EDIT: updated plots

After the unfortunate recent big drawdown of the hedge fund, I have wondered if a stake weighted meta model is still a good choice for Numerai.

Looking at the model performance during the drawdown, it becomes clear that even in such difficult times there were very good performing models, whose contribution to the hedge fund was minimal due to their low stake.

Despite that, Numerai seems still confident in the stake weighted meta model approach, and instead they have been focusing on changing the payout scheme to discourage bad performing models from having large stakes.

I can understand Numerai’s decision to stick to their plan. I do not believe it is obvious how to aggregate models so that the meta model performance are maximized - in fact I mentioned once or twice that this would be a challenge worth a dedicated tournament.

Still, I am curious, so I ran some simple simulations of how the meta model performance would look like by adopting different model aggregation methods:

- model stake weighted (the Numerai preferred choice)
- mean of all submitted models
- mean of all staked models (all models whose stake is >= 1NMR)
- mean of the top 3/10/30 models with highest mean rolling correlation

To compare the performance of these different meta models I used cumulative CORR20V2. I understand that is not exactly the same as comparing the hedge fund performance, though I believe it is a good proxy.

Download the data, then plot

```
#!/usr/bin/env python3
import sys
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
if len(sys.argv) < 2:
print("Usage:")
print(f" {sys.argv[0]} round-xxx-yyy.csv")
sys.exit(1)
CORR_COL='v2Corr20'
df = pd.read_csv(sys.argv[1])
df = df[ df["isDaily"] == False ] # because of the rolling mean we cannot mix daily and weekly rounds
# keep only the needed columns
df = df[ ["modelName","selectedStakeValue","v2Corr20","roundNumber"] ]
# make sure of the sorting
df = df.sort_values(by="roundNumber", ascending=True)
def zscore(df, column):
s = df.groupby(['roundNumber'])[column].transform(lambda x: (x - x.mean()) / x.std())
df[column + 'Zscore'] = s
def rolling_mean(df, column, window, shift):
# shift(...) is required to avoid look-ahead bias
s = df.groupby(['modelName'])[column].transform(lambda x: x.rolling(window=window).mean().shift(shift) )
df[column + 'RollingMean'] = s
rolling_mean(df, CORR_COL, 4, 4) # 4 rounds rolling mean
zscore(df, CORR_COL)
rolling_mean(df, CORR_COL + "Zscore", 4, 4) # 4 rounds rolling mean
df = df.dropna(how="any") # the rolling mean generates nan to avoid look-ahead bias
staked = df[ df["selectedStakeValue"] > 1.0 ]
plt.rcParams["figure.figsize"] = [12,8] # default is [6.4, 4.8]
def plot(s):
ax = ((s.fillna(0.) + 1.0).cumprod() - 1.0).plot(kind='line', legend=True, linewidth=3)
return ax
tmp_series = df.groupby(['roundNumber']).apply(lambda x: x[CORR_COL].mean())
tmp_series.name='All models Mean v2Corr20'
plot(tmp_series)
tmp_series = staked.groupby(['roundNumber']).apply(lambda x: x[CORR_COL].mean())
tmp_series.name='Staked Models Mean v2Corr20'
plot(tmp_series)
tmp_series = df.groupby(['roundNumber']).apply(lambda x: (x[CORR_COL]*x["selectedStakeValue"]).sum()/x["selectedStakeValue"].sum() )
tmp_series.name='Stake Weighted v2Corr20'
plot(tmp_series)
tmp_series = df.groupby(['roundNumber']).apply(lambda x: x.nlargest(3, CORR_COL+"RollingMean")[CORR_COL].mean())
tmp_series.name='Top 3 Model Rolling Mean v2Corr20'
plot(tmp_series)
tmp_series = df.groupby(['roundNumber']).apply(lambda x: x.nlargest(10, CORR_COL+"RollingMean")[CORR_COL].mean())
tmp_series.name='Top 10 Model Rolling Mean v2Corr20'
plot(tmp_series)
tmp_series = df.groupby(['roundNumber']).apply(lambda x: x.nlargest(30, CORR_COL+"RollingMean")[CORR_COL].mean())
tmp_series.name='Top 30 Model Rolling Mean v2Corr20'
ax= plot(tmp_series)
ax.get_figure().savefig(f"cumulative.png")
```