Added Jensen's alpha to statistics
Also improved doc for beta
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@ -29,8 +29,8 @@ Fincal aims to simplify things by allowing you to:
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- [x] Sync two TimeSeries
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- [x] Average rolling return
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- [x] Sharpe ratio
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- [ ] Jensen's Alpha
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- [ ] Beta
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- [x] Jensen's Alpha
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- [x] Beta
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- [ ] Sortino ratio
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- [ ] Correlation & R-squared
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- [ ] Treynor ratio
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@ -22,12 +22,15 @@ def sharpe_ratio(
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prior_match: str = "closest",
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closest: Literal["previous", "next"] = "previous",
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date_format: str = None,
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):
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) -> float:
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"""Calculate the Sharpe ratio of any time series
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Sharpe ratio is a measure of returns per unit of risk,
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where risk is measured by the standard deviation of the returns.
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The formula for Sharpe ratio is:
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(average asset return - risk free rate)/volatility of asset returns
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Parameters
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----------
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time_series_data:
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@ -60,23 +63,30 @@ def sharpe_ratio(
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return_period_value : int
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The value of the specified interval type over which returns needs to be calculated.
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as_on_match:
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as_on_match : str, optional
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The mode of matching the as_on_date. Refer closest.
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prior_match :
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prior_match : str, optional
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The mode of matching the prior_date. Refer closest.
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closest :
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closest : str, optional
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The mode of matching the closest date.
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Valid values are 'exact', 'previous', 'next' and next.
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date_format :
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The date format to use for this operation.
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Should be passed as a datetime library compatible string.
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Sets the date format only for this operation. To set it globally, use FincalOptions.date_format
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Returns
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-------
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_description_
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Value of Sharpe ratio as a float.
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Raises
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------
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ValueError
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_description_
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If risk free data or risk free rate is not provided.
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"""
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interval_days = int(_interval_to_years(return_period_unit, return_period_value) * 365 + 1)
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if from_date is None:
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@ -125,7 +135,54 @@ def beta(
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prior_match: str = "closest",
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closest: Literal["previous", "next"] = "previous",
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date_format: str = None,
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):
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) -> float:
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"""Beta is a measure of sensitivity of asset returns to market returns
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The formula for beta is:
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Parameters
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----------
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asset_data : TimeSeries
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The time series data of the asset
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market_data : TimeSeries
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The time series data of the relevant market index
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from_date:
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Start date from which returns should be calculated.
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Defaults to the first date of the series.
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to_date:
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End date till which returns should be calculated.
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Defaults to the last date of the series.
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frequency:
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The frequency at which returns should be calculated.
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return_period_unit : 'years', 'months', 'days'
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The type of time period to use for return calculation.
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return_period_value : int
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The value of the specified interval type over which returns needs to be calculated.
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as_on_match : str, optional
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The mode of matching the as_on_date. Refer closest.
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prior_match : str, optional
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The mode of matching the prior_date. Refer closest.
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closest : str, optional
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The mode of matching the closest date.
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Valid values are 'exact', 'previous', 'next' and next.
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The date format to use for this operation.
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Should be passed as a datetime library compatible string.
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Sets the date format only for this operation. To set it globally, use FincalOptions.date_format
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Returns
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-------
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The value of beta as a float.
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"""
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interval_years = _interval_to_years(return_period_unit, return_period_value)
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interval_days = int(interval_years * 365 + 1)
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@ -157,3 +214,81 @@ def beta(
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beta = cov / market_var
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return beta
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def jensens_alpha(
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asset_data: TimeSeries,
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market_data: TimeSeries,
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risk_free_data: TimeSeries = None,
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risk_free_rate: float = None,
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from_date: str | datetime.datetime = None,
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to_date: str | datetime.datetime = None,
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frequency: Literal["D", "W", "M", "Q", "H", "Y"] = None,
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return_period_unit: Literal["years", "months", "days"] = "years",
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return_period_value: int = 1,
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as_on_match: str = "closest",
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prior_match: str = "closest",
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closest: Literal["previous", "next"] = "previous",
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date_format: str = None,
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) -> float:
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"""
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This function calculates the Jensen's alpha for a time series.
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The formula for Jensen's alpha is:
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Ri - Rf + B x (Rm - Rf)
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where:
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Ri = Realized return of the portfolio or investment
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Rf = The risk free rate during the return time frame
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B = Beta of the portfolio or investment
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Rm = Realized return of the market index
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"""
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interval_years = _interval_to_years(return_period_unit, return_period_value)
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interval_days = int(interval_years * 365 + 1)
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if from_date is None:
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from_date = asset_data.start_date + datetime.timedelta(days=interval_days)
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if to_date is None:
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to_date = asset_data.end_date
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common_params = {
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"from_date": from_date,
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"to_date": to_date,
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"frequency": frequency,
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"return_period_unit": return_period_unit,
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"return_period_value": return_period_value,
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"as_on_match": as_on_match,
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"prior_match": prior_match,
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"closest": closest,
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"date_format": date_format,
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}
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num_days = (to_date - from_date).days
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compound_realised_returns = True if num_days > 365 else False
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realized_return = asset_data.calculate_returns(
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as_on=to_date,
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return_period_unit="days",
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return_period_value=num_days,
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annual_compounded_returns=compound_realised_returns,
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as_on_match=as_on_match,
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prior_match=prior_match,
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closest=closest,
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date_format=date_format,
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)
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market_return = market_data.calculate_returns(
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as_on=to_date,
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return_period_unit="days",
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return_period_value=num_days,
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annual_compounded_returns=compound_realised_returns,
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as_on_match=as_on_match,
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prior_match=prior_match,
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closest=closest,
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date_format=date_format,
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)
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beta_value = beta(asset_data=asset_data, market_data=market_data, **common_params)
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if risk_free_data is None and risk_free_rate is None:
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raise ValueError("At least one of risk_free_data or risk_free rate is required")
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elif risk_free_data is not None:
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risk_free_rate = risk_free_data.mean()
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jensens_alpha = realized_return[1] - risk_free_rate + beta_value * (market_return[1] - risk_free_rate)
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return jensens_alpha
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