Compute Sortino ratio (#67) (#108)

Addition of Sortino ratio to FinQuant --------- Co-authored-by: Pietropaolo Frisoni <[email protected]> Co-authored-by: Andrei Troie <[email protected]> Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>
fmilthaler · Aug 2, 2023 · a2d01de · a2d01de
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diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md
@@ -15,6 +15,7 @@ Thank you to all the individuals who have contributed to this project!
 - Stephen Pennington (@slpenn13): bug fixing
 - @herrfz: bug fixing
 - @drcsturm: bug fixing
+- @aft90: helped to implement the Sortino Ratio
 
 ## Special Thanks
 

diff --git a/README.md b/README.md
@@ -7,7 +7,7 @@
     <img src="https://img.shields.io/github/stars/fmilthaler/FinQuant.svg?style=social&label=Star" alt='pypi'>
   </a>
   <a href="https://pypi.org/project/FinQuant">
-    <img src="https://img.shields.io/badge/pypi-v0.4.1-brightgreen.svg?style=popout" alt='pypi'>
+    <img src="https://img.shields.io/badge/pypi-v0.5.0-brightgreen.svg?style=popout" alt='pypi'>
   </a>
   <a href="https://github.com/fmilthaler/FinQuant">
     <img src="https://github.com/fmilthaler/finquant/actions/workflows/pytest.yml/badge.svg?branch=master" alt='GitHub Actions'>
@@ -249,8 +249,11 @@ look at the examples provided in `./example`.
 `./example/Example-Analysis.py`: This example shows how to use an instance of `finquant.portfolio.Portfolio`, get the portfolio's quantities, such as
  - Expected Returns,
  - Volatility,
+ - Downside Risk,
+ - Value at Risk, 
  - Sharpe Ratio,
- - Value at Risk.
+ - Sortino Ratio,
+ - Beta parameter.
 
 It also shows how to extract individual stocks from the given portfolio. Moreover it shows how to compute and visualise:
  - the different Returns provided by the module `finquant.returns`,

diff --git a/README.tex.md b/README.tex.md
@@ -7,7 +7,7 @@
     <img src="https://img.shields.io/github/stars/fmilthaler/FinQuant.svg?style=social&label=Star" alt='pypi'>
   </a>
   <a href="https://pypi.org/project/FinQuant">
-    <img src="https://img.shields.io/badge/pypi-v0.4.1-brightgreen.svg?style=popout" alt='pypi'>
+    <img src="https://img.shields.io/badge/pypi-v0.5.0-brightgreen.svg?style=popout" alt='pypi'>
   </a>
   <a href="https://github.com/fmilthaler/FinQuant">
     <img src="https://github.com/fmilthaler/finquant/actions/workflows/pytest.yml/badge.svg?branch=master" alt='GitHub Actions'>
@@ -249,8 +249,11 @@ look at the examples provided in `./example`.
 `./example/Example-Analysis.py`: This example shows how to use an instance of `finquant.portfolio.Portfolio`, get the portfolio's quantities, such as
  - Expected Returns,
  - Volatility,
+ - Downside Risk,
+ - Value at Risk, 
  - Sharpe Ratio,
- - Value at Risk.
+ - Sortino Ratio,
+ - Beta parameter.
 
 It also shows how to extract individual stocks from the given portfolio. Moreover it shows how to compute and visualise:
  - the different Returns provided by the module `finquant.returns`,

diff --git a/example/Example-Analysis.py b/example/Example-Analysis.py
@@ -50,10 +50,12 @@
 
 # <markdowncell>
 
-# ## Expected Return, Volatility, Sharpe Ratio and Value at Risk of Portfolio
-# The annualised expected return and volatility, as well as the Sharpe Ratio and Value at Risk are automatically computed. They are obtained as shown below.
+# ## Expected Return, Volatility, Sharpe Ratio, Sortino Ratio, and Value at Risk of Portfolio
+# The annualised expected return and volatility, as well as the Sharpe Ratio, the Sortino Ratio, and Value at Risk are automatically computed.
+# They are obtained as shown below.
 # The expected return and volatility are based on 252 trading days by default.
-# The Sharpe Ratio is computed with a risk free rate of 0.005 by default. The Value at Risk is computed with a confidence level of 0.95 by default.
+# The Sharpe Ratio and the Sortino ratio are computed with a risk free rate of 0.005 by default.
+# The Value at Risk is computed with a confidence level of 0.95 by default.
 
 # <codecell>
 
@@ -67,11 +69,16 @@
 
 # <codecell>
 
-# Sharpe ratio (computed with a risk free rate of 0.005 by default)
+# Sharpe Ratio (computed with a risk free rate of 0.005 by default)
 print(pf.sharpe)
 
 # <codecell>
 
+# Sortino Ratio (computed with a risk free rate of 0.005 by default)
+print(pf.sortino)
+
+# <codecell>
+
 # Value at Risk (computed with a confidence level of 0.95 by default)
 print(pf.var)
 
@@ -90,7 +97,7 @@
 # <markdowncell>
 
 # ## Nicely printing out portfolio quantities
-# To print the expected annualised return, volatility, Sharpe ratio, skewness and Kurtosis of the portfolio and its stocks, one can simply do `pf.properties()`.
+# To print the expected annualised return, volatility, Sharpe Ratio, Sortino Ratio, skewness and Kurtosis of the portfolio and its stocks, one can simply do `pf.properties()`.
 
 # <codecell>
 

diff --git a/finquant/portfolio.py b/finquant/portfolio.py
@@ -17,8 +17,10 @@
 - daily log returns of the portfolio's stocks,
 - Expected (annualised) Return,
 - Volatility,
-- Sharpe Ratio,
+- Downside Risk,
 - Value at Risk,
+- Sharpe Ratio,
+- Sortino Ratio,
 - Beta parameter (optional),
 - skewness of the portfolio's stocks,
 - Kurtosis of the portfolio's stocks,
@@ -59,7 +61,14 @@
 from finquant.efficient_frontier import EfficientFrontier
 from finquant.market import Market
 from finquant.monte_carlo import MonteCarloOpt
-from finquant.quants import sharpe_ratio, value_at_risk, weighted_mean, weighted_std
+from finquant.quants import (
+    downside_risk,
+    sharpe_ratio,
+    sortino_ratio,
+    value_at_risk,
+    weighted_mean,
+    weighted_std,
+)
 from finquant.returns import (
     cumulative_returns,
     daily_log_returns,
@@ -85,8 +94,10 @@ def __init__(self):
         self.data = pd.DataFrame()
         self.expected_return = None
         self.volatility = None
-        self.sharpe = None
+        self.downside_risk = None
         self.var = None
+        self.sharpe = None
+        self.sortino = None
         self.skew = None
         self.kurtosis = None
         self.totalinvestment = None
@@ -226,8 +237,10 @@ def _update(self):
             self.totalinvestment = self.portfolio.Allocation.sum()
             self.expected_return = self.comp_expected_return(freq=self.freq)
             self.volatility = self.comp_volatility(freq=self.freq)
-            self.sharpe = self.comp_sharpe()
+            self.downside_risk = self.comp_downside_risk(freq=self.freq)
             self.var = self.comp_var()
+            self.sharpe = self.comp_sharpe()
+            self.sortino = self.comp_sortino()
             self.skew = self._comp_skew()
             self.kurtosis = self._comp_kurtosis()
             if self.market_index is not None:
@@ -349,6 +362,22 @@ def comp_volatility(self, freq=252):
         self.volatility = volatility
         return volatility
 
+    def comp_downside_risk(self, freq=252):
+        """Computes the downside risk of the portfolio.
+
+        :Input:
+         :freq: ``int`` (default: ``252``), number of trading days, default
+             value corresponds to trading days in a year
+
+        :Output:
+         :downside risk: ``float`` downside risk of the portfolio.
+        """
+        downs_risk = downside_risk(
+            self.data, self.comp_weights(), self.risk_free_rate
+        ) * np.sqrt(freq)
+        self.downside_risk = downs_risk
+        return downs_risk
+
     def comp_cov(self):
         """Compute and return a ``pandas.DataFrame`` of the covariance matrix
         of the portfolio.
@@ -403,6 +432,17 @@ def comp_beta(self) -> float:
         self.beta = beta
         return beta
 
+    def comp_sortino(self, freq=252):
+        """Compute and return the Sortino Ratio of the portfolio
+
+        :Output:
+         :sortino: ``float``, the Sortino Ratio of the portfolio
+         May be NaN if the portoflio outperformed the risk free rate at every point
+        """
+        return sortino_ratio(
+            self.expected_return, self.downside_risk, self.risk_free_rate
+        )
+
     def _comp_skew(self):
         """Computes and returns the skewness of the stocks in the portfolio."""
         return self.data.skew()
@@ -664,8 +704,11 @@ def properties(self):
 
         - Expected Return,
         - Volatility,
+        - Downside Risk,
+        - Value at Risk (VaR),
+        - Confidence level of VaR,
         - Sharpe Ratio,
-        - Value at Risk,
+        - Sortino Ratio,
         - Beta (optional),
         - skewness,
         - Kurtosis
@@ -682,10 +725,12 @@ def properties(self):
         string += f"\nRisk free rate: {self.risk_free_rate}"
         string += f"\nPortfolio Expected Return: {self.expected_return:0.3f}"
         string += f"\nPortfolio Volatility: {self.volatility:0.3f}"
-        string += f"\nPortfolio Sharpe Ratio: {self.sharpe:0.3f}"
+        string += f"\nPortfolio Downside Risk: {self.downside_risk:0.3f}"
         string += f"\nPortfolio Value at Risk: {self.var:0.3f}"
         string += f"\nConfidence level of Value at Risk: "
         string += f"{self.var_confidence_level * 100:0.2f} %"
+        string += f"\nPortfolio Sharpe Ratio: {self.sharpe:0.3f}"
+        string += f"\nPortfolio Sortino Ratio: {self.sortino:0.3f}"
         if self.beta is not None:
             string += f"\nPortfolio Beta: {self.beta:0.3f}"
         string += "\n\nSkewness:"
@@ -1214,7 +1259,9 @@ def build_portfolio(**kwargs):
         or not pf.stocks
         or pf.expected_return is None
         or pf.volatility is None
+        or pf.downside_risk is None
         or pf.sharpe is None
+        or pf.sortino is None
         or pf.skew is None
         or pf.kurtosis is None
     ):

diff --git a/finquant/quants.py b/finquant/quants.py
@@ -8,6 +8,8 @@
 import pandas as pd
 from scipy.stats import norm
 
+from finquant.returns import weighted_mean_daily_returns
+
 
 def weighted_mean(means, weights):
     """Computes the weighted mean/average, or in the case of a
@@ -75,6 +77,60 @@ def sharpe_ratio(exp_return, volatility, risk_free_rate=0.005):
     return (exp_return - risk_free_rate) / float(volatility)
 
 
+def sortino_ratio(exp_return, downside_risk, risk_free_rate=0.005):
+    """Computes the Sortino Ratio
+
+    :Input:
+     :exp_return: ``int``/``float``, Expected Return of a portfolio
+     :downside_risk: ``int``/``float``, Downside Risk of a portfolio
+     :risk_free_rate: ``int``/``float`` (default= ``0.005``), risk free rate
+
+    :Output:
+     :sortino ratio: ``float``/``NaN`` ``(exp_return - risk_free_rate)/float(downside_risk)``.
+     Can be ``NaN`` if ``downside_risk`` is zero
+    """
+    if not isinstance(
+        exp_return, (int, float, np.int32, np.int64, np.float32, np.float64)
+    ):
+        raise ValueError("exp_return is expected to be an integer or float.")
+    if not isinstance(
+        downside_risk, (int, float, np.int32, np.int64, np.float32, np.float64)
+    ):
+        raise ValueError("volatility is expected to be an integer or float.")
+    if not isinstance(
+        risk_free_rate, (int, float, np.int32, np.int64, np.float32, np.float64)
+    ):
+        raise ValueError("risk_free_rate is expected to be an integer or float.")
+    if float(downside_risk) == 0:
+        return np.nan
+    else:
+        return (exp_return - risk_free_rate) / float(downside_risk)
+
+
+def downside_risk(data: pd.DataFrame, weights, risk_free_rate=0.005) -> float:
+    """Computes the downside risk (target downside deviation of returns).
+
+    :Input:
+      :data: ``pandas.DataFrame`` with daily stock prices
+      :weights: ``numpy.ndarray``/``pd.Series`` of weights
+      :risk_free_rate: ``int``/``float`` (default=``0.005``), risk free rate
+
+    :Output:
+      :downside_risk: ``float``, target downside deviation
+    """
+    if not isinstance(data, pd.DataFrame):
+        raise ValueError("data is expected to be a Pandas.DataFrame.")
+    if not isinstance(weights, (pd.Series, np.ndarray)):
+        raise ValueError("weights is expected to be a pandas.Series/np.ndarray.")
+    if not isinstance(
+        risk_free_rate, (int, float, np.int32, np.int64, np.float32, np.float64)
+    ):
+        raise ValueError("risk_free_rate is expected to be an integer or float.")
+
+    wtd_daily_mean = weighted_mean_daily_returns(data, weights)
+    return np.sqrt(np.mean(np.minimum(0, wtd_daily_mean - risk_free_rate) ** 2))
+
+
 def value_at_risk(investment, mu, sigma, conf_level=0.95) -> float:
     """Computes and returns the expected value at risk of an investment/assets.
 

diff --git a/finquant/returns.py b/finquant/returns.py
@@ -36,6 +36,19 @@ def daily_returns(data):
     return data.pct_change().dropna(how="all").replace([np.inf, -np.inf], np.nan)
 
 
+def weighted_mean_daily_returns(data, weights):
+    """Returns DataFrame with the daily weighted mean returns
+
+    :Input:
+      :data: ``pandas.DataFrame`` with daily stock prices
+      :weights: ``numpy.ndarray``/``pd.Series`` of weights
+
+    :Output:
+      :ret: ``numpy.array`` of weighted mean daily percentage change of Returns
+    """
+    return np.dot(daily_returns(data), weights)
+
+
 def daily_log_returns(data):
     """
     Returns DataFrame with daily log returns

diff --git a/tests/test_quants.py b/tests/test_quants.py
@@ -1,9 +1,14 @@
+import pdb
+
 import numpy as np
+import pandas as pd
 import pytest
 
 from finquant.quants import (
     annualised_portfolio_quantities,
+    downside_risk,
     sharpe_ratio,
+    sortino_ratio,
     value_at_risk,
     weighted_mean,
     weighted_std,
@@ -34,6 +39,11 @@ def test_sharpe_ratio():
     assert sharpe_ratio(0.5, 0.22, 0.005) == 2.25
 
 
+def test_sortino_ratio():
+    assert sortino_ratio(0.5, 0.0, 0.02) is np.NaN
+    assert sortino_ratio(0.005, 8.5, 0.005) == 0.0
+
+
 def test_value_at_risk():
     assert abs(value_at_risk(1e2, 0.5, 0.25, 0.95) - 91.12) <= 1e-1
     assert abs(value_at_risk(1e3, 0.8, 0.5, 0.99) - 1963.17) <= 1e-1
@@ -77,3 +87,17 @@ def test_annualised_portfolio_quantities():
     orig = (1764, 347.79304190854657, 5.071981861166303)
     for i in range(len(res)):
         assert abs(res[i] - orig[i]) <= 1e-15
+
+
+def test_downside_risk():
+    data1 = pd.DataFrame({"1": [1, 2, 4, 8], "2": [1, 2, 3, 4]})
+    weights = np.array([0.25, 0.75])
+    rf_rate = 0.005
+    dr1 = downside_risk(data1, weights, rf_rate)
+    assert dr1 == 0
+
+    data2 = pd.DataFrame({"1": [7, 6, 5, 4, 3]})
+    weights = np.array([1])
+    rf_rate = 0.0
+    dr2 = downside_risk(data2, weights, rf_rate)
+    assert abs(dr2 - 0.19409143531019335) <= 1e-15
diff --git a/tests/test_returns.py b/tests/test_returns.py
@@ -1,10 +1,12 @@
+import numpy as np
 import pandas as pd
 
 from finquant.returns import (
     cumulative_returns,
     daily_log_returns,
     daily_returns,
     historical_mean_return,
+    weighted_mean_daily_returns,
 )
 
 
@@ -41,6 +43,23 @@ def test_daily_returns():
     assert all(abs(ret["2"].values - orig[1]) <= 1e-15)
 
 
+def test_weighted_daily_mean_returns():
+    l1 = [1.0, 1.5, 2.25, 3.375]
+    l2 = [1.0, 2.0, 4.0, 8.0]
+    expected = [0.5 * 0.25 + 1 * 0.75 for i in range(len(l1) - 1)]
+    weights = np.array([0.25, 0.75])
+    d = {"1": l1, "2": l2}
+    df = pd.DataFrame(d)
+    ret = weighted_mean_daily_returns(df, weights)
+    assert all(abs(ret - expected) <= 1e-15)
+
+    d = {"1": l1}
+    expected = [0.5 for i in range(len(l1) - 1)]
+    df = pd.DataFrame(d)
+    ret = weighted_mean_daily_returns(df, np.array([1]))
+    assert all(abs(ret - expected) <= 1e-15)
+
+
 def test_daily_log_returns():
     orig = [
         [