import numpy as np
import matplotlib.pyplot as plt

T = 252                       # 252 days ~ 52 weeks of 5 days ~ 12 months of 21 days
for period in [1, 5, 21]:     # sample every 1 day, 1 week, or 1 month
    x = np.arange(0, T, period)
    y = 100 + x + 3 * np.sin(x)
    returns = (y[1:] / y[:-1] - 1)     # will be daily, weekly, monthly returns
    plt.plot(x, y)
    plt.show()
    plt.plot(returns)
    plt.show()
    print 'Sharpe Ratio: %.5f' % (np.sqrt(T/period) * returns.mean() / returns.std())
    # sqrt(T/period) is sqrt(252), ~ sqrt(52), sqrt(12)