def plot_table(returns,
w,
MAR=0,
alpha=0.05,
height=9,
width=12,
t_factor=252,
ax=None):
r"""
Create a table with information about risk measures and risk adjusted
return ratios.
Parameters
----------
returns : DataFrame
Assets returns.
w : DataFrame
Portfolio weights.
MAR: float, optional
Minimum acceptable return.
alpha: float, optional
Significance level for VaR, CVaR, EVaR, DaR and CDaR.
height : float, optional
Height of the image in inches. The default is 9.
width : float, optional
Width of the image in inches. The default is 12.
t_factor : float, optional
Factor used to annualize expected return and expected risks for
risk measures based on returns (not drawdowns). The default is 252.
.. math::
\begin{align}
\text{Annualized Return} & = \text{Return} \, \times \, \text{t_factor} \\
\text{Annualized Risk} & = \text{Risk} \, \times \, \sqrt{\text{t_factor}}
\end{align}
ax : matplotlib axis, optional
If provided, plot on this axis. The default is None.
Raises
------
ValueError
When the value cannot be calculated.
Returns
-------
ax : matplotlib axis
Returns the Axes object with the plot for further tweaking.
Example
-------
::
ax = plf.plot_table(returns=Y, w=w1, MAR=0, alpha=0.05, ax=None)
.. image:: images/Port_Table.png
"""
if not isinstance(returns, pd.DataFrame):
raise ValueError("returns must be a DataFrame")
if not isinstance(w, pd.DataFrame):
raise ValueError("w must be a DataFrame")
if returns.shape[1] != w.shape[0]:
a1 = str(returns.shape)
a2 = str(w.shape)
raise ValueError("shapes " + a1 + " and " + a2 + " not aligned")
if ax is None:
ax = plt.gca()
fig = plt.gcf()
fig.set_figwidth(width)
fig.set_figheight(height)
mu = returns.mean()
cov = returns.cov()
days = (returns.index[-1] - returns.index[0]).days + 1
X = returns @ w
X = X.to_numpy().ravel()
rowLabels = [
"Profitability and Other Inputs",
"Mean Return (1)",
"Compound Annual Growth Rate (CAGR)",
"Minimum Acceptable Return (MAR) (1)",
"Significance Level",
"",
"Risk Measures based on Returns",
"Standard Deviation (2)",
"Mean Absolute Deviation (MAD) (2)",
"Semi Standard Deviation (2)",
"First Lower Partial Moment (FLPM) (2)",
"Second Lower Partial Moment (SLPM) (2)",
"Value at Risk (VaR) (2)",
"Conditional Value at Risk (CVaR) (2)",
"Entropic Value at Risk (EVaR) (2)",
"Worst Realization (2)",
"Skewness",
"Kurtosis",
"",
"Risk Measures based on Drawdowns (3)",
"Max Drawdown (MDD)",
"Average Drawdown (ADD)",
"Drawdown at Risk (DaR)",
"Conditional Drawdown at Risk (CDaR)",
"Ulcer Index",
"(1) Annualized, multiplied by " + str(t_factor),
"(2) Annualized, multiplied by √" + str(t_factor),
"(3) Based on uncompounded cumulated returns",
]
indicators = [
"",
(mu @ w).to_numpy().item() * t_factor,
np.power(np.prod(1 + X), 360 / days) - 1,
MAR,
alpha,
"",
"",
np.sqrt(w.T @ cov @ w).to_numpy().item() * t_factor**0.5,
rk.MAD(X) * t_factor**0.5,
rk.SemiDeviation(X) * t_factor**0.5,
rk.LPM(X, MAR=MAR, p=1) * t_factor**0.5,
rk.LPM(X, MAR=MAR, p=2) * t_factor**0.5,
rk.VaR_Hist(X, alpha=alpha) * t_factor**0.5,
rk.CVaR_Hist(X, alpha=alpha) * t_factor**0.5,
rk.EVaR_Hist(X, alpha=alpha)[0] * t_factor**0.5,
rk.WR(X) * t_factor**0.5,
st.skew(X, bias=False),
st.kurtosis(X, bias=False),
"",
"",
rk.MDD_Abs(X),
rk.ADD_Abs(X),
rk.DaR_Abs(X),
rk.CDaR_Abs(X, alpha=alpha),
rk.UCI_Abs(X),
"",
"",
"",
]
ratios = []
for i in range(len(indicators)):
if i < 6 or indicators[i] == "" or rowLabels[i] in [
"Skewness", "Kurtosis"
]:
ratios.append("")
else:
ratio = (indicators[1] - MAR) / indicators[i]
ratios.append(ratio)
for i in range(len(indicators)):
if indicators[i] != "":
if rowLabels[i] in ["Skewness", "Kurtosis"]:
indicators[i] = "{:.5f}".format(indicators[i])
else:
indicators[i] = "{:.4%}".format(indicators[i])
if ratios[i] != "":
ratios[i] = "{:.6f}".format(ratios[i])
data = pd.DataFrame({
"A": rowLabels,
"B": indicators,
"C": ratios
}).to_numpy()
ax.set_axis_off()
ax.axis("tight")
ax.axis("off")
colLabels = ["", "Values", "(Return - MAR)/Risk"]
colWidths = [0.45, 0.275, 0.275]
rowHeight = 0.07
table = ax.table(
cellText=data,
colLabels=colLabels,
colWidths=colWidths,
cellLoc="center",
loc="upper left",
bbox=[-0.03, 0, 1, 1],
)
table.auto_set_font_size(False)
cellDict = table.get_celld()
k = 1
rowHeight = 1 / len(rowLabels)
ncols = len(colLabels)
nrows = len(rowLabels)
for i in range(0, ncols):
cellDict[(0, i)].set_text_props(weight="bold",
color="white",
size="x-large")
cellDict[(0, i)].set_facecolor("darkblue")
cellDict[(0, i)].set_edgecolor("white")
cellDict[(0, i)].set_height(rowHeight)
for j in range(1, nrows + 1):
cellDict[(j, 0)].set_text_props(weight="bold",
color="black",
size="x-large",
ha="left")
cellDict[(j, i)].set_text_props(color="black", size="x-large")
cellDict[(j, 0)].set_edgecolor("white")
cellDict[(j, i)].set_edgecolor("white")
if k % 2 != 0:
cellDict[(j, 0)].set_facecolor("whitesmoke")
cellDict[(j, i)].set_facecolor("whitesmoke")
if j in [6, 19]:
cellDict[(j, 0)].set_facecolor("white")
cellDict[(j, i)].set_facecolor("white")
if j in [1, 7, 20]:
cellDict[(j, 0)].set_text_props(color="white")
cellDict[(j, 0)].set_facecolor("orange")
cellDict[(j, i)].set_facecolor("orange")
k = 1
k += 1
cellDict[(j, i)].set_height(rowHeight)
for i in range(0, ncols):
for j in range(nrows - 2, nrows + 1):
cellDict[(j, i)].set_text_props(weight="normal",
color="black",
size="large")
cellDict[(j, i)].set_facecolor("white")
fig = plt.gcf()
fig.tight_layout()
return ax
def plot_hist(returns, w, alpha=0.05, bins=50, height=6, width=10, ax=None):
r"""
Create a histogram of portfolio returns with the risk measures.
Parameters
----------
returns : DataFrame
Assets returns.
w : DataFrame of shape (n_assets, 1)
Portfolio weights.
alpha : float, optional
Significante level of VaR, CVaR and EVaR. The default is 0.05.
bins : float, optional
Number of bins of the histogram. The default is 50.
height : float, optional
Height of the image in inches. The default is 6.
width : float, optional
Width of the image in inches. The default is 10.
ax : matplotlib axis, optional
If provided, plot on this axis. The default is None.
Raises
------
ValueError
When the value cannot be calculated.
Returns
-------
ax : matplotlib axis.
Returns the Axes object with the plot for further tweaking.
Example
-------
::
ax = plf.plot_hist(returns=Y, w=w1, alpha=0.05, bins=50, height=6,
width=10, ax=None)
.. image:: images/Histogram.png
"""
if not isinstance(returns, pd.DataFrame):
raise ValueError("returns must be a DataFrame")
if not isinstance(w, pd.DataFrame):
raise ValueError("w must be a DataFrame")
if w.shape[1] > 1 and w.shape[0] == 0:
w = w.T
elif w.shape[1] > 1 and w.shape[0] > 0:
raise ValueError("w must be a DataFrame")
if returns.shape[1] != w.shape[0]:
a1 = str(returns.shape)
a2 = str(w.shape)
raise ValueError("shapes " + a1 + " and " + a2 + " not aligned")
if ax is None:
ax = plt.gca()
fig = plt.gcf()
fig.set_figwidth(width)
fig.set_figheight(height)
a = np.array(returns, ndmin=2) @ np.array(w, ndmin=2)
ax.set_title("Portfolio Returns Histogram")
n, bins1, patches = ax.hist(a,
bins,
density=1,
edgecolor="skyblue",
color="skyblue",
alpha=0.5)
mu = np.mean(a)
sigma = np.std(a, axis=0, ddof=1).item()
risk = [
mu,
mu - sigma,
mu - rk.MAD(a),
-rk.VaR_Hist(a, alpha),
-rk.CVaR_Hist(a, alpha),
-rk.EVaR_Hist(a, alpha)[0],
-rk.WR(a),
]
label = [
"Mean: " + "{0:.2%}".format(risk[0]),
"Mean - Std. Dev.(" + "{0:.2%}".format(-risk[1] + mu) + "): " +
"{0:.2%}".format(risk[1]),
"Mean - MAD(" + "{0:.2%}".format(-risk[2] + mu) + "): " +
"{0:.2%}".format(risk[2]),
"{0:.2%}".format(
(1 - alpha)) + " Confidence VaR: " + "{0:.2%}".format(risk[3]),
"{0:.2%}".format(
(1 - alpha)) + " Confidence CVaR: " + "{0:.2%}".format(risk[4]),
"{0:.2%}".format(
(1 - alpha)) + " Confidence EVaR: " + "{0:.2%}".format(risk[5]),
"Worst Realization: " + "{0:.2%}".format(risk[6]),
]
color = [
"b", "r", "fuchsia", "darkorange", "limegreen", "dodgerblue",
"darkgrey"
]
for i, j, k in zip(risk, label, color):
ax.axvline(x=i, color=k, linestyle="-", label=j)
# add a 'best fit' line
y = (1 / (np.sqrt(2 * np.pi) * sigma)) * np.exp(-0.5 * (1 / sigma *
(bins1 - mu))**2)
ax.plot(
bins1,
y,
"--",
color="orange",
label="Normal: $\mu=" + "{0:.2%}".format(mu) + "$%, $\sigma=" +
"{0:.2%}".format(sigma) + "$%",
)
factor = (np.max(a) - np.min(a)) / bins
ax.xaxis.set_major_locator(plt.AutoLocator())
ax.set_xticklabels(["{:3.2%}".format(x) for x in ax.get_xticks()])
ax.set_yticklabels(["{:3.2%}".format(x * factor) for x in ax.get_yticks()])
ax.legend(loc="upper right") # , fontsize = 'x-small')
ax.grid(linestyle=":")
ax.set_ylabel("Probability Density")
fig = plt.gcf()
fig.tight_layout()
return ax
def efficient_frontier(self, model="Classic", rm="MV", points=20, rf=0, hist=True):
r"""
Method that calculates several portfolios in the efficient frontier
of the selected risk measure, available with current assets and
constraints.
Parameters
----------
model : str, optional
Methodology used to estimate input parameters.
The default is 'Classic'.
rm : str, optional
Risk measure used by the optimization model. The default is 'MV'.
points : scalar, optional
Number of point calculated from the efficient frontier.
The default is 50.
rf : scalar, optional
Risk free rate. The default is 0.
hist : bool, optional
Indicate if uses historical or factor estimation of returns to
calculate risk measures that depends on scenarios (All except
'MV' risk measure). The default is True.
Returns
-------
frontier : DataFrame
A dataframe that containts the weights of the portfolios.
Notes
-----
It's recommendable that don't use this method when there are too many
assets (more than 100) and you are using a scenario based risk measure
(all except standard deviation). It's preferable to use frontier_limits
method (faster) to know the range of expected return and expected risk.
"""
mu = None
sigma = None
returns = None
if model == "Classic":
mu = np.matrix(self.mu)
sigma = np.matrix(self.cov)
returns = np.matrix(self.returns)
nav = np.matrix(self.nav)
elif model == "FM":
mu = np.matrix(self.mu_fm)
if hist == False:
sigma = np.matrix(self.cov_fm)
returns = np.matrix(self.returns_fm)
nav = np.matrix(self.nav_fm)
elif hist == True:
sigma = np.matrix(self.cov)
returns = np.matrix(self.returns)
nav = np.matrix(self.nav)
elif model == "BL":
mu = np.matrix(self.mu_bl)
if hist == False:
sigma = np.matrix(self.cov_bl)
elif hist == True:
sigma = np.matrix(self.cov)
returns = np.matrix(self.returns)
nav = np.matrix(self.nav)
elif model == "BL_FM":
mu = np.matrix(self.mu_bl_fm_2)
if hist == False:
sigma = np.matrix(self.cov_bl_fm_2)
returns = np.matrix(self.returns_fm)
nav = np.matrix(self.nav_fm)
elif hist == True:
sigma = np.matrix(self.cov)
returns = np.matrix(self.returns)
nav = np.matrix(self.nav)
alpha1 = self.alpha
limits = self.frontier_limits(model="Classic", rm=rm, rf=rf, hist=hist)
w_min = np.matrix(limits.iloc[:, 0]).T
w_max = np.matrix(limits.iloc[:, 1]).T
ret_min = (mu * w_min).item()
ret_max = (mu * w_max).item()
if rm == "MV":
risk_min = np.sqrt(w_min.T * sigma * w_min).item()
risk_max = np.sqrt(w_max.T * sigma * w_max).item()
elif rm == "MAD":
risk_min = rk.MAD(returns * w_min)
risk_max = rk.MAD(returns * w_max)
elif rm == "MSV":
risk_min = rk.SemiDeviation(returns * w_min)
risk_max = rk.SemiDeviation(returns * w_max)
elif rm == "CVaR":
risk_min = rk.CVaR_Hist(returns * w_min, alpha1)
risk_max = rk.CVaR_Hist(returns * w_max, alpha1)
elif rm == "WR":
risk_min = rk.WR(returns * w_min)
risk_max = rk.WR(returns * w_max)
elif rm == "FLPM":
risk_min = rk.LPM(returns * w_min, rf, 1)
risk_max = rk.LPM(returns * w_max, rf, 1)
elif rm == "SLPM":
risk_min = rk.LPM(returns * w_min, rf, 2)
risk_max = rk.LPM(returns * w_max, rf, 2)
elif rm == "MDD":
risk_min = rk.MaxAbsDD(returns * w_min)
risk_max = rk.MaxAbsDD(returns * w_max)
elif rm == "ADD":
risk_min = rk.AvgAbsDD(returns * w_min)
risk_max = rk.AvgAbsDD(returns * w_max)
elif rm == "CDaR":
risk_min = rk.ConAbsDD(returns * w_min, alpha1)
risk_max = rk.ConAbsDD(returns * w_max, alpha1)
mus = np.linspace(ret_min, ret_max + (ret_max - ret_min) / (points), points + 1)
risks = np.linspace(
risk_min, risk_max + (risk_max - risk_min) / (points), points + 1
)
risk_lims = [
"upperdev",
"uppermad",
"uppersdev",
"upperCVaR",
"upperwr",
"upperflpm",
"upperslpm",
"uppermdd",
"upperadd",
"upperCDaR",
]
risk_names = [
"MV",
"MAD",
"MSV",
"CVaR",
"WR",
"FLPM",
"SLPM",
"MDD",
"ADD",
"CDaR",
]
item = risk_names.index(rm)
frontier = []
n = 0
for i in range(len(risks)):
try:
if n == 0:
w = self.optimization(
model=model, rm=rm, obj="MinRisk", rf=rf, l=0, hist=hist
)
else:
setattr(self, risk_lims[item], risks[i])
w = self.optimization(
model=model, rm=rm, obj="MaxRet", rf=rf, l=0, hist=hist
)
n += 1
frontier.append(w)
except:
pass
setattr(self, risk_lims[item], None)
frontier = pd.concat(frontier, axis=1)
frontier.columns = list(range(len(risks)))
return frontier