def plot_table(
returns, w, MAR=0, alpha=0.05, height=9, width=12, t_factor=252, ini_days=1, 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}
ini_days : float, optional
If provided, it is the number of days of compounding for first return.
It is used to calculate Compound Annual Growth Rate (CAGR). This value
depend on assumptions used in t_factor, for example if data is monthly
you can use 21 (252 days per year) or 30 (360 days per year). The
default is 1 for daily returns.
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 + ini_days
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)",
"Ulcer Index (UCI)",
"Average Drawdown (ADD)",
"Drawdown at Risk (DaR)",
"Conditional Drawdown at Risk (CDaR)",
"Entropic Drawdown at Risk (EDaR)",
"Max Drawdown (MDD)",
"(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.UCI_Abs(X),
rk.ADD_Abs(X),
rk.DaR_Abs(X),
rk.CDaR_Abs(X, alpha=alpha),
rk.EDaR_Abs(X, alpha=alpha)[0],
rk.MDD_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_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.UCI_Abs(a),
-rk.ADD_Abs(a),
-rk.DaR_Abs(a, alpha),
-rk.CDaR_Abs(a, alpha),
-rk.EDaR_Abs(a, alpha)[0],
-rk.MDD_Abs(a),
]
label = [
"Ulcer Index: " + "{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]),
"{0:.2%}".format((1 - alpha))
+ " Confidence EDaR: "
+ "{0:.2%}".format(risk[4]),
"Maximum Drawdown: " + "{0:.2%}".format(risk[5]),
]
color2 = ["b", "r", "fuchsia", "limegreen", "dodgerblue", "darkgrey"]
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"))
ticks_loc = i.get_yticks().tolist()
i.set_yticks(i.get_yticks())
i.set_yticklabels(["{:3.2%}".format(x) for x in ticks_loc])
i.grid(linestyle=":")
j = j + 1
fig = plt.gcf()
fig.tight_layout()
return ax
def excel_report(returns,
w,
rf=0,
alpha=0.05,
t_factor=252,
ini_days=1,
name="report"):
r"""
Create an Excel report (with formulas) with useful information to analyze
risk and profitability of investment portfolios.
Parameters
----------
returns : DataFrame
Assets returns.
w : DataFrame of size (n_assets, n_portfolios)
Portfolio weights.
rf : float, optional
Risk free rate or minimum aceptable return. The default is 0.
alpha : float, optional
Significante level of VaR, CVaR, EVaR, DaR and CDaR.
The default is 0.05.
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}
ini_days : float, optional
If provided, it is the number of days of compounding for first return.
It is used to calculate Compound Annual Growth Rate (CAGR). This value
depend on assumptions used in t_factor, for example if data is monthly
you can use 21 (252 days per year) or 30 (360 days per year). The
default is 1 for daily returns.
name : str, optional
Name or name with path where the Excel report will be saved. If no
path is provided the report will be saved in the same path of
current file.
Raises
------
ValueError
When the report cannot be built.
Example
-------
::
rp.excel_report(returns, w, MAR=0, alpha=0.05, name='report', files=None)
.. image:: images/Excel.png
"""
n1 = w.shape[0]
n2 = returns.shape[0]
portfolios = w.columns.tolist()
dates = returns.index.tolist()
year = str(datetime.datetime.now().year)
days = (returns.index[-1] - returns.index[0]).days + ini_days
# Create a Pandas Excel writer using XlsxWriter as the engine.
writer = pd.ExcelWriter(name + ".xlsx", engine="xlsxwriter")
# Convert the dataframe to an XlsxWriter Excel object.
w.to_excel(writer, sheet_name="Resume", startrow=36, startcol=0)
returns.to_excel(writer, sheet_name="Returns", index_label=["Date"])
# Get the xlsxwriter objects from the dataframe writer object.
workbook = writer.book
worksheet1 = writer.sheets["Resume"]
worksheet2 = writer.sheets["Returns"]
worksheet3 = workbook.add_worksheet("Portfolios")
worksheet4 = workbook.add_worksheet("Absdev")
worksheet5 = workbook.add_worksheet("CumRet")
worksheet6 = workbook.add_worksheet("Drawdown")
worksheet7 = workbook.add_worksheet("devBelowTarget")
worksheet8 = workbook.add_worksheet("devBelowMean")
worksheet1.hide_gridlines(2)
worksheet2.hide_gridlines(2)
worksheet3.hide_gridlines(2)
worksheet4.hide_gridlines(2)
worksheet5.hide_gridlines(2)
worksheet6.hide_gridlines(2)
worksheet7.hide_gridlines(2)
worksheet8.hide_gridlines(2)
# Cell Formats
cell_format1 = workbook.add_format({"bold": True, "border": True})
cell_format2 = workbook.add_format({
"bold": True,
"font_size": 28,
"right": True
})
cell_format3 = workbook.add_format({"num_format": "0.0000%"})
cell_format4 = workbook.add_format({
"num_format": "0.0000%",
"border": True
})
cell_format5 = workbook.add_format({
"num_format": "yyyy-mm-dd",
"bold": True
})
cell_format6 = workbook.add_format({
"num_format": "0.0000",
"border": True
})
cell_format7 = workbook.add_format({
"num_format": "yyyy-mm-dd",
"bold": True,
"border": True
})
cell_format8 = workbook.add_format({"num_format": "0,000", "border": True})
cols = xl_col_to_name(1) + ":" + xl_col_to_name(n2)
worksheet1.set_column(cols, 11, cell_format3)
worksheet2.set_column(cols, 9, cell_format3)
worksheet2.write(0, 0, "Date", cell_format1)
worksheet3.write(0, 0, "Date", cell_format1)
worksheet4.write(0, 0, "Date", cell_format1)
worksheet5.write(0, 0, "Date", cell_format1)
worksheet6.write(0, 0, "Date", cell_format1)
worksheet7.write(0, 0, "Date", cell_format1)
worksheet8.write(0, 0, "Date", cell_format1)
worksheet1.set_column("A:A", 36)
worksheet2.set_column("A:A", 10, cell_format5)
worksheet3.set_column("A:A", 10, cell_format5)
worksheet4.set_column("A:A", 10, cell_format5)
worksheet5.set_column("A:A", 10, cell_format5)
worksheet6.set_column("A:A", 10, cell_format5)
worksheet7.set_column("A:A", 10, cell_format5)
worksheet8.set_column("A:A", 10, cell_format5)
for i in range(0, n2):
r = xl_rowcol_to_cell(i + 1, 0)
formula = "=Returns!" + r + ""
worksheet2.write(i + 1, 0, dates[i], cell_format7)
worksheet3.write_formula(i + 1, 0, formula, cell_format7)
worksheet4.write_formula(i + 1, 0, formula, cell_format7)
worksheet5.write_formula(i + 1, 0, formula, cell_format7)
worksheet6.write_formula(i + 1, 0, formula, cell_format7)
worksheet7.write_formula(i + 1, 0, formula, cell_format7)
worksheet8.write_formula(i + 1, 0, formula, cell_format7)
labels_1 = [
"",
"",
"",
"",
"Profitability and Other Inputs",
"Total Days in DataBase",
"Mean Return (1)",
"Compound Annual Growth Rate (CAGR)",
"Minimum Acceptable Return (MAR) (1)",
"Alpha",
"",
"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)",
"Ulcer Index (UCI)",
"Average Drawdown (ADD)",
"Drawdown at Risk (DaR)",
"Conditional Drawdown at Risk (CDaR)",
"Entropic Drawdown at Risk (CDaR)",
"Max Drawdown (MDD)",
]
for i in range(0, len(labels_1)):
if labels_1[i] != "":
worksheet1.write(i, 0, labels_1[i], cell_format1)
for i in range(0, len(portfolios)):
a = "Portfolio " + str(i + 1)
worksheet1.write(3, 1 + i, a, cell_format1)
worksheet1.write(36, 1 + i, a, cell_format1)
worksheet3.write(0, 1 + i, a, cell_format1)
worksheet4.write(0, 1 + i, a, cell_format1)
worksheet5.write(0, 1 + i, a, cell_format1)
worksheet6.write(0, 1 + i, a, cell_format1)
worksheet7.write(0, 1 + i, a, cell_format1)
worksheet8.write(0, 1 + i, a, cell_format1)
for j in range(0, len(portfolios)):
r_0 = xl_rowcol_to_cell(8, 1 + j) # MAR cell
r_1 = xl_range_abs(37, 1 + j, 36 + n1, 1 + j)
r_2 = xl_range_abs(1, 1 + j, n2, 1 + j)
for i in range(0, n2):
r_3 = xl_range(i + 1, 1, i + 1, n1)
r_4 = xl_rowcol_to_cell(i + 1, 1 + j)
r_5 = xl_range_abs(1, 1 + j, i + 1, 1 + j)
formula1 = "{=MMULT(" + "Returns!" + r_3 + ",Resume!" + r_1 + ")}"
formula2 = "=ABS(Portfolios!" + r_4 + "-AVERAGE(Portfolios!" + r_2 + "))"
formula3 = "=SUM(Portfolios!" + r_5 + ")"
formula4 = "=MAX(CumRet!" + r_5 + ")-CumRet!" + r_4
formula5 = ("=MAX(Resume!" + r_0 + "/ " + str(t_factor) +
"-Portfolios!" + r_4 + ", 0)")
formula6 = "=MAX(AVERAGE(Portfolios!" + r_2 + ")-Portfolios!" + r_4 + ", 0)"
worksheet3.write_formula(i + 1, 1 + j, formula1, cell_format3)
worksheet4.write_formula(i + 1, 1 + j, formula2, cell_format3)
worksheet5.write_formula(i + 1, 1 + j, formula3, cell_format3)
worksheet6.write_formula(i + 1, 1 + j, formula4, cell_format3)
worksheet7.write_formula(i + 1, 1 + j, formula5, cell_format3)
worksheet8.write_formula(i + 1, 1 + j, formula6, cell_format3)
r_6 = xl_rowcol_to_cell(9, 1 + j) # Alpha cell
r_7 = xl_rowcol_to_cell(17, 1 + j) # Value at Risk cell
AVG = "=AVERAGE(Portfolios!" + r_2 + ") * " + str(t_factor) + ""
CUM = "{=PRODUCT(1 + Portfolios!" + r_2 + ")^(360/" + str(
days) + ")-1}"
STDEV = "=STDEV(Portfolios!" + r_2 + ") * SQRT(" + str(t_factor) + ")"
MAD = "=AVERAGE(Absdev!" + r_2 + ") * SQRT(" + str(t_factor) + ")"
ALPHA = "=" + str(alpha)
VaR = ("=-SMALL(Portfolios!" + r_2 + ",ROUNDUP(COUNT(Portfolios!" +
r_2 + ")*" + r_6 + ",0)) * SQRT(" + str(t_factor) + ")")
CVaR = ("=-((SUMIF(Portfolios!" + r_2 + ',"<="&(-' + r_7 + "/SQRT(" +
str(t_factor) + ")),Portfolios!" + r_2 + ")")
CVaR += ("-ROUNDUP(COUNT(Portfolios!" + r_2 + ")*" + r_6 + ",0)*(-" +
r_7 + "/SQRT(" + str(t_factor) + ")))/(COUNT(Portfolios!" +
r_2 + ")*" + r_6 + ")-" + r_7 + "/SQRT(" + str(t_factor) +
")) * SQRT(" + str(t_factor) + ")")
EVaR = ("=" + str(rk.EVaR_Hist(returns @ w, alpha=alpha)[0]) +
" * SQRT(" + str(t_factor) + ")")
WR = "=-MIN(Portfolios!" + r_2 + ") * SQRT(" + str(t_factor) + ")"
MDD = "=MAX(Drawdown!" + r_2 + ")"
ADD = "=AVERAGE(Drawdown!" + r_2 + ")"
DaR = ("=+LARGE(Drawdown!" + r_2 + ",ROUNDUP(COUNT(Drawdown!" + r_2 +
")*" + r_6 + ",0))")
CDaR = ("=((SUMIF(Drawdown!" + r_2 + ',">="&' + DaR[2:] +
",Drawdown!" + r_2 + ")")
CDaR += ("-ROUNDUP(COUNT(Drawdown!" + r_2 + ")*" + r_6 + ",0)*" +
DaR[2:] + ")/(COUNT(Drawdown!" + r_2 + ")*" + r_6 + ")+" +
DaR[2:] + ")")
EDaR = "=" + str(rk.EDaR_Abs(returns @ w, alpha=alpha)[0])
UCI = "=SQRT(SUMSQ(Drawdown!" + r_2 + ")/COUNT(Drawdown!" + r_2 + "))"
MAR = "=" + str(rf)
FLPM = "=AVERAGE(devBelowTarget!" + r_2 + ") * SQRT(" + str(
t_factor) + ")"
SLPM = ("=SQRT(SUMSQ(devBelowTarget!" + r_2 +
")/(COUNT(devBelowTarget!" + r_2 + ") - 1))" + " * SQRT(" +
str(t_factor) + ")")
SDEV = ("=SQRT(SUMSQ(devBelowMean!" + r_2 + ")/(COUNT(devBelowMean!" +
r_2 + ") - 1))" + " * SQRT(" + str(t_factor) + ")")
SKEW = "=SKEW(Portfolios!" + r_2 + ")"
KURT = "=KURT(Portfolios!" + r_2 + ")"
labels_2 = [
"",
"",
"",
"",
"",
str(days),
AVG,
CUM,
MAR,
ALPHA,
"",
"",
STDEV,
MAD,
SDEV,
FLPM,
SLPM,
VaR,
CVaR,
EVaR,
WR,
SKEW,
KURT,
"",
"",
UCI,
ADD,
DaR,
CDaR,
EDaR,
MDD,
]
for i in range(0, len(labels_2)):
if labels_1[i] in ["Skewness", "Kurtosis"]:
worksheet1.write_formula(i, 1 + j, labels_2[i], cell_format6)
elif labels_1[i] in ["Total Days in DataBase"]:
worksheet1.write_formula(i, 1 + j, labels_2[i], cell_format8)
elif labels_2[i] != "":
worksheet1.write_formula(i, 1 + j, labels_2[i], cell_format4)
merge_format = workbook.add_format({"align": "Left", "valign": "vjustify"})
merge_format.set_text_wrap()
worksheet1.set_row(1, 215)
worksheet1.merge_range("A2:K2", __LICENSE__.replace("2021", year),
merge_format)
worksheet1.write(2, 0, "https://github.com/dcajasn/Riskfolio-Lib")
worksheet1.write(31, 0, "(1) Annualized, multiplied by " + str(t_factor))
worksheet1.write(32, 0, "(2) Annualized, multiplied by √" + str(t_factor))
worksheet1.write(33, 0, "(3) Based on uncompounded cumulated returns")
worksheet1.write(0, 0, "Riskfolio-Lib Report", cell_format2)
writer.save()
workbook.close()