Use of 0.02 default risk-free rate can surprise users

[Beliavsky]

The output of

import numpy as np
import pandas as pd
from pypfopt.efficient_frontier import EfficientFrontier

np.set_printoptions(precision=3)
n = 2
mu = (np.arange(n) + 1)**2
print("mu:", mu)
cov = np.zeros(shape=[n, n])
for i in range(n):
    cov[i, i] = (1+i)**2
print("cov:\n", cov, sep="")
ef = EfficientFrontier(mu, cov)
weights = pd.Series(ef.max_sharpe()).to_numpy()
print("weights:", weights)

is

mu: [1 4]
cov:
[[1. 0.]
 [0. 4.]]
weights: [0.496 0.504]

When I compute the tangent portfolio using numpy directly and normalize the sum of the absolute values to 1, I get weights of

[0.5, 0.5]

With calculations being done in double precision, I am surprised that the round-off error from pypfopt is so large.

Thanks for the project.

[Beliavsky]

Now I see that max_sharpe uses a default risk-free rate of 0.02. If I use

max_sharpe(risk_free_rate=0.0)

the problem goes away. I think the package should use a default risk-free rate of 0.0. Users could either set the risk-free rate themselves or pass expected excess returns.