7.7Lesson 7.7 · Module 7 — The CAPM and APT

CAPM and APT in Practice

From market exposure to a defensible investment conclusion. A synthesis and mastery lesson that moves through the full Module 7 reasoning chain.

Connected module recap
Guided mixed practice (6 categories)
Error diagnosis
Integrated Orion Fund case
Randomized mastery check

Start

Central question

Can you move from portfolio theory to a defensible conclusion about an investment’s risk, required return, and performance?

7.7.1Phase 1 · Connected module recap

The Module 7 reasoning chain

One connected sequence from portfolio theory to multiple factors. Select any stage to see the question it answers, its formula, the key interpretation, and a common mistake.

Stage 2 · CAPM equilibrium

Why must the tangency portfolio become the market portfolio?

T = M

Key interpretation

The tangency portfolio is defined by optimization. The market portfolio is defined by asset supply. In CAPM equilibrium, prices adjust until the two coincide.

Common mistake

Saying “T = M by definition.” It holds only under equilibrium and CAPM assumptions, not as a definition.

Note

This map is the reasoning chain for the whole module. The rest of the lesson asks you to move through it end to end — from market exposure to a defensible investment conclusion.

7.7.2Phase 2 · Guided mixed practice

Calculate, interpret, and apply

Six categories of structured practice. For each problem, calculate, submit, then interpret. A numerically correct answer with a wrong interpretation is not complete.

Guided mixed practice

Six categories. Calculate, submit, then interpret. Progress is saved as you go.

0 / 6 complete

Category A

Market portfolio & equilibrium

○In progress

Problem A1 · Market clearing

Every investor wants the tangency portfolio $T = 60% Atlas + 40% Beacon$ , but the market supply is $M = 75% Atlas + 25% Beacon$ . Trace the adjustment.

1. Is this an equilibrium?

2. Which asset is over-demanded?

3. What happens to Beacon’s price?

4. What happens to Beacon’s expected return (for a fixed anticipated payoff)?

5. How does that affect Beacon’s desired tangency-portfolio weight?

6. What must ultimately be true in equilibrium?

Problem A2 · Market portfolio misconceptions

“The market portfolio treats all risky assets as one value-weighted portfolio.”

“A large-cap stock index is necessarily the complete theoretical market portfolio.”

“Market weights mean the largest companies are judged to be the best investments.”

“CAPM investors may choose different total risk while holding the same risky portfolio.”

Category B

Beta & portfolio exposure

○In progress

Problem B1 · Portfolio beta

Asset	Market fund	Defensive fund	Cyclical fund
Weight	45%	35%	20%
Beta	1.00	0.60	1.50

Weighted contributions (wᵢ × βᵢ)

β_P = Σ wᵢ βᵢ.

Market (0.45 × 1.00)

Defensive (0.35 × 0.60)

Cyclical (0.20 × 1.50)

β_P (sum)

Problem B2 · Positive and negative markets

With $β_{P} = 0.96$ :

R_{M} - R_{f} = 10% \Rightarrow 0.96 (10%) = 9.6%

R_{M} - R_{f} = - 10% \Rightarrow 0.96 (- 10%) = - 9.6%

Will the portfolio’s realized excess return necessarily equal these amounts?

Problem B3 · Same volatility, different beta

Asset	Asset X	Asset Y
Standard deviation	28%	28%
Beta	1.35	0.45

Which asset has larger total return swings?

Which asset has greater systematic market exposure?

Why can the answers differ?

Category C

Security Market Line

○In progress

Problem C1 · Required return

Given $R_{f} = 3.5%$ , $E [R_{M}] - R_{f} = 6.5%$ , and $β_{i} = 1.2$ .

R_i = R_f + β(E[R_M] − R_f) = 3.5% + 1.2 × 6.5%.

Required return R_i

Problem C2 · Is the forecast sufficient?

An analyst forecasts $E [R_{i}]^{forecast} = 12.4%$ . The difference is $12.4% - 11.3% = 1.1%$ .

Choose the most defensible conclusion.

Problem C3 · CML or SML?

Efficient combinations of the market portfolio and risk-free asset.

Required return for an individual stock.

Horizontal axis is standard deviation.

Horizontal axis is beta.

Applies to any asset or project.

Applies only to efficient complete portfolios.

Category D

Beta estimation

○In progress

Problem D1 · Read the regression

R_{i} - R_{f} = 0.08% + 1.35 (R_{M} - R_{f}) + ε_{i}

R²

30%

SE(β̂)

0.16

β̂

1.35

Interpret β̂ = 1.35.

Interpret R² = 30%.

Interpret SE(β̂) = 0.16.

What is the residual ε?

Problem D2 · Choose a relevant beta

Measure	10-year	5-year	2-year
Beta	0.75	0.95	1.40

In the last two years the company sold a stable consumer division, acquired a cyclical technology business, and increased financial leverage.

Which is the most defensible choice of beta for a forward-looking CAPM analysis?

Problem D3 · Slope versus fit

Pair 1 — same beta

Asset A · β / R²1.2 / 70%

Asset B · β / R²1.2 / 18%

Same sensitivity; very different tightness around the line.

Pair 2 — same R²

Asset C · β / R²0.6 / 45%

Asset D · β / R²1.5 / 45%

Same fit; different response magnitude.

Which quantity measures sensitivity to the market?

Which quantity measures explanatory power?

What does the spread of points around the line represent?

Category E

Alpha & performance

○In progress

Problem E1 · Same return, different alpha

$R_{f} = 4%, E [R_{M}] - R_{f} = 6%$ . Each fund earned 12%.

Fund	A	B	C
Average return	12%	12%	12%
Beta	0.6	1.0	1.4

Required return and CAPM alpha per fund

Required = 4% + β×6%. Alpha = 12% − required.

R_A required (β=0.6)

α_A = 12% − R_A

R_B required (β=1.0)

α_B = 12% − R_B

R_C required (β=1.4)

α_C = 12% − R_C

Problem E2 · Does positive alpha prove skill?

CAPM alpha4.5%

A first reading of α_CAPM = 4.5% suggests outperformance. Is this proof of skill?

Category F

APT & multifactor models

○In progress

Problem F1 · Multifactor required return

Factor premiums

λ_M (market)5%

λ_S (size)2%

λ_V (value)1.5%

Asset exposures

β_M1.1

β_S0.5

β_V−0.2

E[R] = 3% + 1.1×5% + 0.5×2% − 0.2×1.5%.

E[R_i] required

Problem F2 · APT pricing pressure

Portfolio	X	Y
Market beta	1.0	1.0
Factor 2 beta	0.4	0.4
Expected return	11%	8%

Construct long X − short Y. Net market exposure $1.0 - 1.0 = 0$ ; net factor-2 exposure $0.4 - 0.4 = 0$ ; expected-return difference $11% - 8% = 3%$ .

What should price pressure do to the 3% gap?

Which qualification matters most for a real trade?

Problem F3 · CAPM versus APT

One market factor.

Multiple possible systematic factors.

Market-clearing equilibrium.

No-arbitrage pricing pressure.

Identifies a theoretical market portfolio.

Does not determine the correct factors.

7.7.3Phase 3 · Model comparison & error diagnosis

Find the broken reasoning

Five analyst statements each contain one error. Identify the faulty phrase and choose the corrected interpretation.

Find the broken reasoning

Five analysts each made one error. Identify the faulty phrase and choose the corrected interpretation for each.

“This portfolio has beta 1.4, so it is 40% more volatile than the market.”