Lead lag · Hou and Moskowitz (2005)

Price Delay (R-Squared)

One minus the ratio of R-squared from a regression of daily returns on contemporaneous market return alone to R-squared from a regression also including four lags of market return. Long high minus short low quintile portfolio of stocks above the NYSE 20th size percentile, value-weighted, re-sorted monthly, hedged each month with a rolling 5-year market beta from prior months only (β = −0.24 at the end of the sample). Quarterly, 1930Q4 to 2024Q2.

Predicted alphareturn · posterior mean, % per year, averaged over the window

Next quarter

2027Q1

1.01%

95% interval −2.29% to 3.57%

Next year

2027Q1–2027Q4

1.03%

95% interval −2.23% to 3.56%

Next five years

2027Q1–2031Q4

1.09%

95% interval −2.01% to 3.58%

Forecast made 1 Oct 2026, conditioning on this portfolio's returns, which end 2024Q2 with Open Source Asset Pricing's data for the signal (PriceDelayRsq). The 10 quarters between then and 2027Q1 are unobserved and are integrated out under the model.

Portfolio

Market hedge

Prior beliefsDefault

Half life of shocks to the edge

Long-run performance

Time variation in risk-adjusted returns

Quintile and decile portfolios are sorted each month over common stocks on the NYSE, AMEX and Nasdaq whose market value is above the NYSE 20th percentile, with breakpoints computed over those same stocks, so every signal is measured on one universe. Original paper is Open Source Asset Pricing's replication of the paper's own portfolio, with its sort, weighting, stock screens and rebalancing.

Cumulative market-hedged returnreturn, unhedged

+128% since 1930Q4 · log scale

Past performance, annualized

Window	AlphaReturn	Vol.	Info. ratioSharpe ratio	t-stat
1930Q4–2024Q2	1.52%	11.47%	0.13	1.28
2019Q3–2024Q2	−4.59%	14.85%	−0.31	−0.69
2023Q3–2024Q2	−9.11%	7.19%	−1.27	−1.27
1930Q4–2024Q2	2.17%	9.91%	0.22	2.12
2019Q3–2024Q2	−8.11%	8.91%	−0.91	−2.04
2023Q3–2024Q2	−3.29%	4.04%	−0.81	−0.81
1930Q4–2024Q2	1.73%	13.98%	0.12	1.20
2019Q3–2024Q2	−10.61%	13.95%	−0.76	−1.70
2023Q3–2024Q2	−6.17%	10.60%	−0.58	−0.58
1930Q4–2024Q2	2.01%	11.07%	0.18	1.76
2019Q3–2024Q2	−13.45%	11.82%	−1.14	−2.54
2023Q3–2024Q2	−5.10%	6.16%	−0.83	−0.83
1930Q4–2024Q2	9.24%	17.36%	0.53	5.15
2019Q3–2024Q2	−4.58%	16.66%	−0.27	−0.61
2023Q3–2024Q2	−22.49%	6.59%	−3.41	−3.41
1927Q4–2024Q2	1.37%	11.16%	0.12	1.21
2019Q3–2024Q2	−3.89%	14.79%	−0.26	−0.59
2023Q3–2024Q2	−8.32%	6.98%	−1.19	−1.19
1927Q4–2024Q2	1.97%	9.56%	0.21	2.03
2019Q3–2024Q2	−4.78%	10.75%	−0.44	−0.99
2023Q3–2024Q2	1.01%	3.77%	0.27	0.27
1927Q4–2024Q2	2.05%	13.45%	0.15	1.50
2019Q3–2024Q2	−10.61%	13.73%	−0.77	−1.73
2023Q3–2024Q2	−6.23%	10.50%	−0.59	−0.59
1927Q4–2024Q2	1.96%	10.75%	0.18	1.79
2019Q3–2024Q2	−10.15%	13.05%	−0.78	−1.74
2023Q3–2024Q2	−0.70%	5.38%	−0.13	−0.13
1927Q4–2024Q2	8.12%	17.47%	0.46	4.57
2019Q3–2024Q2	−2.73%	17.48%	−0.16	−0.35
2023Q3–2024Q2	−20.67%	7.31%	−2.83	−2.83
1927Q4–2024Q2	−0.91%	11.62%	−0.08	−0.77
2019Q3–2024Q2	−7.44%	15.82%	−0.47	−1.05
2023Q3–2024Q2	−13.19%	8.37%	−1.58	−1.58
1927Q4–2024Q2	−0.82%	10.47%	−0.08	−0.77
2019Q3–2024Q2	−9.22%	8.87%	−1.04	−2.32
2023Q3–2024Q2	−4.82%	4.73%	−1.02	−1.02
1927Q4–2024Q2	−1.19%	13.97%	−0.09	−0.84
2019Q3–2024Q2	−15.49%	16.13%	−0.96	−2.15
2023Q3–2024Q2	−13.07%	11.99%	−1.09	−1.09
1927Q4–2024Q2	−1.55%	12.29%	−0.13	−1.24
2019Q3–2024Q2	−15.62%	11.92%	−1.31	−2.93
2023Q3–2024Q2	−7.94%	7.50%	−1.06	−1.06
1927Q4–2024Q2	5.29%	16.53%	0.32	3.15
2019Q3–2024Q2	−7.06%	16.39%	−0.43	−0.96
2023Q3–2024Q2	−25.91%	5.28%	−4.91	−4.91

Forecast information ratioSharpe ratio, annualized

Window	Mean	95% interval	P(neg)
2027Q1	0.09	−0.20 – 0.31	0.21
2027Q1–2027Q4	0.09	−0.19 – 0.31	0.21
2027Q1–2031Q4	0.10	−0.15 – 0.31	0.19
Prior changed from site default.
2027Q1	0.05	−0.40 – 0.37	0.37
2027Q1–2027Q4	0.06	−0.36 – 0.37	0.35
2027Q1–2031Q4	0.09	−0.25 – 0.37	0.29
Prior changed from site default.
2027Q1	0.05	−0.30 – 0.30	0.31
2027Q1–2027Q4	0.06	−0.27 – 0.30	0.30
2027Q1–2031Q4	0.07	−0.20 – 0.30	0.27
Prior changed from site default.
2027Q1	−0.25	−0.75 – 0.26	0.79
2027Q1–2027Q4	−0.21	−0.66 – 0.26	0.78
2027Q1–2031Q4	−0.11	−0.44 – 0.26	0.71
Prior changed from site default.
2027Q1	0.32	−0.15 – 0.65	0.09
2027Q1–2027Q4	0.32	−0.13 – 0.65	0.08
2027Q1–2031Q4	0.33	−0.06 – 0.65	0.05
Prior changed from site default.
2027Q1	0.09	−0.17 – 0.30	0.20
2027Q1–2027Q4	0.09	−0.16 – 0.30	0.20
2027Q1–2031Q4	0.10	−0.13 – 0.30	0.19
Prior changed from site default.
2027Q1	0.16	−0.10 – 0.38	0.09
2027Q1–2027Q4	0.17	−0.09 – 0.38	0.09
2027Q1–2031Q4	0.17	−0.07 – 0.38	0.07
Prior changed from site default.
2027Q1	0.08	−0.27 – 0.32	0.26
2027Q1–2027Q4	0.08	−0.25 – 0.32	0.25
2027Q1–2031Q4	0.09	−0.18 – 0.32	0.22
Prior changed from site default.
2027Q1	0.06	−0.37 – 0.35	0.31
2027Q1–2027Q4	0.07	−0.34 – 0.35	0.30
2027Q1–2031Q4	0.09	−0.23 – 0.35	0.26
Prior changed from site default.
2027Q1	0.29	−0.13 – 0.59	0.08
2027Q1–2027Q4	0.29	−0.11 – 0.59	0.08
2027Q1–2031Q4	0.30	−0.06 – 0.59	0.05
Prior changed from site default.
2027Q1	−0.10	−0.37 – 0.11	0.81
2027Q1–2027Q4	−0.10	−0.35 – 0.11	0.81
2027Q1–2031Q4	−0.09	−0.30 – 0.11	0.80
Prior changed from site default.
2027Q1	−0.10	−0.36 – 0.11	0.80
2027Q1–2027Q4	−0.09	−0.34 – 0.11	0.80
2027Q1–2031Q4	−0.09	−0.30 – 0.11	0.80
Prior changed from site default.
2027Q1	−0.15	−0.50 – 0.10	0.86
2027Q1–2027Q4	−0.14	−0.47 – 0.10	0.86
2027Q1–2031Q4	−0.12	−0.37 – 0.10	0.85
Prior changed from site default.
2027Q1	−0.20	−0.60 – 0.06	0.92
2027Q1–2027Q4	−0.19	−0.56 – 0.06	0.92
2027Q1–2031Q4	−0.17	−0.43 – 0.06	0.92
Prior changed from site default.
2027Q1	0.09	−0.36 – 0.44	0.33
2027Q1–2027Q4	0.10	−0.32 – 0.44	0.31
2027Q1–2031Q4	0.13	−0.20 – 0.44	0.24
Prior changed from site default.

Closest tradable stand-in

Portfolio

Long MTUM iShares Momentum Short XLK SPDR Technology Sector

Correlation: 0.64; held out, Jan 2023 – Aug 2024
Beta: 0.54; ± 0.07
Alpha: −3.0%; per year · t-stat = −0.43

Matched against this site's VW quintiles long-short series, rebuilt day by day from the same holdings. Chosen out of every pair of the ~870 ETFs with >$1m/day in volume throughout 2020–2024. Pairs chosen 2020–2022, metrics calculated over Jan 2023 – Aug 2024. Alpha and Beta from a regression of stand-in portfolio on paper returns of anomaly portfolio. Beta of 0.54 means stand-in moves 0.54% for each 1% move of the anomaly. Alpha of −3.0% means the stand-in returned 3.0 percentage points a year less than its exposure to the anomaly implies. At t = −0.43 it is not statistically significant, which is the usual outcome over 20 months — the window is too short to resolve an alpha of this size either way. This is a resemblance, not a replication, and nothing here is advice.