Leverage · Leverage · Bhandari (1988)

Market leverage

Long minus short quintile portfolio, value-weighted, market-adjusted. Quarterly, 1951Q3 to 2024Q4.

Expected return · posterior mean, % per quarter

Next quarter

0.54%

95% interval −0.38% to 1.48%

Next year

0.55%

95% interval −0.41% to 1.50%

Next five years

0.57%

95% interval −0.47% to 1.57%

Next quarter

1.76%

95% interval 0.82% to 2.67%

Next year

1.73%

95% interval 0.80% to 2.66%

Next five years

1.64%

95% interval 0.60% to 2.64%

Next quarter

0.91%

95% interval −0.31% to 2.12%

Next year

0.92%

95% interval −0.31% to 2.13%

Next five years

0.95%

95% interval −0.33% to 2.18%

Next quarter

2.39%

95% interval 1.22% to 3.48%

Next year

2.32%

95% interval 1.17% to 3.46%

Next five years

2.11%

95% interval 0.75% to 3.42%

Cumulative market-adjusted return

+134% since 1951Q3 · log scale

Window	Mean	Vol.	Sharpe	t
1951Q3–2024Q4	2.58%	16.93%	0.15	1.31
2020Q1–2024Q4	−0.66%	29.62%	−0.02	−0.05
2024Q1–2024Q4	−1.82%	12.69%	−0.14	−0.14
1951Q3–2024Q4	7.20%	16.51%	0.44	3.74
2020Q1–2024Q4	15.90%	26.04%	0.61	1.37
2024Q1–2024Q4	2.22%	12.36%	0.18	0.18
1951Q3–2024Q4	4.26%	21.48%	0.20	1.70
2020Q1–2024Q4	−1.28%	34.89%	−0.04	−0.08
2024Q1–2024Q4	−6.49%	14.94%	−0.43	−0.43
1951Q3–2024Q4	9.32%	19.77%	0.47	4.04
2020Q1–2024Q4	20.15%	30.76%	0.66	1.46
2024Q1–2024Q4	6.85%	12.61%	0.54	0.54

Horizon	Mean	95% interval	P(neg)
Next quarter	0.064	−0.045 – 0.175	0.13
Next year	0.064	−0.048 – 0.177	0.13
Next five years	0.067	−0.056 – 0.186	0.13
Next quarter	0.214	0.100 – 0.324	0.00
Next year	0.210	0.097 – 0.323	0.00
Next five years	0.199	0.072 – 0.321	0.00
Next quarter	0.085	−0.029 – 0.198	0.07
Next year	0.086	−0.029 – 0.198	0.07
Next five years	0.089	−0.030 – 0.203	0.07
Next quarter	0.242	0.123 – 0.355	0.00
Next year	0.235	0.118 – 0.351	0.00
Next five years	0.213	0.075 – 0.344	0.00