Section 4 - Empirical Tests of CAPM, APT, Factor Models

Value Stock

Low market price relative to book value

Growth Stock

High market price relative to book value

Roll’s Critique

• CAPM testing is only really a joint test of is the market proxy mean variance efficient or not Since we cannot observe the true market portfolio (requires real estate, human capital and every possible asset)

• So we can’t outline that CAPM fails outright for example, just that our proxy has failed

Why we still use CAPM

1. Reasonable market proxies exist even if they aren’t perfect

2. It gives clean intuition about the risk-return trade-off

3. Missing risk factors can be added via multi-factor models rather than discarding the framework entirely

4. Assumptions can be relaxed one at a time

5. It central intuition remain valid regardless of which specific model turns out to be giht

APT’s advantage

• It is derived from weaker assumptions (no need for investor optimisation, homogeneous beliefs, or a correctly identified market portfolio)

• Only needs the Law of One Price and enough assets to diversify away idiosyncratic risk

APT Disdvantage

• The theory doesn’t tell you what the factors are, that has to come from somewhere else

Tracking portfolio

Represent the risk profile (factor sensitivities) of a benchmark

• constructed by setting the tracking portfolio’s factor betas equal to the benchmark

• Used for hedging, corporate risk management

• Cost of capital estimation via APT

Factor investing - Limitations

1. Many premium-generating factors (momentun, value, size) lack a clean economic story, unlike credit risk e.g. it makes future behaviour unreliable

2. Even factors with sound economic backing tend to be small in magnitude

3. Open questions: is factor investing still “worth it” once croweded, Sustainability/ ESG interactions?

Efficient Market Hypothesis

• Jensen: A market is efficient w.r.t. an information set if it is impossible to earn economic profit by trading on

• Matlier: a market is efficient if it fully and correctly reflects all relevant information on prices

• Components: the information set used, whether it can be exploited in a trading strategy, whether the test is measured in economic (risk-adjusted, net-of-cost) profits

Does the Evidence Support EMH

• Markets appear efficient with respect to any information set

• Evidence of slow adjustment to public information in some settings; there are investors who consistently generate excess returns

• Hard to reconcile with strict EMH, though it could be seen as uncommon luck