: ERP = RF + [(ERM − RF) / σM] × σP y = b + m × x

Let us map it to y = mx + b. Your y is the expected return (ERP). Your x is the risk (σP). Your intercept (b) is RF — when risk is zero, your return is the risk-free rate. And your slope (m) is (ERM − RF) / σM, which is the Sharpe Ratio. That is it. The CML is y = mx + b where the slope happens to be the Sharpe Ratio.

The Security Market Line (SML)

The SML shows the relationship between beta (systematic risk) and expected return for any individual security or portfolio.

This is the CAPM equation plotted on a graph. The x-axis is beta. The y-axis is expected return. The intercept is RF (when beta is zero, you earn the risk-free rate). The line passes through the market portfolio at the point where beta equals 1 and the expected return equals ERM.

SML: ERi = RF + βi(ERM − RF) y = b + m × x

Same exercise. Your y is the expected return (ERi). Your x is beta (βi). Your intercept (b) is RF — again, when beta is zero, your return is the risk-free rate. And your slope (m) is (ERM − RF), which is the Market Risk Premium. The SML is y = mx + b where the slope happens to be the market risk premium.

That is the whole game. Both lines are y = mx + b. Both start at RF. The difference is what goes on the x-axis (standard deviation vs beta) and what the slope represents (Sharpe Ratio vs Market Risk Premium). Once you see it this way, you will never confuse them again.

The critical difference beyond the formula: the CML is only for efficient portfolios. The SML is for everything — individual stocks, inefficient portfolios, any asset. If a security plots above the SML, it is undervalued (earning more return than its risk justifies). If it plots below the SML, it is overvalued (not earning enough for the risk). If it sits directly on the line, it is fairly priced.

Capital Market Line (CML) Security Market Line (SML)
X-axis Total risk (standard deviation, σ) Systematic risk (beta, β)
Y-axis Expected return Expected return
Applies to Efficient portfolios only Any security or portfolio
Slope Sharpe Ratio = (ERM − RF) / σM Market Risk Premium = ERM − RF
Intercept RF RF
In y = mx + b y = ERP, x = σP, m = Sharpe Ratio, b = RF y = ERi, x = βi, m = Market Risk Premium, b = RF

The Sharpe Ratio

We keep mentioning the Sharpe Ratio, so let us give it the attention it deserves.

Sharpe Ratio = (ERP − RF) / σP Excess return per unit of total risk

The Sharpe Ratio answers a simple but powerful question: for every unit of risk I am taking, how much excess return am I generating?

The numerator is your excess return — how much more you earned above the risk-free rate. The denominator is your total risk — the standard deviation of your portfolio's returns. The higher the ratio, the better your risk-adjusted performance.

A Sharpe Ratio of 1.0 means you are earning one unit of excess return for every unit of risk. A ratio of 0.5 means you are only earning half a unit of excess return per unit of risk. A ratio of 2.0 is exceptional — you are being very well compensated for the risk you are taking.

Here is why it matters in the context of CAPM: the Sharpe Ratio is the slope of the Capital Market Line. That means the CML's steepness tells you how efficiently the market compensates investors for bearing risk. A steeper CML means a higher Sharpe Ratio, which means the market is giving you more return per unit of risk. A flatter CML means the opposite.

Three things the Sharpe Ratio tells you: (1) It is the slope of the CML. (2) It measures portfolio performance — higher is better. (3) It tells you how much excess return you are generating for every unit of risk taken. If someone asks you "how is your portfolio performing?" the Sharpe Ratio is one of the cleanest answers you can give.
Test Yourself
Portfolio A has an expected return of 12% and a standard deviation of 20%. Portfolio B has an expected return of 9% and a standard deviation of 10%. The risk-free rate is 3%. Which portfolio has the better risk-adjusted performance?
  • A. Portfolio A
  • B. Portfolio B
  • C. They are equal
  • D. Cannot be determined
Correct: B. Sharpe Ratio for A = (12% − 3%) / 20% = 0.45. Sharpe Ratio for B = (9% − 3%) / 10% = 0.60. Portfolio B has a higher Sharpe Ratio, meaning it generates more excess return per unit of risk. Even though Portfolio A has a higher raw return, Portfolio B is more efficient — it is doing more with less risk.

The Graph Intuition

If you are a visual thinker, this section is going to tie everything together. Let us build the CAPM graph from scratch.

Start with the efficient frontier. Imagine you plot every possible portfolio on a graph with risk (standard deviation) on the x-axis and expected return on the y-axis. You get a cloud of dots. The upper boundary of that cloud — the curve that gives you the maximum return for every level of risk — is the efficient frontier. It is a hyperbolic shape, curving upward and to the right.

Now add the risk-free asset. Plot RF on the y-axis. This is a point with zero risk and a guaranteed return. It sits on the vertical axis because its standard deviation is zero.

Draw a line from RF to the efficient frontier. The steepest line you can draw from RF that just barely touches the efficient frontier hits it at one specific point — the tangent portfolio. This tangent portfolio is the market portfolio in CAPM. It is the single most efficient risky portfolio available.

That line is the Capital Market Line. Every point on it represents a combination of the risk-free asset and the market portfolio. Below the tangent point, you are splitting your money between the T-Bill and the market. At the tangent point, you are fully invested in the market. Above it, you are borrowing money at the risk-free rate to invest even more in the market — leveraging up.

The beauty of this graph is the intuition it provides:

Point A (the origin): Zero expected return, zero risk. You are doing nothing with your money.

Point B (the y-intercept): RF — the risk-free rate. You are guaranteed this return with no risk. This is your baseline.

Point C (anywhere on the CML): A combination of the risk-free asset and the market portfolio. The further right you go, the more you have allocated to the market.

Point T (the tangent point): The market portfolio. 100% invested in the most efficient risky portfolio. This is where the CML touches the efficient frontier.

Beyond T: You are borrowing at RF and putting more than 100% into the market. Higher risk, higher expected return — but also higher potential losses.

Now here is the key connection back to CAPM. The CML uses standard deviation (total risk) on the x-axis. But CAPM — the SML — uses beta (systematic risk) on the x-axis. Why? Because for a well-diversified portfolio, total risk and systematic risk are the same thing. Unsystematic risk has been diversified away. But for individual stocks, they are not the same — which is why the SML applies to everything and the CML only applies to efficient portfolios.

Test Yourself
A security plots below the Security Market Line (SML). This means:
  • A. The security is undervalued and investors should buy it
  • B. The security has lower risk than the market
  • C. The security is overvalued — it is not earning enough return for its level of risk
  • D. The security has a negative beta
Correct: C. The SML shows the expected return for every level of beta. If a security sits below the line, it is generating less return than CAPM predicts it should for its level of systematic risk. That means the market is not compensating investors enough — making the security overvalued. Rational investors would sell it, pushing the price down until the expected return rises back to the SML.

Watch It

If you want to see this explained step by step with visuals and walkthroughs, check out this video where I break down CAPM, the CML, the SML, and how to solve problems from start to finish.

Keep Going

If you want to practice CAPM problems — computing expected returns, interpreting beta, comparing Sharpe Ratios — we have a full set of practice problems in our content hub. Free, interactive, and ready to go.

Practice CAPM Problems

And if you want to talk through anything — finance, careers, or just life — I am always down for a conversation.

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Ismail Francillon
Ismail Francillon
Ex-McKinsey · Adjunct Finance Professor at Concordia · Co-Founder at Atwater Partners
Ismail Francillon
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