BPEBM · Leverage · Penman, Richardson and Tuna (2007)

Leverage component of BM

Long minus short decile portfolio, value-weighted, market-adjusted. Quarterly, 1962Q3 to 2024Q4.

Expected return · posterior mean, % per year, averaged over the window

Next quarter

2026Q4

0.45%

95% interval −1.36% to 2.29%

Next year

2026Q4–2027Q3

0.45%

95% interval −1.37% to 2.30%

Next five years

2026Q4–2031Q3

0.45%

95% interval −1.40% to 2.32%

Forecast made 16 Sep 2026, conditioning on this portfolio's OAP returns, which end 2024Q4. The 7 quarters between then and 2026Q4 are unobserved and are integrated out under the model.

Cumulative market-adjusted return

+12% since 1962Q3 · log scale

Past performance, annualized

Window	Mean	Vol.	Sharpe	t
1962Q3–2024Q4	1.40%	7.07%	0.20	1.57
2020Q1–2024Q4	1.69%	9.27%	0.18	0.41
2024Q1–2024Q4	2.38%	8.48%	0.28	0.28
1962Q3–2024Q4	0.82%	6.15%	0.13	1.06
2020Q1–2024Q4	−4.28%	8.02%	−0.53	−1.19
2024Q1–2024Q4	−5.23%	4.43%	−1.18	−1.18
1962Q3–2024Q4	0.51%	8.07%	0.06	0.50
2020Q1–2024Q4	1.56%	9.29%	0.17	0.37
2024Q1–2024Q4	2.72%	4.90%	0.55	0.55
1962Q3–2024Q4	1.09%	5.20%	0.21	1.65
2020Q1–2024Q4	−0.97%	5.30%	−0.18	−0.41
2024Q1–2024Q4	−4.71%	0.51%	−9.22	−9.22

Forecast Sharpe ratio, annualized

Window	Mean	95% interval	P(neg)
2026Q4	0.18	−0.05 – 0.42	0.07
2026Q4–2027Q3	0.18	−0.05 – 0.41	0.07
2026Q4–2031Q3	0.17	−0.06 – 0.41	0.07
2026Q4	−0.15	−0.48 – 0.24	0.78
2026Q4–2027Q3	−0.12	−0.42 – 0.23	0.75
2026Q4–2031Q3	−0.05	−0.30 – 0.24	0.66
2026Q4	0.06	−0.17 – 0.28	0.30
2026Q4–2027Q3	0.06	−0.17 – 0.29	0.30
2026Q4–2031Q3	0.06	−0.18 – 0.29	0.30
2026Q4	−0.03	−0.29 – 0.27	0.58
2026Q4–2027Q3	−0.01	−0.26 – 0.27	0.55
2026Q4–2031Q3	0.02	−0.19 – 0.26	0.45