Inverse Drowdwon portfolio

Portfolio with weights proportional to the inverse of the portfolio component maximum drawdowns, periodically rebalanced.

It is a naïve representation of the market wisdom that positions in an assets that had experienced larger maximum drawdown should be smaller.

The drawdowns are monitored for a predefined period, prior to the rebalancing events.

There are 2 support classes:

  • InvDDEngine: computes portfolio weights

  • Port_InvDD : performs portfolio backtesting, out-of-sample analysis.

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InvDDEngine class

class azapy.Engines.InvDDEngine.InvDDEngine(mktdata=None, colname='adjusted', freq='Q', hlength=3.25, name=None, verbose=False)

Bases: InvVolEngine

Inverse maximum drawdown portfolio.

Attributes
  • status : int - computation status (0 - success, any other value indicates an error)

  • ww : pandas.Series - portfolio weights

  • name : str - portfolio name

Methods

getPositions([nshares, cash, ww, nsh_round, ...])

Computes the rebalanced number of shares.

getWeights([mktdata])

Computes the optimal portfolio weights.

set_mktdata(mktdata[, colname, freq, ...])

Sets historical market data.

set_rrate(rrate)

Sets portfolio components historical rates of return in the format "date", "symbol1", "symbol2", etc.

__init__(mktdata=None, colname='adjusted', freq='Q', hlength=3.25, name=None, verbose=False)

Constructor

Parameters:
mktdatapandas.DataFrame, optional

Historic daily market data for portfolio components in the format returned by azapy.mktData function. The default is None.

colnamestr, optional

Name of the price column from mktdata used in the weights calibration. The default is ‘adjusted’.

freqstr, optional

Rate of return horizon. It could be ‘Q’ for a quarter or ‘M’ for a month. The default is ‘Q’.

hlengthfloat, optional

History length in number of years used for calibration. A fractional number will be rounded to an integer number of months. The default is 3.25 years.

namestr, optional

Portfolio name. Default value is None

verboseBoolean, optional

If it is set to True, then computational info (meant as warnings) are printed. The default is False.

Returns:
The object.
getPositions(nshares=None, cash=0.0, ww=None, nsh_round=True, verbose=True)

Computes the rebalanced number of shares.

Parameters:
nsharespanda.Series, optional

Initial number of shares per portfolio component. A missing component entry will be considered 0. A None value assumes that all components entries are 0. The name of the components must be present in the mrkdata. The default is None.

cashfloat, optional

Additional cash to be added to the capital. A negative entry assumes a reduction in the total capital available for rebalance. The total capital cannot be < 0. The default is 0.

wwpanda.Series, optional

External overwrite portfolio weights. If it not set to None these weights will overwrite the calibration results. The default is None.

nsh_roundBoolean, optional

If it is True the invested numbers of shares are round to the nearest integer and the residual cash capital (positive or negative) is carried to the next reinvestment cycle. A value of False assumes investments with fractional number of shares (no rounding). The default is True.

verboseBoolean, optional

Is it set to True the function prints the closing prices date. The default is True.

Returns:
`pandas.DataFrame`the rolling information.
Columns:
  • ‘old_nsh’ :

    initial number of shares per portfolio component and the additional cash. These are input values.

  • ‘new_nsh’ :

    the new number of shares per component plus the residual cash (due to the rounding to an integer number of shares). A negative entry means that the investor needs to add more cash to cover for the roundup shortfall. It has a small value.

  • ‘diff_nsh’ :

    number of shares (buy/sale) needed to rebalance the portfolio.

  • ‘weights’ :

    portfolio weights used for rebalancing. The cash entry is the new portfolio value (invested capital).

  • ‘prices’ :

    the share prices used for rebalance evaluations.

Note: Since the prices are closing prices, the rebalance can be computed after the market close and before the trading execution (next day). Additional cash slippage may occur due to share price differential between the previous day closing and execution time.

getWeights(mktdata=None, **params)

Computes the optimal portfolio weights.

Parameters:
mktdatapandas.DataFrame, optional

The portfolio components historical, prices or rates of return, see ‘pclose’ definition below. If it is not None, it will overwrite the set of historical rates of return computed in the constructor from ‘mktdata’. The default is None.

**paramsother optional parameters

Most common:

verboseBoolean, optional

If it is set to True, then it will print a computation messages. The default is False.

pcloseBoolean, optional

If it is absent then the mktdata is considered to contain rates of return, with columns the asset symbols and indexed by the observation dates,

True : assumes mktdata contains closing prices only, with columns the asset symbols and indexed by the observation dates,

False : assumes mktdata is in the usual format returned by azapy.mktData function.

Returns:
`pandas.Series`Portfolio weights.
set_mktdata(mktdata, colname='adjusted', freq=None, hlength=None, pclose=False)

Sets historical market data. It will overwrite the choice made in the constructor.

Parameters:
mktdatapandas.DataFrame

Historic daily market data for portfolio components in the format returned by azapy.mktData function.

colnamestr, optional

Name of the price column from mktdata used in the weight’s calibration. The default is ‘adjusted’.

freqstr, optional

Rate of return horizon. It could be ‘Q’ for a quarter or ‘M’ for a month. The default is ‘Q’.

hlengthfloat, optional

History length in number of years used for calibration. A fractional number will be rounded to an integer number of months. The default is 3.25.

pcloseBoolean, optional

True : assumes mktdata contains closing prices only, with columns the asset symbols and indexed by the observation dates,

False : assumes mktdata is in the usual format returned by azapy.mktData function.

Returns:
None
set_rrate(rrate)

Sets portfolio components historical rates of return in the format “date”, “symbol1”, “symbol2”, etc.

Parameters:
rratepandas.DataFrame

The portfolio components historical rates of return. If it is not None, it will overwrite the rrate computed in the constructor from mktdata. The default is None.

Returns:
None

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Example InvDDEngine

# Examples
import pandas as pd
import azapy as az
print(f"azapy version {az.version()}", flush=True)

#=============================================================================
# Collect some market data
mktdir = '../../MkTdata'
sdate = '2012-01-01'
edate = '2021-07-27'
symb = ['GLD', 'TLT', 'XLV', 'IHI', 'VGT']

mktdata = az.readMkT(symb, sdate=sdate, edate=edate, file_dir=mktdir)

#=============================================================================
# Example: weights evaluation
hlength = 1.25

cr1 = az.InvDDEngine(mktdata, hlength=hlength)
ww1 = cr1.getWeights()
print(f"weights\n{ww1}")

#=============================================================================
# Example of rebalancing positions
# existing positions and cash
ns = pd.Series(100, index=symb)
cash = 0.

# new positions and rolling info
pos1 = cr1.getPositions(nshares=ns, cash=0.)
print(f" Full: New position report\n {pos1}")

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Port_InvDD class

class azapy.PortOpt.Port_InvDD.Port_InvDD(mktdata, symb=None, sdate=None, edate=None, col_price='close', col_divd='divd', col_ref='adjusted', col_calib='adjusted', pname='Port', pcolname=None, capital=100000, schedule=None, freq='Q', noffset=-3, fixoffset=-1, histoffset=3.25, calendar=None, multithreading=True, nsh_round=True)

Bases: _Port_Generator

Backtesting Inverse Maximum Drawdown portfolio periodically rebalanced.

Attributes
  • pname : str - portfolio name

  • ww : pandasDataFrame - portfolio weights at each rebalancing date

  • port : pandas.Series - portfolio historical time-series

  • schedule : pandas.DataFrame - rebalancing schedule

The most important method is set_model. It must be called before any other method.

Methods

get_account([fancy])

Returns additional bookkeeping information regarding rebalancing (e.g., residual cash due rounding number of shares, previous period dividend cash accumulation, etc.)

get_mktdata()

Returns the actual market data used for portfolio evaluations.

get_nshares()

Returns the number of shares held after each rolling date.

get_port()

Returns the portfolio time-series.

get_weights([fancy])

Returns the portfolio weights at each rebalancing period.

port_annual_returns([withcomp, componly, fancy])

Portfolio annual (calendar) rates of returns.

port_drawdown([top, fancy, withcomp, componly])

Computes the portfolio drawdowns.

port_monthly_returns([withcomp, componly, fancy])

Portfolio monthly (calendar) rate of returns.

port_perf([componly, fancy])

Brief description of portfolio and its components performances in terms of average historical rate of returns and maximum drawdowns.

port_period_perf([fancy])

Returns portfolio performance for each rolling period i.e. the rate of return, the rolling min and max returns, and max drawdown during the period.

port_period_returns([fancy])

Computes the rolling periods rate of returns.

port_view([emas, bollinger])

Plots the portfolio time series together with optional technical indicators.

port_view_all([sdate, edate, componly])

Plots the portfolio and its component time-series on a relative basis.

set_model([hlength, verbose])

Set model parameters and evaluate the portfolio time-series.

__init__(mktdata, symb=None, sdate=None, edate=None, col_price='close', col_divd='divd', col_ref='adjusted', col_calib='adjusted', pname='Port', pcolname=None, capital=100000, schedule=None, freq='Q', noffset=-3, fixoffset=-1, histoffset=3.25, calendar=None, multithreading=True, nsh_round=True)

Constructor

Parameters:
mktdatapandas.DataFrame

MkT data in the format “symbol”, “date”, “open”, “high”, “low”, “close”, “volume”, “adjusted”, “divd”, “split” (e.g., as returned by azapy.readMkT function).

symblist, optional

List of symbols for the basket components. All symbols MkT data should be included in mktdata. If set to None the symb will be set to include all the symbols from mktdata. The default is None.

sdatedate like, optional

Start date for historical data. If set to None the sdate will be set to the earliest date in mktdata. The default is None.

edatedate like, optional

End date for historical dates and so the simulation. Must be greater than sdate. If it is None then edate will be set to the latest date in mktdata. The default is None.

col_pricestr, optional

Column name in the mktdata DataFrame that will be considered for portfolio aggregation. The default is ‘close’.

col_divdstr, optional

Column name in the mktdata DataFrame that holds the dividend information. The default is ‘dvid’.

col_refstr, optional

Column name in the mktdata DataFrame that will be used as a price reference for portfolio components. The default is ‘adjusted’.

col_calibstr, optional

Column name used for historical weights calibrations. The default is ‘adjusted’.

pnamestr, optional

The name of the portfolio. The default is ‘Port’.

pcolnamestr, optional

Name of the portfolio price column. If it set to None then pcolname=pname. The default is None.

capitalfloat, optional

Initial portfolio Capital in dollars. The default is 100000.

schedulepandas.DataFrame, optional

Rebalancing schedule, with columns for ‘Droll’ rolling date and ‘Dfix’ fixing date. If it is None than the schedule will be set using the freq, noffset, fixoffset and calendar information. The default is None.

freqstr, optional

Rebalancing frequency. It can be ‘Q’ for quarterly or ‘M’ for monthly rebalancing, respectively. It is relevant only if the schedule is None. The default is ‘Q’.

noffsetint, optional

Number of business days offset for rebalancing date ‘Droll’ relative to the end of the period (quart or month). A positive value add business days beyond the calendar end of the period while a negative value subtracts business days. It is relevant only if the schedule is None. The default is -3.

fixoffsetint, optional

Number of business day offset of fixing date ‘Dfix’ relative to the rebalancing date ‘Droll’. It can be 0 or negative. It is relevant only if the schedule is None. The default is -1.

calendarnumpy.busdaycalendar, optional

Business calendar. If it is None then it will be set to NYSE business calendar. The default value is None.

multithreadingBoolean, optional

If it is True, then the rebalancing weights will be computed concurrent. The default is True.

nsh_roundBoolean, optional

If it is True the invested numbers of shares are round to the nearest integer and the residual cash capital (positive or negative) is carried to the next reinvestment cycle. A value of False assumes investments with fractional number of shares (no rounding). The default is True.

Returns:
The object.
get_account(fancy=False)

Returns additional bookkeeping information regarding rebalancing (e.g., residual cash due rounding number of shares, previous period dividend cash accumulation, etc.)

Parameters:
fancyBoolean, optional
  • False: the values are reported in unaltered algebraic format.

  • True : the values are reported rounded.

The default is False.

Returns:
`pandas.DataFrame`Reports, for each rolling period identified by ‘Droll’,
  • number of shares hold for each symbol,

  • ‘cash_invst’ : cash invested at the beginning of period,

  • ‘cash_roll’ : cash rolled to the next period,

  • ‘cash_divd’ : cash dividend accumulated in the previous period.

Note: The capital at the beginning of the period is cash_invst + cash_roll. It is also equal to the previous period: value of the shares on the fixing date + cash_roll + cash_divd. There are 2 sources for the cash_roll. The roundup to integer number of shares and the shares close price differences between the fixing (computation) and rolling (execution) dates. It could be positive or negative. The finance of the cash_roll during each rolling period is assumed to be done separately by the investor.

get_mktdata()

Returns the actual market data used for portfolio evaluations.

Returns:
`pandas.DataFrame`market data.
get_nshares()

Returns the number of shares held after each rolling date.

Returns:
`pandas.DataFrame`number of shares per symbol.
get_port()

Returns the portfolio time-series.

Returns:
`pandas.DataFrame`portfolio time-series.
get_weights(fancy=False)

Returns the portfolio weights at each rebalancing period.

Parameters:
fancyBoolean, optional
  • False: reports the weights in algebraic format.

  • True: reports the weights in percentage rounded to 2 decimals.

The default is False.

Returns:
`pandas.DataFrame`portfolio weights per symbol.
port_annual_returns(withcomp=False, componly=False, fancy=False)

Portfolio annual (calendar) rates of returns.

Parameters:
withcompBoolean, optional

If True, adds the portfolio components annual returns to the report. The default is False.

componlyBoolean, optional

If True, only the portfolio components annual returns are reported. The flag is active only if withcomp=True. The default is False.

fancyBoolean, optional
  • False : The rates are reported in unaltered algebraic format.

  • True :The rates are reported in percentage rounded to 2 decimals and presented is color style.

The default is False.

Returns:
`pandas.DataFrame`the report.
port_drawdown(top=5, fancy=False, withcomp=False, componly=False)

Computes the portfolio drawdowns.

Parameters:
topint, optional

The number of largest drawdowns that will be reported. The default is 5.

fancyBoolean, optional
  • FalseThe drawdowns values are reported in unaltered

    algebraic format.

  • TrueThe drawdowns values are reported in percentage

    rounded to 2 decimals.

The default is False.

withcompBoolean, optional

If True, the portfolio components drawdowns are also reported. The default is False.

componlyBoolean, optional

If True, only the portfolio components drawdowns are reported. The flag is active only if withcomp=True. The default is False.

Returns:
`panda.DataFrame`Table of drawdown events.
Columns:
  • ‘DD’ : drawdown rate

  • ‘Date’ : recorded date of the drawdown

  • ‘Star’ : start date of the drawdown

  • ‘End’ : end date of the drawdown

port_monthly_returns(withcomp=False, componly=False, fancy=False)

Portfolio monthly (calendar) rate of returns.

Parameters:
withcompBoolean, optional

If True, adds the portfolio components monthly returns to the report. The default is False.

componlyBoolean, optional

If True, only the portfolio components monthly returns are reported. The flag is active only if withcomp=True. The default is False.

fancyBoolean, optional
  • False : The rates are reported in unaltered algebraic format.

  • True : The rates are reported in percentage rounded to 2 decimals and presented is color style.

The default is False.

Returns:
`pandas.DataFrame`the report.
port_perf(componly=False, fancy=False)

Brief description of portfolio and its components performances in terms of average historical rate of returns and maximum drawdowns.

Parameters:
componlyBoolean, optional

If True, only the portfolio components maximum drawdowns are reported. The default is False.

fancyBoolean, optional
  • False : The rate of returns and drawdown values are reported in unaltered algebraic format.

  • True : The rate of returns and drawdown values are reported in percentage rounded to 2 decimals.

The default is False.

Returns:
`pandas.DataFrame`Performance information.
Columns
  • ‘RR’ : rate of returns

  • ‘DD’ : maximum rate of drawdown

  • ‘RoMaD’ : abs(RR/DD), Rate of Return over Maximum Drawdown

  • ‘DD_date’ : recorder date of maximum drawdown

  • ‘DD_start’ : start date of maximum drawdown

  • ‘DD_end’ : end date of maximum drawdown

port_period_perf(fancy=False)

Returns portfolio performance for each rolling period i.e. the rate of return, the rolling min and max returns, and max drawdown during the period.

Parameters:
fancyBoolean, optional
  • False: returns in algebraic form.

  • True: returns percentage rounded to 2 decimals.

The default is `False`.
Returns:
pandas.DataFrame
  • ‘Droll’ - indicates the start of the period.

  • ‘RR’ - period rate of return.

  • ‘RR_Min’ - minimum rolling rate of return in the period.

  • ‘RR_Max’ - maximum rolling rate of return in the period.

  • ‘DD_Max’ - maximum drawdown in the period.

  • ‘RR_Min_Date’ - date of ‘RR_Min’.

  • ‘RR_Max_Date’ - date of ‘RR_Max’.

  • ‘DD_Max_Date’ - date of ‘DD_Max’.

port_period_returns(fancy=False)

Computes the rolling periods rate of returns.

Parameters:
fancyBoolean, optional
  • False: returns in algebraic form.

  • True: returns percentage rounded to 2 decimals.

The default is `False`.
Returns:
`pandas.DataFrame`The report.

Each rolling period is indicated by its start date, ‘Droll’. Included are the fixing data, ‘Dfix’, and the portfolio weights.

port_view(emas=[30, 200], bollinger=False, **opt)

Plots the portfolio time series together with optional technical indicators.

Parameters:
emaslist of int, optional

List of EMA durations. The default is [30, 200].

bollingerBoolean, optional

If set True it adds the Bollinger bands. The default is False.

**optother optional parameters
  • fancyBoolean, optional
    • False : it uses the matplotlib capabilities.

    • True : it uses plotly library for interactive time-series view.

    The default is False.

  • title : str, optional plot title. The default is ‘Port performance’.

  • xlabel : str, optional name of x-axis. The default is ‘date’.

  • ylabel : str; optional name of y-axis. The default is None.

  • savetostr, optional

    The name of the file where to save the plot. The default is None.

Returns:
`pandas.DataFrame`Contains the time-series included in plot.
port_view_all(sdate=None, edate=None, componly=False, **opt)

Plots the portfolio and its component time-series on a relative basis.

Parameters:
sdatedate like, optional

Start date of plotted time-series. If it is set to None then the sdate is set to the earliest date in the time-series. The default is None.

edatedate like, optional

End date of plotted time-series. If it set to None, then the edate is set to the most recent date of the time-series. The default is None.

componlyBoolean, optional
  • True : only the portfolio components time-series are plotted.

  • False: the portfolio and its components times-series are plotted.

The default is True.

**optother parameters
  • fancyBoolean, optional
    • False : it uses the pandas plot (matplotlib) capabilities.

    • True : it uses plotly library for interactive time-series view.

    The default is False.

  • title : str, optional plot title. The default is ‘Relative performance’.

  • xlabel : str, optional name of x-axis. The default is ‘date’.

  • ylabel : str; optional name of y-axis. The default is None.

  • savetostr, optional

    The name of the file where to save the plot. The default is None.

Returns:
`pandas.DataFrame`A Data Frame containing the time-series.
set_model(hlength=3.25, verbose=False)

Set model parameters and evaluate the portfolio time-series.

Parameters:
hlengthfloat, optional

The length in year of the historical calibration period relative to ‘Dfix’. A fractional number will be rounded to an integer number of months. The default is 3.25 years.

verboseBoolean, optional

Sets verbose mode. The default is False.

Returns:
`pandas.DataFrame`The portfolio time-series in the format ‘date’,
‘pcolname’.

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Example Port_InvDD

# Examples
import time
import pandas as pd
import azapy as az

#=============================================================================
# Collect market data
mktdir = '../../MkTdata'
sdate = '2012-01-01'
edate = 'today'
symb = ['GLD', 'TLT', 'XLV', 'IHI', 'VGT', 'OIH']

mktdata = az.readMkT(symb, sdate=sdate, edate=edate, file_dir=mktdir)

#=============================================================================
# Compute portfolio
p3 = az.Port_InvDD(mktdata, pname='InvDDPort')    

tic = time.perf_counter()
port3 = p3.set_model()   
toc = time.perf_counter()
print(f"time get_port: {toc-tic:f}")

ww = p3.get_weights()
_ = p3.port_view()
_ = p3.port_view_all()
drawdown = p3.port_drawdown(fancy=True)
perf = p3.port_perf(fancy=True)
annual = p3.port_annual_returns()
monthly = p3.port_monthly_returns()
period = p3.port_period_returns()
nsh = p3.get_nshares()
acc = p3.get_account(fancy=True)

with pd.option_context('display.max_columns', None):
    print(f"Portfolio Drawdown\n{drawdown}")
    print(f"Portfolio performance\n{perf}")
    print(f"Annual Returns\n{annual}")
    print(f"Monthly Returns\n{monthly}")
    print(f"Investment Period Returns\n{period.round(4)}")
    print(f"Number of Shares invested\n{nsh}")
    print(f"Accounting Info\n{acc}")

#=============================================================================
# Test using the Port_Rebalanced, weights = ww (from above)
p2 = az.Port_Rebalanced(mktdata, pname='TestPort')
port2  = p2.set_model(ww)     

# must be identical   
pp = az.Port_Simple([port2, port3])
_ = pp.set_model()
_ = pp.port_view_all(componly=True)
                 

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