Incorrect values of Annualised Returns and Volatility with week or Month level data

[khannavivek]

While calculating day_returns the Data is resampled to Day, but for Monthly and Weekly data the value is not correct and provides incorrect values wherever day_returns or annual_trading_days is used.

if isinstance(index, pd.DatetimeIndex):
    day_returns = equity_df['Equity'].resample('D').last().dropna().pct_change()
    gmean_day_return = geometric_mean(day_returns)
    annual_trading_days = float(
        365 if index.dayofweek.to_series().between(5, 6).mean() > 2/7 * .6 else
        252) 

# Annualized return and risk metrics are computed based on the (mostly correct)
# assumption that the returns are compounded. See: https://dx.doi.org/10.2139/ssrn.3054517
# Our annualized return matches `empyrical.annual_return(day_returns)` whereas
# our risk doesn't; they use the simpler approach below.
annualized_return = (1 + gmean_day_return)**annual_trading_days - 1
s.loc['Return (Ann.) [%]'] = annualized_return * 100
s.loc['Volatility (Ann.) [%]'] = np.sqrt((day_returns.var(ddof=int(bool(day_returns.shape))) + (1 + gmean_day_return)**2)**annual_trading_days - (1 + gmean_day_return)**(2*annual_trading_days)) * 100  # noqa: E501

I tried to figure out it like this:

   annual_trading_days = annual_trading_days /12 ##in case of month
   annual_trading_days = annual_trading_days /52 ##in case of week

Let me know if this can be implemented if it's correct or some better way to solve this.