7.3Lesson 7.3 · Module 7 — The CAPM and APT

The Security Market Line: What Return Is Enough for This Beta?

Beta measures how much market risk an investment carries. CAPM turns that exposure into a required expected return through one equilibrium price for market risk.

Market risk premium = E[ $R_{M}$ ] − $R_{f}$
Required return = $R_{f}$ + β × (E[ $R_{M}$ ] − $R_{f}$ )
Beta = quantity of exposure; premium = price per unit
The SML is a straight line
Required return ≠ guaranteed realized return

Start

Central question

Beta tells us how much market risk an investment carries. How much expected return should investors require as compensation for carrying it?

7.3.1Section 1 · The missing piece

Higher expected return, higher systematic exposure

From Lesson 7.2, beta measures how aggressively an asset participates in market movements. Consider two portfolios:

Portfolio	Beta	Expected return
Defensive	0.5	7%
Aggressive	1.5	13%

The question we cannot yet answer

Is the aggressive portfolio automatically better because its expected return is higher?

The aggressive portfolio offers more expected return.
It also bears more systematic market exposure.
Returns must be evaluated relative to beta — not in isolation.

Required conclusion

Beta tells us how much market risk an investment carries, but not whether the offered expected return is enough compensation.

7.3.2Section 2 · The price of market risk

The market risk premium

To judge whether a return is sufficient, we first need the compensation investors require for one unit of market exposure.

Market risk premium

E [R_{M}] - R_{f}

The market risk premium is the expected return on the market portfolio minus the risk-free rate.

$R_{f}$: The return available without taking market exposure.
$E [R_{M}]$: The expected return on the market portfolio (one full unit of market exposure).

E [R_{M}] - R_{f} = 10% - 4%

= 6%

Investors require 6 percentage points of additional expected return for bearing one full unit of market exposure.

Beta

Quantity of market risk

Market risk premium

Compensation per unit

β × premium

Total compensation for systematic risk

7.3.3Section 3 · Build the CAPM equation

Base return plus systematic-risk compensation

Combine the risk-free base with compensation proportional to beta.

CAPM required return

E [R_{i}] = R_{f} + β_{i} (E [R_{M}] - R_{f})

Required expected return equals the risk-free return plus compensation for the investment's systematic market exposure.

$E [R_{i}]$: Required expected return for investment i.
$R_{f}$: Base return with no market exposure.
$β_{i}$: Quantity of market exposure for investment i.
$(E [R_{M}] - R_{f})$: Price per unit of market exposure (the market risk premium).

Required return = base compensation + systematic-risk compensation. This is an equilibrium benchmark, not a guaranteed future return.

Labeled components

required expected return E [R_{i}] = base return R_{f} + quantity of market exposure β_{i} \times price per unit of market exposure (E [R_{M}] - R_{f})

Definition · Plain-language statement

Required return equals the risk-free return plus compensation for the investment's systematic market exposure.

Note

The CAPM result is a required expected return — an equilibrium benchmark. It is not a promise of what the investment will actually deliver.

7.3.4Section 4 · Why the relationship is a straight line

One price per unit of market risk

With a 6% market risk premium, every unit of beta earns the same compensation.

Beta	Risk compensation (β × 6%)
0.0	0%
0.5	3%
1.0	6%
1.5	9%
2.0	12%

Every additional unit of beta receives the same 6-percentage-point premium.
Doubling beta doubles systematic-risk compensation.
A constant price per unit creates a linear relationship.

Required conclusion

CAPM assigns one equilibrium price to market risk. Each additional unit of beta adds the same market risk premium to required return.

7.3.5Section 5 · Construct the Security Market Line

Plot beta against required return

The Security Market Line puts $β$ on the horizontal axis and $E [R]$ on the vertical axis. Its intercept is $R_{f}$ and its slope is the market risk premium.

β = 0 \Rightarrow E [R] = 4%

β = 0.5 \Rightarrow E [R] = 7%

β = 1 \Rightarrow E [R] = 10%

β = 1.5 \Rightarrow E [R] = 13%

The SML: intercept (0, 4%), market point (1, 10%), slope = 6%. The purple point shows a negative-beta asset.

β = - 0.25 \Rightarrow E [R] = 4% + (- 0.25) (6%) = 2.5%

Definition · Negative beta

A negative-beta asset may have a required return below the risk-free rate because it tends to move opposite the market and can offer hedging value. This is introduced briefly — most assets have positive beta.

7.3.6Interaction · Build the Security Market Line

Compute, then place, then read

Find the market risk premium, locate the line, compute required returns for several betas, and explain why each is what it is. The full SML appears only after correct submission.

Price of market riskLocate the lineRequired returnsRead the SML

Given $R_{f} = 4%$ and $E [R_{M}] = 10%$ , what is the market risk premium $E [R_{M}] - R_{f}$ ? This is the compensation investors require for one full unit of market exposure.

Market risk premium (percentage points):

7.3.7Section 6 · Higher return is compensation, not superiority

All three can be fairly priced at once

Return to the defensive, market-like, and aggressive portfolios — now with their CAPM-required returns.

Portfolio	Beta	CAPM-required return
Defensive	0.5	7%
Market-like	1.0	10%
Aggressive	1.5	13%

All three portfolios may be fairly priced at the same time. The aggressive portfolio is not automatically better — its higher required return compensates investors for:

stronger participation in market gains;
stronger participation in market losses;
greater non-diversifiable exposure.

Required takeaway

CAPM does not tell investors to seek the highest expected return. It tells them to compare expected return with the amount of beta required to earn it.

7.3.8Section 7 · Required return is not realized return

Three different concepts of return

Do not confuse the equilibrium benchmark with a forecast or with what actually happens.

Required return

The return investors demand for the investment's beta.

Forecast expected return

The return an analyst currently believes the investment may produce.

Realized return

The return that actually occurs after uncertainty is resolved.

R_{i}^{required} = 11.2%

The realized result for the same investment might be any of:

30%, 4%, - 18%

Required statement

Required return is an equilibrium benchmark, not a guaranteed realized outcome.

7.3.9Section 8 · Forecast return versus required return

When a forecast differs from the benchmark

If an analyst's forecast exceeds the CAPM-required return, the gap is a signal — not yet proof.

Required return for β = 1.2

R_{i}^{required} = R_{f} + β_{i} (E [R_{M}] - R_{f})

R_{i}^{required} = 4% + 1.2 \times 6%

= 11.2%

With $R_{f}$ = 4% and a market risk premium of 6%, an asset with β = 1.2 requires an expected return of 11.2%.

Analyst forecast

E [R_{i}]^{forecast} = 13%

Difference

13% - 11.2% = 1.8%

The 1.8% gap could mean any of the following:

the investment may be underpriced;
the forecast may be overly optimistic;
beta may be estimated incorrectly;
CAPM may omit another relevant source of risk.

Note

The difference will later become the basis for measuring alpha, but it is not proof of mispricing or skill. Alpha belongs to Lesson 7.5.

7.3.10Section 9 · Why prices move assets toward the SML

Same beta, different offered return

Equilibrium logic: if two assets carry identical systematic risk, prices must adjust until their required returns match.

Asset A

β_{A} = 1, E [R_{A}] = 10%

Asset B

β_{B} = 1, E [R_{B}] = 14%

1Investors prefer B for the same systematic exposure.
2Demand for B raises its current price.
3A higher current price lowers its expected return.
4Weaker demand lowers A's current price.
5A lower price raises A's expected return.

Required conclusion

Under CAPM equilibrium, investments with the same beta should offer the same required expected return. This is the same market-clearing price logic introduced in Lesson 7.1.

7.3.11Section 10 · Security Market Line versus Capital Market Line

Two lines, two risk measures

Both lines look similar, but they price different kinds of risk. Read the axes carefully.

	Capital Market Line	Security Market Line
Risk measure	Standard deviation	Beta
Applies to	Efficient complete portfolios	Any asset, portfolio, or project
Horizontal axis	Total volatility	Market exposure
Main use	Efficient risk-return combinations	Required return for systematic risk

Capital Market Line

E [R_{P}] = R_{f} + \frac{σ _{P}}{σ _{M}} (E [R_{M}] - R_{f})

Security Market Line

E [R_{i}] = R_{f} + β_{i} (E [R_{M}] - R_{f})

Definition · Memory aid

CML: total risk of efficient portfolios.SML: priced market risk of any investment.

7.3.12Interaction · Change the price of market risk

Predict what a steeper SML does

Hold R_f constant and compare a 4% market risk premium against an 8% one. Predict the intercept, the slope, and which betas move most — then see the lines.

Setup

Hold $R_{f} = 4%$ constant. Compare two economies: one with a market risk premium of $4%$ (calmer markets, lower required compensation) and one with a market risk premium of $8%$ (investors demand more return per unit of market risk).

Predict first. The graphs reveal only after you answer all three questions.

When the market risk premium rises, does the intercept at β = 0 move?

Does the slope of the SML change?

Which beta levels see the largest increase in required return?

7.3.13Section 11 · Three interpretations of required return

Investor, company, and project

The same number answers three different questions, depending on who asks.

Investor

The expected return I require for bearing this equity risk.

Company

The return shareholders require, so this is the company's cost of equity.

Project

The opportunity cost for a project with comparable systematic risk.

investor required return = company cost of equity = opportunity cost for comparable risk

Project example

A company with beta 0.7 considers a project whose comparable businesses have beta 1.3. With $R_{f} = 4%$ and a market risk premium of $5.5%$ :

R_{project} = 4% + 1.3 \times 5.5%

R_{project} = 11.15%

Note

The discount rate should reflect the project's systematic risk, not automatically the parent company's existing beta.

7.3.14Exercise · Is the return enough?

Compute, then classify, then judge

With $R_{f} = 3.5%$ and a market risk premium of $6%$ , compute each required return and compare it to the forecast. The classification appears only after you check.

CAPM-required returns (R_f = 3.5%, MRP = 6%)

E[R] = 3.5% + β × 6%.

R_A for β = 0.6

R_B for β = 1.0

R_C for β = 1.4

7.3.15Explicit ending · The takeaway

Required return = base + compensation for systematic risk

This conclusion must be visible before the completion gate.

required return = R_{f} + β \times market risk premium

Beta measures the quantity of systematic market exposure.
The market risk premium measures the price of that exposure.
The Security Market Line combines them to determine the required expected return.
A higher expected return is not automatically better. It must be evaluated relative to beta.

7.3.16Final check · The core conclusions

Confirm what the SML does and does not mean

Five questions on required return, linearity, and the distinction between concepts of return.

1. What does the market risk premium represent?

2. Why is the SML a straight line?

3. Is a higher required return a sign of a better investment?

4. Is the required return guaranteed to be realized?

5. What risk measure does the SML use?

7.3.17Transition · Toward estimating beta

CAPM can compute a required return — once beta is known

The SML turns beta into a required return. But where does a company's beta actually come from?

In reality, beta is not directly observable. It must be estimated from how the security moved relative to a market benchmark — and that estimate is uncertain.

E [R_{i}] = R_{f} + \hat{β}_{i} (E [R_{M}] - R_{f})

The hat means “estimated from data.” Lesson 7.4 builds beta from return data and explains why the estimate is not a permanent label.

Try itMastery check

Pass with 4 of 6 correct

Answer all questions, then check your work. You can retry any time — mastery is based on correctness, not speed.

01
What does the market risk premium E[ $R_{M}$ ] − $R_{f}$ represent?
02
Why is the Security Market Line a straight line?
03
With $R_{f}$ = 4% and a market risk premium of 6%, what is the required return for β = 1.5?
04
Does a higher required return mean an investment is superior?
05
What distinguishes the Security Market Line from the Capital Market Line?
06
Is the CAPM required return a guaranteed realized outcome?

Lesson summary

1Beta measures the quantity of systematic market exposure an investment carries.
2The market risk premium E[ $R_{M}$ ] − $R_{f}$ is the price of one unit of market exposure.
3Required return = $R_{f}$ + β × (E[ $R_{M}$ ] − $R_{f}$ ): base compensation plus systematic-risk compensation.
4Each additional unit of beta earns the same premium, so the SML is a straight line.
5The SML plots β on the horizontal axis and E[R] on the vertical axis, with intercept $R_{f}$ and slope equal to the market risk premium.
6A negative-beta asset may have a required return below $R_{f}$ because of its hedging value.
7Higher expected return compensates for higher systematic risk; it is not a sign of superiority.
8Required return is an equilibrium benchmark, distinct from a forecast and from the realized return that actually occurs.
9The CML uses total volatility of efficient portfolios; the SML uses priced market risk (beta) of any investment.
10The same required return is, from different viewpoints, investor required return, company cost of equity, and project opportunity cost.

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