Evidence tables
Sharpe ratio, mean ± sd over 5 seeds [min, max]
| Agent |
Reported |
Share env + turbulence rule |
Share env, no rule |
Benchmark paper-2021 |
| DDPG |
1.38 |
1.16 ± 0.19 [0.92, 1.43] |
1.06 ± 0.18 [0.80, 1.24] |
0.70 ± 0.17 [0.57, 0.97] |
| TD3 |
1.37 |
1.10 ± 0.34 [0.57, 1.37] |
1.00 ± 0.30 [0.53, 1.37] |
0.70 ± 0.21 [0.43, 1.01] |
| SAC |
1.33 |
1.23 ± 0.13 [1.07, 1.42] |
1.23 ± 0.18 [1.01, 1.49] |
0.66 ± 0.26 [0.19, 0.82] |
| PPO |
1.09 |
1.17 ± 0.21 [0.80, 1.32] |
0.95 ± 0.21 [0.74, 1.21] |
0.98 ± 0.04 [0.93, 1.02] |
| A2C |
0.82 |
1.09 ± 0.15 [0.91, 1.27] |
0.97 ± 0.15 [0.80, 1.16] |
1.03 ± 0.01 [1.01, 1.05] |
| LSTM forecast |
1.19 |
– |
– |
0.75 ± 0.29 [0.45, 1.08] |
| 1/N buy and hold |
– |
1.10 |
1.10 |
1.11 |
Annual return, mean ± sd over 5 seeds [min, max]
| Agent |
Reported |
Share env + turbulence rule |
Share env, no rule |
Benchmark paper-2021 |
| DDPG |
55.51% |
24.6% ± 5.9 [15.9%, 30.4%] |
30.6% ± 8.3 [18.5%, 40.5%] |
16.2% ± 5.4 [12.0%, 25.0%] |
| TD3 |
42.00% |
23.3% ± 9.4 [8.8%, 31.3%] |
28.7% ± 12.3 [10.8%, 44.9%] |
15.7% ± 5.8 [8.5%, 24.4%] |
| SAC |
38.95% |
25.1% ± 2.5 [21.1%, 27.8%] |
38.5% ± 7.0 [27.8%, 46.0%] |
15.1% ± 7.6 [1.6%, 19.7%] |
| PPO |
27.89% |
16.0% ± 4.7 [10.6%, 22.3%] |
25.3% ± 7.9 [15.6%, 33.3%] |
23.9% ± 1.2 [22.3%, 25.4%] |
| A2C |
20.47% |
21.5% ± 5.1 [16.5%, 28.2%] |
26.0% ± 6.5 [19.0%, 35.4%] |
25.1% ± 0.4 [24.7%, 25.8%] |
| LSTM forecast |
16.99% |
– |
– |
17.9% ± 9.5 [9.1%, 28.3%] |
| 1/N buy and hold |
– |
29.7% |
29.7% |
29.9% |
Maximum drawdown, mean over 5 seeds [worst, best]
| Agent |
Reported |
Share env + turbulence rule |
Share env, no rule |
Benchmark paper-2021 |
| DDPG |
-33.52% |
-18.0% [-18.6%, -17.4%] |
-27.8% [-30.8%, -25.7%] |
-29.3% [-31.7%, -27.4%] |
| TD3 |
-25.24% |
-19.0% [-20.2%, -17.5%] |
-28.2% [-32.7%, -25.0%] |
-29.3% [-33.7%, -26.5%] |
| SAC |
-24.19% |
-17.7% [-21.8%, -14.8%] |
-27.0% [-32.2%, -22.5%] |
-30.2% [-33.7%, -28.1%] |
| PPO |
-25.33% |
-9.2% [-11.7%, -6.7%] |
-27.4% [-32.0%, -25.3%] |
-28.1% [-28.6%, -27.6%] |
| A2C |
-31.11% |
-17.2% [-18.9%, -14.5%] |
-29.0% [-31.2%, -26.5%] |
-28.2% [-28.3%, -28.0%] |
| LSTM forecast |
−9.57% |
– |
– |
-26.5% [-28.8%, -23.8%] |
| 1/N buy and hold |
– |
– |
– |
-29.4% |
Sharpe against 1/N, seed-averaged returns (one-sided paired stationary bootstrap)
Share env (A, B): from paper-2021-share-env-equity.json, alpha, beta and the Newey-West t of the
seed-averaged daily returns. Benchmark (C): alpha, beta and t as in leaderboard/LEADERBOARD.md
(per-seed values averaged). 'Seeds above' counts seeds whose own Sharpe exceeds that setup's 1/N Sharpe.
| Setup |
Agent |
Sharpe of seed-avg returns |
ΔSharpe vs 1/N |
p |
Alpha |
Alpha t (HAC) |
Beta |
Seeds above 1/N |
| Share env + turbulence rule |
DDPG |
1.22 |
+0.12 |
0.320 |
7.4% |
0.9 |
0.56 |
3/5 |
| Share env + turbulence rule |
TD3 |
1.20 |
+0.09 |
0.328 |
6.4% |
0.9 |
0.55 |
3/5 |
| Share env + turbulence rule |
SAC |
1.33 |
+0.22 |
0.218 |
8.9% |
1.2 |
0.52 |
4/5 |
| Share env + turbulence rule |
PPO |
1.26 |
+0.15 |
0.339 |
6.7% |
1.1 |
0.30 |
4/5 |
| Share env + turbulence rule |
A2C |
1.14 |
+0.04 |
0.398 |
5.4% |
0.7 |
0.54 |
2/5 |
| Share env, no rule |
DDPG |
1.11 |
+0.00 |
0.496 |
1.2% |
0.3 |
1.00 |
3/5 |
| Share env, no rule |
TD3 |
1.06 |
-0.04 |
0.654 |
-0.2% |
-0.0 |
0.99 |
1/5 |
| Share env, no rule |
SAC |
1.32 |
+0.22 |
0.133 |
7.5% |
1.6 |
1.00 |
4/5 |
| Share env, no rule |
PPO |
1.00 |
-0.11 |
0.713 |
-2.0% |
-0.4 |
0.95 |
1/5 |
| Share env, no rule |
A2C |
0.99 |
-0.11 |
0.792 |
-2.3% |
-0.6 |
0.98 |
1/5 |
Benchmark paper-2021 |
DDPG |
0.71 |
-0.40 |
0.985 |
-9.9% |
-2.2 |
0.95 |
0/5 |
Benchmark paper-2021 |
TD3 |
0.71 |
-0.40 |
0.977 |
-9.4% |
-1.7 |
0.91 |
0/5 |
Benchmark paper-2021 |
SAC |
0.68 |
-0.43 |
0.998 |
-10.8% |
-2.2 |
0.95 |
0/5 |
Benchmark paper-2021 |
PPO |
0.98 |
-0.13 |
0.898 |
-2.9% |
-1.2 |
0.92 |
0/5 |
Benchmark paper-2021 |
A2C |
1.03 |
-0.08 |
0.825 |
-1.8% |
-0.8 |
0.92 |
0/5 |
Benchmark paper-2021 |
LSTM forecast |
0.84 |
-0.27 |
0.831 |
-4.4% |
-0.5 |
0.81 |
0/5 |
Sessions with unchanged equity (|daily return| < 1e-9)
| Setting |
Runs |
Runs with no such session |
Distinct sets of such sessions |
Sessions |
| Share env + turbulence rule |
25 |
0 |
1 |
2020-03-17, 2020-03-20, 2020-03-23, 2020-03-24, 2020-03-25 |
| Share env, no rule |
25 |
25 |
1 |
– |
Per-seed Sharpe ratio
| Setup |
Agent |
Seed 0 |
Seed 1 |
Seed 2 |
Seed 3 |
Seed 4 |
| Share env + turbulence rule |
DDPG |
1.43 |
1.08 |
1.18 |
1.20 |
0.92 |
| Share env + turbulence rule |
TD3 |
1.37 |
0.98 |
0.57 |
1.28 |
1.31 |
| Share env + turbulence rule |
SAC |
1.42 |
1.07 |
1.27 |
1.21 |
1.20 |
| Share env + turbulence rule |
PPO |
1.32 |
1.19 |
0.80 |
1.32 |
1.21 |
| Share env + turbulence rule |
A2C |
1.27 |
1.09 |
1.20 |
1.00 |
0.91 |
| Share env, no rule |
DDPG |
1.24 |
0.98 |
1.11 |
1.18 |
0.80 |
| Share env, no rule |
TD3 |
1.37 |
0.96 |
0.53 |
1.05 |
1.07 |
| Share env, no rule |
SAC |
1.49 |
1.01 |
1.33 |
1.17 |
1.14 |
| Share env, no rule |
PPO |
1.09 |
0.76 |
0.74 |
0.94 |
1.21 |
| Share env, no rule |
A2C |
1.16 |
0.98 |
1.03 |
0.80 |
0.85 |
Benchmark paper-2021 |
DDPG |
0.57 |
0.61 |
0.97 |
0.77 |
0.59 |
Benchmark paper-2021 |
TD3 |
0.72 |
1.01 |
0.61 |
0.72 |
0.43 |
Benchmark paper-2021 |
SAC |
0.19 |
0.82 |
0.71 |
0.77 |
0.80 |
Benchmark paper-2021 |
PPO |
0.93 |
1.02 |
0.98 |
0.97 |
1.01 |
Benchmark paper-2021 |
A2C |
1.02 |
1.02 |
1.05 |
1.01 |
1.03 |
Benchmark paper-2021 |
LSTM forecast |
0.63 |
0.56 |
1.08 |
1.05 |
0.45 |
Per-seed annual return
| Setup |
Agent |
Seed 0 |
Seed 1 |
Seed 2 |
Seed 3 |
Seed 4 |
| Share env + turbulence rule |
DDPG |
30.4% |
21.9% |
25.7% |
29.0% |
15.9% |
| Share env + turbulence rule |
TD3 |
31.3% |
18.8% |
8.8% |
28.9% |
28.7% |
| Share env + turbulence rule |
SAC |
27.8% |
21.1% |
25.3% |
26.2% |
25.1% |
| Share env + turbulence rule |
PPO |
22.3% |
12.2% |
10.6% |
17.3% |
17.5% |
| Share env + turbulence rule |
A2C |
28.2% |
21.9% |
24.5% |
16.5% |
16.6% |
| Share env, no rule |
DDPG |
35.2% |
27.1% |
31.8% |
40.5% |
18.5% |
| Share env, no rule |
TD3 |
44.9% |
25.9% |
10.8% |
29.9% |
32.3% |
| Share env, no rule |
SAC |
46.0% |
27.8% |
42.3% |
40.6% |
35.8% |
| Share env, no rule |
PPO |
32.8% |
15.6% |
19.3% |
25.3% |
33.3% |
| Share env, no rule |
A2C |
35.4% |
26.3% |
28.1% |
19.0% |
21.0% |
Benchmark paper-2021 |
DDPG |
12.0% |
12.3% |
25.0% |
17.6% |
14.0% |
Benchmark paper-2021 |
TD3 |
16.1% |
24.4% |
13.7% |
15.9% |
8.5% |
Benchmark paper-2021 |
SAC |
1.6% |
19.5% |
17.3% |
17.3% |
19.7% |
Benchmark paper-2021 |
PPO |
22.3% |
25.4% |
23.6% |
23.5% |
24.5% |
Benchmark paper-2021 |
A2C |
24.9% |
25.0% |
25.8% |
24.7% |
25.3% |
Verdict by setup (same rule everywhere)
| Claim |
Share env + turbulence rule |
Share env, no rule |
Benchmark paper-2021 |
ddpg-annual-return |
✗ |
✗ |
✗ |
ddpg-sharpe |
◐ |
✗ |
✗ |
td3-sharpe |
◐ |
◐ |
✗ |
sac-sharpe |
◐ |
◐ |
✗ |
ppo-sharpe |
◐ |
◐ |
✗ |
a2c-sharpe |
◐ |
◐ |
◐ |