Anomaly Outlook
Profitability alt · Hirschleifer, Hsu and Li (2013)

Patents per R&D Dollar

Patents granted in a year divided by a distributed lag of research-and-development spending over the prior five years, among firms below NYSE-median size. Long high minus short low portfolio built as the original paper built it (its sort, weighting and stock screens, as replicated by Open Source Asset Pricing), hedged each month with a rolling 5-year market beta from prior months only (β = −1.57 at the end of the sample). Quarterly, 1980Q3 to 2018Q2. It stops at 2018Q2 rather than 2023Q2: after gaps in the series, too few of the 60 months before each later quarter are present to estimate a rolling beta (36 are needed).

Predicted alphareturn · posterior mean, % per year, averaged over the window
Next quarter
2027Q1
−2.86%
95% interval −13.56% to 5.96%
Next year
2027Q1–2027Q4
−2.74%
95% interval −13.36% to 6.01%
Next five years
2027Q1–2031Q4
−2.24%
95% interval −12.50% to 6.26%

Forecast made 1 Oct 2026, conditioning on this portfolio's returns, which end 2018Q2 with Open Source Asset Pricing's data for the signal (PatentsRD). The 34 quarters between then and 2027Q1 are unobserved and are integrated out under the model.

Market hedge
Prior beliefsDefault
Half life of shocks to the edge How long an edge lasts once it appears. The model treats the edge -- the expected alpha under a market hedge, the expected return without one -- as a mean-reverting state; this is the prior on its half-life. A short half-life pulls the forecast back toward the long-run mean quickly, so recent performance counts for less. Short U(0, 5 years)Default U(0, 10 years)Long U(0, 20 years)
Long-run performance How much long-run edge the model is willing to believe in before the data insists on it. The prior on the portfolio's annualized risk-adjusted return (its information ratio under a hedge, Sharpe ratio without one) is centred on zero; this is its width. A narrow prior takes more evidence to move, so every forecast is pulled harder toward zero. Skeptical N(0, 0.2²)Default N(0, 0.4²)Permissive N(0, 0.6²)
Time variation in risk-adjusted returns How far an edge swings around its long-run level. The previous row sets how large that long-run level may be; this one sets how much the portfolio's risk-adjusted return wanders above and below it from quarter to quarter. Allow more, and a good or bad run reads as news about the edge rather than as noise. Conservative U(0, 0.25)Default U(0, 0.5)Aggressive U(0, 0.75)

This signal takes only a few distinct values, so it cannot be cut into quintiles or deciles. Only the original paper's portfolio, as replicated by Open Source Asset Pricing, is shown.

Cumulative market-hedged returnreturn, unhedged

−28% since 1980Q3 · log scale

Past performance, annualized

Window AlphaReturn Vol. Info. ratioSharpe ratio t-stat
1980Q3–2018Q2 0.87% 18.64% 0.05 0.26
2005Q4–2018Q2 −15.32% 43.45% −0.35 −0.79
2017Q3–2018Q2 −73.13% 40.77% −1.79 −1.79

Forecast information ratioSharpe ratio, annualized

Window Mean 95% interval P(neg)
2027Q1 −0.15 −0.73 – 0.32 0.69
2027Q1–2027Q4 −0.13 −0.63 – 0.31 0.68
2027Q1–2031Q4 −0.07 −0.42 – 0.29 0.66
Prior changed from site default.
Category
Profitability alt
Form
Discrete
Sorted on
High minus low
Names per leg
354 long / 852 short median · 2 at the 10th pctile
Original sample
1982–2008