Lecture 3 CAPM, APT & Factor Investing

Question 1

CAPM Overview

What is the key insight of CAPM?

Answer 1

All investors select the same market portfolio (M), which contains all securities weighted by their market values, and the Capital Allocation Line (CAL) becomes the Capital Market Line (CML).

If Speperation theorem holds –> select same stocks and weights for

Question 2

Mutual Fund Theorem (MFT)

What does the Mutual Fund Theorem state?

Answer 2

All investors hold a combination of the market portfolio and risk-free asset, making investing in a market-index fund and a risk-free asset efficient.

Key assumptions:
1. Rational investors
2. homogeneous expectations
3. no taxes
4. no transaction costs.

for passive strategies efficient in real life fund mangers produce different input lists

Question 3

CAPM Analytical Derivation (1)

How is the market price of risk defined in CAPM?

Answer 3

Equilibrium occurs when the reward-to-risk ratio is equal for all investments.

Question 4

CAPM Analytical Derivation (2)

What is the CAPM equation for expected return?

Answer 4

Question 5

Security Market Line (SML)

What does the SML represent?

Answer 5

The SML plots the expected return-beta relationship for individual securities.

• Above SML: Underpriced stocks.
• Below SML: Overpriced stocks.

Question 6

Empirical CAPM

How is the empirical CAPM model expressed?

Answer 6

alpha = non market premium beta RM(t) = Systematic Premium e = Firm speficic risk

Question 7

Total Risk Decomposition

How is total risk decomposed in empirical CAPM?

Answer 7

Question 8

Importance of the Factor Model

What is the importance of the factor model under CAPM?

Answer 8

• Reduces the complexity of the variance-covariance (VCV) matrix.
• Diversification eliminates firm-specific risk σ^2(ei) leaving only systematic risk.

Question 9

Portfolio Construction - Active Investing

How does active investing differ in CAPM?

Answer 9

Active managers seek securities with non-zero alphas (α > 0 undervalued, α < 0 overvalued) and construct under-diversified portfolios, focusing on superior security analysis.

Question 10

Optimal Risky Portfolio

What trade-off exists between active and passive investing?

Answer 10

• Passive Investing: Diversify completely σ^2(eP)=0
• Active Investing: Target securities with positive alphas, incurring higher idiosyncratic risk.

Question 11

Information Ratio (IR)

What does the Information Ratio measure?

Answer 11

• The IR measures excess return per unit of firm-specific risk.
• A higher IR indicates better security selection.
• Maximizing this ratio maximizes the SHarp Ratio

Question 12

Multi-Factor Models

What is a multi-factor model?

Answer 12

Extension of the single factor model by adding n factors

F(k) = systematic risk ß1,2 = exposure of stock i to the factor of k

Question 13

Arbitrage Pricing Theory (APT)

What are the assumptions of APT?

Answer 13

1. Returns have a factor structure.
2. Markets are well-functioning, allowing arbitrage.
3. Well-diversified portfolios are available.

Question 14

Choosing Factors

What are the two types of factors used in multi-factor models?

Answer 14

1. Macroeconomic factors (observed): GDP growth, inflation, etc.
2. Fundamental factors (unobserved): Derived from firm characteristics like size, value, momentum.