def plot_drawdown(nav, w, alpha=0.05, height=8, width=10, ax=None):
r"""
Create a chart with the evolution of portfolio prices and drawdown.
Parameters
----------
nav : DataFrame
Cumulative assets returns.
w : DataFrame, optional
A portfolio specified by the user to compare with the efficient
frontier. The default is None.
alpha : float, optional
Significante level of DaR and CDaR. The default is 0.05.
height : float, optional
Height of the image in inches. The default is 8.
width : float, optional
Width of the image in inches. The default is 10.
ax : matplotlib axis of size (2,1), 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
-------
::
nav=port.nav
ax = plf.plot_drawdown(nav=nav, w=w1, alpha=0.05, height=8, width=10, ax=None)
.. image:: images/Drawdown.png
"""
if not isinstance(nav, pd.DataFrame):
raise ValueError("nav 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 nav.shape[1] != w.shape[0]:
a1 = str(nav.shape)
a2 = str(w.shape)
raise ValueError("shapes " + a1 + " and " + a2 + " not aligned")
if ax is None:
fig = plt.gcf()
ax = fig.subplots(nrows=2, ncols=1)
ax = ax.flatten()
fig.set_figwidth(width)
fig.set_figheight(height)
index = nav.index.tolist()
a = np.array(nav, ndmin=2)
a = np.insert(a, 0, 0, axis=0)
a = np.diff(a, axis=0)
a = np.array(a, ndmin=2) @ np.array(w, ndmin=2)
prices = 1 + np.insert(a, 0, 0, axis=0)
prices = np.cumprod(prices, axis=0)
prices = np.ravel(prices).tolist()
prices2 = 1 + np.array(np.cumsum(a, axis=0))
prices2 = np.ravel(prices2).tolist()
del prices[0]
DD = []
peak = -99999
for i in range(0, len(prices)):
if prices2[i] > peak:
peak = prices2[i]
DD.append((peak - prices2[i]))
DD = -np.array(DD)
titles = [
"Historical Compounded Cumulative Returns",
"Historical Uncompounded Drawdown",
]
data = [prices, DD]
color1 = ["b", "orange"]
risk = [
-rk.MDD_Abs(a),
-rk.ADD_Abs(a),
-rk.DaR_Abs(a, alpha),
-rk.CDaR_Abs(a, alpha),
-rk.UCI_Abs(a),
]
label = [
"Maximum Drawdown: " + "{0:.2%}".format(risk[0]),
"Average Drawdown: " + "{0:.2%}".format(risk[1]),
"{0:.2%}".format(
(1 - alpha)) + " Confidence DaR: " + "{0:.2%}".format(risk[2]),
"{0:.2%}".format(
(1 - alpha)) + " Confidence CDaR: " + "{0:.2%}".format(risk[3]),
"Ulcer Index: " + "{0:.2%}".format(risk[4]),
]
color2 = ["r", "b", "limegreen", "dodgerblue", "fuchsia"]
j = 0
ymin = np.min(DD) * 1.5
for i in ax:
i.clear()
i.plot_date(index, data[j], "-", color=color1[j])
if j == 1:
i.fill_between(index, 0, data[j], facecolor=color1[j], alpha=0.3)
for k in range(0, len(risk)):
i.axhline(y=risk[k],
color=color2[k],
linestyle="-",
label=label[k])
i.set_ylim(ymin, 0)
i.legend(loc="lower right") # , fontsize = 'x-small')
i.set_title(titles[j])
i.xaxis.set_major_locator(
mdates.AutoDateLocator(tz=None, minticks=5, maxticks=10))
i.xaxis.set_major_formatter(mdates.DateFormatter("%Y-%m"))
i.set_yticklabels(["{:3.2%}".format(x) for x in i.get_yticks()])
i.grid(linestyle=":")
j = j + 1
fig = plt.gcf()
fig.tight_layout()
return ax
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