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

Leverage component of BM

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

Expected return · posterior mean, % per quarter

Next quarter

0.32%

95% interval −0.10% to 0.72%

Next year

0.32%

95% interval −0.11% to 0.73%

Next five years

0.31%

95% interval −0.14% to 0.76%

Next quarter

−0.31%

95% interval −0.70% to 0.23%

Next year

−0.22%

95% interval −0.65% to 0.27%

Next five years

0.03%

95% interval −0.50% to 0.53%

Next quarter

0.12%

95% interval −0.35% to 0.59%

Next year

0.12%

95% interval −0.36% to 0.60%

Next five years

0.11%

95% interval −0.37% to 0.61%

Next quarter

−0.10%

95% interval −0.37% to 0.21%

Next year

−0.04%

95% interval −0.36% to 0.29%

Next five years

0.12%

95% interval −0.34% to 0.57%

Cumulative market-adjusted return

+105% since 1962Q3 · log scale

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

Horizon	Mean	95% interval	P(neg)
Next quarter	0.090	−0.027 – 0.205	0.07
Next year	0.089	−0.030 – 0.207	0.07
Next five years	0.088	−0.041 – 0.214	0.09
Next quarter	−0.101	−0.233 – 0.074	0.90
Next year	−0.072	−0.213 – 0.088	0.83
Next five years	0.009	−0.163 – 0.171	0.45
Next quarter	0.029	−0.087 – 0.147	0.31
Next year	0.029	−0.088 – 0.148	0.31
Next five years	0.028	−0.093 – 0.151	0.32
Next quarter	−0.038	−0.147 – 0.083	0.75
Next year	−0.016	−0.142 – 0.113	0.60
Next five years	0.046	−0.131 – 0.218	0.30