Week 5 recap: the textbook claim that a stock’s expected return depends only on its sensitivity to the market.

The Capital Asset Pricing Model (1960s) says expected returns depend on one thing only:

\[E[R_i] - R_f = \beta_i \times (E[R_m] - R_f)\]

• \(R_f\): the risk-free rate (1-month T-bill return, the “safe” benchmark)
• \(E[R_m]\): the expected market return; \(E[R_m] - R_f\) is the equity risk premium
• \(\beta_i\): slope from regressing stock \(i\)’s excess returns on the market’s excess returns — how much stock \(i\) moves with the market
• High beta → high expected return (compensation for risk)
• Low beta → low expected return

Implication: The only way to earn more is to take more market risk. No other characteristic should matter.

Fama and French (1992) tested CAPM’s predictions on US stocks (1963–1990) using cross-sectional regressions (regressing average returns across firms on β, size, and B/M):

Fama and French (1993) proposed a model with three long-short portfolios:

On the 25 US size × B/M–sorted portfolios (1963–1991), this model explains ~90% of time-series return variation, versus ~70% for CAPM alone. R² depends on the test assets and sample — it is not a universal number.

Fama and French (2015) added two more factors:

For this module we use the Jensen, Kelly, and Pedersen (2023) global factor dataset:

• 71 countries, monthly frequency
• 14 factor return series (including MKT, SMB, HML, MOM, RMW, CMA)
• US sample: January 1926 to December 2023 (1,176 months)
• UK sample: January 1986 to December 2023 (456 months)
• Within portfolios: value-weighted (bigger firms get more weight)
• Breakpoints: NYSE-capitalisation quantiles (so microcaps don’t dominate the sort)

Wesley Gray (Alpha Architect, Quantitative Value, Quantitative Momentum) bridges academic research and practice:

• Backtested returns ≠ implementable returns
• Transaction costs, execution timing, and capacity constraints all erode the premium
• The academically optimal strategy and the investable strategy are often different

We build up in layers:

All figures below are annualised percentage returns. Loadings are betas (unitless). MKT in the table is already the market excess return, so the MKT factor return is \(R_m - R_f\).

A fund returned 12% last year. Market returned 8%. Risk-free rate: 2%.

Step 1: Excess return = 12% − 2% = 10%

Step 2: Suppose factor loadings are:

Step 3: Alpha = 10.0% − 8.2% = 1.8% (annualised)

A different fund returned 9% last year. Risk-free rate: 2%. Factor returns same as before.

Factor loadings: β_MKT = 0.95, β_SMB = −0.10, β_HML = 0.30, β_RMW = 0.20, β_CMA = 0.05

An alpha of 0.44% per year sounds small. Is it statistically different from zero?

To answer this, we need a t-statistic: \(t = \frac{\hat{\alpha}}{SE(\hat{\alpha})}\)

(Rough rule from Week 3 stats: |t| > 2 ≈ “probably not zero” at the 5% level.)

Researchers have documented over 300 characteristics that predict stock returns (Harvey, Liu, and Zhu 2016):

• Size, value, momentum, profitability, investment, quality, accruals, share issuance, asset growth, earnings surprise, analyst revisions, short interest, idiosyncratic volatility, …

The problem: with 300 tests and a 5% significance level, you expect 15 false discoveries — significant t-statistics that happen by chance rather than because the factor is real — assuming independent tests. Real tests are correlated, which can make this worse, not better.

McLean and Pontiff (2016) tested 97 published factors after their papers appeared:

Jensen, Kelly, and Pedersen (2024) systematically replicated factors across 93 countries:

• 153 factors tested with consistent methodology
• Standardised construction: same breakpoints, same weighting
• Result: many factors replicate, but premia are smaller than originally published

After multiple testing corrections, out-of-sample testing, and international replication:

When you interpret factor results in Lab 9 or CW2, remember:

1. Use HAC standard errors — OLS overstates significance
2. Compare in-sample to out-of-sample — split your sample or use rolling windows
3. Check multiple testing — a single significant result is not enough
4. Report Sharpe ratios and economic magnitude — not just t-statistics
5. Discuss construction choices — JKP’s methodology affects your numbers

Detzel, Novy-Marx, and Velikov (2023) show that accounting for transaction costs can reverse the ranking of factor models:

When a factor strategy becomes popular, more capital chases the same stocks:

1. Prices of “long” stocks are bid up → future returns decline
2. Prices of “short” stocks are pushed down → future short returns decline
3. The premium compresses

Momentum crash of 2009:

• Momentum lost ~73% over roughly three months (March–May 2009) as beaten-down stocks surged in the recovery
• Stocks that had been losing (the “short” side) rebounded violently
• This is a systematic risk, not a data error

Value drought (2007–2020):

• Value stocks underperformed growth by roughly 40 percentage points cumulative over the period
• Tech dominance (FAANG) rewarded growth characteristics
• Tested investor patience severely

What the evidence supports:

1. Factors are real: systematic return differences associated with firm characteristics exist
2. Premia are modest: Sharpe ratios of 0.2–0.4, not lottery tickets
3. Not all survive: multiple testing, publication bias, and decay reduce the “zoo” to 5–7 robust factors
4. Costs matter: transaction costs can eliminate premia, especially for high-turnover strategies
5. Patience required: factors can underperform for years; discipline is essential

CW2 Scaffold B (Tree-Based Factor Investing):

• Uses JKP UK monthly factors
• Walk-forward OLS, Ridge, tree-based models
• SHAP feature importance
• 2,500-word reflective report

What the report must cover:

Walk-forward, Ridge, and SHAP are previewed in Week 10 — don’t worry if the names are unfamiliar today.

Standard lab (60–90 min):

• Part 1: Simulate autocorrelation, compare OLS vs HAC
• Part 2: Alpha tests and economic interpretation
• Part 3: Robustness (sample split, rolling windows)
• Part 4: Transaction costs and selection bias

Advanced extension (optional, ~30 min):

• Build a momentum factor from individual S&P 500 stock prices
• Compare your DIY factor to JKP MOM
• Discover how construction choices affect results
• Directly relevant to CW2 “Data quality” section

1. Factors are long-short portfolios built from firm characteristics; they represent systematic tilts, not stock picks

2. Premia are real but modest — Sharpe ratios of 0.2–0.4, and many published factors fail replication

3. Honest inference requires HAC standard errors — OLS understates uncertainty in autocorrelated data

4. Costs can eliminate premia — especially for high-turnover strategies like momentum, even though momentum survives gross-of-cost tests

5. Critical evaluation matters — your CW2 report should discuss limitations, not just results

Chapter: Chapter 9: Factor Investing

Essential reading:

• Jensen, Kelly, and Pedersen (2024) — Is there a replication crisis in finance?
• Fama and French (2015) — Five-factor model
• Harvey, Liu, and Zhu (2016) — … and the cross-section of expected returns
• McLean and Pontiff (2016) — Post-publication decay (directly relevant to CW2 out-of-sample discussion)

Practitioner:

• Gray and Vogel (2016) — Quantitative Momentum (implementability)
• Gray and Carlisle (2012) — Quantitative Value

Further:

• Detzel, Novy-Marx, and Velikov (2023) — Transaction costs and factor models

📧 b.quinn1@ulster.ac.uk 🏢 Office hours by appointment

Resources:

• Chapter 9: Factor Investing
• Lab 9: Factor Replication
• CW2 Scaffold B