Equity index future returns#

This category group contains daily local-currency equity index future returns. The returns are conceptually based on leveraged positions in the most liquid local currency-denominated indices.

Equity index future returns in % of notional#

Ticker: EQXR_NSA

Label: Equity index future returns in % of notional.

Definition: Return on front future of main country equity index, % of notional of the contract.

Notes:

  • The return is simply the % change of the futures price. The return calculation assumes rolling futures (from front to second) on IMM (international monetary markets) days.

  • See Appendix 1 for the list of equity indicies used for each currency area in futures return calculations.

Vol-targeted equity index future return#

Ticker: EQXR_VT10

Label: Equity index future return for 10% vol target.

Definition: Return on front future of main country equity index, % of risk capital on position scaled to 10% (annualized) volatility target.

Notes:

  • Positions are scaled to a 10% volatility target based on the historic standard deviation for an exponential moving average with a half-life of 11 days. Positions are rebalanced at the end of each month.

  • See the important notes under “Equity index future returns in % of notional” (EQXR_NSA).

Imports#

Only the standard Python data science packages and the specialized macrosynergy package are needed.

import os
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import math

import json
import yaml

import macrosynergy.management as msm
import macrosynergy.panel as msp
import macrosynergy.signal as mss
import macrosynergy.pnl as msn


from macrosynergy.download import JPMaQSDownload

from timeit import default_timer as timer
from datetime import timedelta, date, datetime

import warnings

warnings.simplefilter("ignore")

The JPMaQS indicators we consider are downloaded using the J.P. Morgan Dataquery API interface within the macrosynergy package. This is done by specifying ticker strings, formed by appending an indicator category code <category> to a currency area code <cross_section>. These constitute the main part of a full quantamental indicator ticker, taking the form DB(JPMAQS,<cross_section>_<category>,<info>), where <info> denotes the time series of information for the given cross-section and category. The following types of information are available:

  • value giving the latest available values for the indicator

  • eop_lag referring to days elapsed since the end of the observation period

  • mop_lag referring to the number of days elapsed since the mean observation period

  • grade denoting a grade of the observation, giving a metric of real time information quality.

After instantiating the JPMaQSDownload class within the macrosynergy.download module, one can use the download(tickers,start_date,metrics) method to easily download the necessary data, where tickers is an array of ticker strings, start_date is the first collection date to be considered and metrics is an array comprising the times series information to be downloaded.

# Cross-sections of interest

cids_dmeq = ["AUD", "CAD", "CHF", "EUR", "GBP", "JPY", "SEK", "USD"]
cids_eueq = ["DEM", "ESP", "FRF", "ITL", "NLG"]
cids_aseq = ["CNY", "HKD", "INR", "KRW", "MYR", "SGD", "THB", "TWD"]
cids_exeq = ["BRL", "TRY", "ZAR"]
cids_nueq = ["MXN", "PLN"]

cids = sorted(cids_dmeq + cids_eueq + cids_aseq + cids_exeq + cids_nueq)
main = ["EQXR_NSA", "EQXR_VT10"]

econ = ["BXBGDPRATIO_NSA_12MMA", "CABGDPRATIO_NSA_12MMA"]  # economic context

mark = [
    "EQCRR_NSA",
    "EQCRR_VT10",
    "FXXR_NSA",
    "FXTARGETED_NSA",
    "FXUNTRADABLE_NSA",
]  # market links

xcats = main + econ + mark
# Download series from J.P. Morgan DataQuery by tickers

start_date = "2000-01-01"
tickers = [cid + "_" + xcat for cid in cids for xcat in xcats]
print(f"Maximum number of tickers is {len(tickers)}")

# Retrieve credentials

client_id: str = os.getenv("DQ_CLIENT_ID")
client_secret: str = os.getenv("DQ_CLIENT_SECRET")

# Download from DataQuery

with JPMaQSDownload(client_id=client_id, client_secret=client_secret) as downloader:
    start = timer()
    assert downloader.check_connection()
    df = downloader.download(
        tickers=tickers,
        start_date=start_date,
        metrics=["value", "eop_lag", "mop_lag", "grading"],
        suppress_warning=True,
        show_progress=True,
    )
    end = timer()

dfd = df

print("Download time from DQ: " + str(timedelta(seconds=end - start)))
Maximum number of tickers is 234
Downloading data from JPMaQS.
Timestamp UTC:  2023-09-06 13:18:44
Connection successful!
Number of expressions requested: 936
Requesting data: 100%|█████████████████████████████████████████████████████████████████| 47/47 [00:14<00:00,  3.22it/s]
Downloading data: 100%|████████████████████████████████████████████████████████████████| 47/47 [00:40<00:00,  1.17it/s]
Download time from DQ: 0:01:07.746815

Availability#

cids_exp = cids  # cids expected in category panels
msm.missing_in_df(dfd, xcats=main, cids=cids_exp)
Missing xcats across df:  []
Missing cids for EQXR_NSA:  []
Missing cids for EQXR_VT10:  []

For most countries the series start in the 1990s, but China’s and Poland’s return series only begin the 2010s.

For the explanation of currency symbols, which are related to currency areas or countries for which categories are available, please view Appendix 1.

xcatx = main
cidx = cids_exp

dfx = msm.reduce_df(dfd, xcats=xcatx, cids=cidx)
dfs = msm.check_startyears(
    dfx,
)
msm.visual_paneldates(dfs, size=(18, 2))

print("Last updated:", date.today())
../_images/Equity index future returns_16_0.png
Last updated: 2023-09-06
xcatx = main
cidx = cids_exp

plot = msm.check_availability(
    dfd, xcats=xcatx, cids=cidx, start_size=(18, 1), start_years=False
)
../_images/Equity index future returns_17_0.png
xcatx = main
cidx = cids_exp

plot = msp.heatmap_grades(
    dfd,
    xcats=xcatx,
    cids=cidx,
    size=(18, 2),
    title=f"Average vintage grades from {start_date} onwards",
)
../_images/Equity index future returns_18_0.png
xcatx = main
cidx = cids_exp

msp.view_ranges(
    dfd,
    xcats=xcatx,
    cids=cidx,
    val="eop_lag",
    title="End of observation period lags (ranges of time elapsed since end of observation period in days)",
    start=start_date,
    kind="box",
    size=(16, 4),
)
msp.view_ranges(
    dfd,
    xcats=xcatx,
    cids=cidx,
    val="mop_lag",
    title="Median of observation period lags (ranges of time elapsed since middle of observation period in days)",
    start=start_date,
    kind="box",
    size=(16, 4),
)
../_images/Equity index future returns_19_0.png ../_images/Equity index future returns_19_1.png

History#

Equity index future returns in % of notional#

Long-term return distributions have been more homogeneous across currency areas than the distributions of FX or interest rate swap returns.

xcatx = ["EQXR_NSA"]
cidx = cids_exp

msp.view_ranges(
    dfd,
    xcats=xcatx,
    cids=cidx,
    sort_cids_by="std",
    start=start_date,
    kind="box",
    title="Boxplots of equity index future returns, % of notional, since 2000",
    xcat_labels=["Equity index future returns"],
    size=(16, 8),
)
../_images/Equity index future returns_23_0.png
xcatx = ["EQXR_NSA"]
cidx = cids_exp

msp.view_timelines(
    dfd,
    xcats=xcatx,
    cids=cidx,
    start=start_date,
    title="Cumulative returns on main local-currency equity index future, % of notional",
    title_fontsize=27,
    title_adj=1.02,
    title_xadj=0.51,
    cumsum=True,
    ncol=4,
    same_y=True,
    size=(12, 7),
    aspect=1.7,
    all_xticks=True,
)
../_images/Equity index future returns_24_0.png

Unsurprisingly, cross-country correlations of daily equity future returns have been all positive since 2000. China displayed the lowest correlation with other countries.

xcatx = "EQXR_NSA"
cidx = cids_exp

msp.correl_matrix(
    dfd,
    xcats=xcatx,
    cids=cidx,
    title="Cross-sectional correlations of main local-currency equity index futures, since 2000",
    size=(20, 14),
)
../_images/Equity index future returns_26_0.png

Vol-targeted equity index future returns#

Volatility targeting reduces the relative cumulative performance of most emerging market indices relative to the developed world.

xcatx = ["EQXR_NSA", "EQXR_VT10"]
cidx = cids_exp

msp.view_timelines(
    dfd,
    xcats=xcatx,
    cids=cidx,
    start=start_date,
    title="Cumulative outright and vol-targeted returns on main local-currency equity index futures",
    xcat_labels=["Outright", "Vol-targeted"],
    title_adj=1.02,
    title_xadj=0.45,
    legend_fontsize=17,
    label_adj=0.075,
    title_fontsize=27,
    cumsum=True,
    ncol=4,
    same_y=False,
    size=(12, 7),
    aspect=1.7,
    all_xticks=True,
)
../_images/Equity index future returns_29_0.png

Importance#

Empirical Clues#

In the medium-term, local-currency equity and FX forward returns have been positively correlated. This suggests that capital flows and local economic conditions, which drive the positive correlation, have been more powerful than exchange rate shocks, which usually push FX and local-currency equity returns in different directions.

dfb = dfd[dfd["xcat"].isin(["FXTARGETED_NSA", "FXUNTRADABLE_NSA"])].loc[
    :, ["cid", "xcat", "real_date", "value"]
]
dfba = (
    dfb.groupby(["cid", "real_date"])
    .aggregate(value=pd.NamedAgg(column="value", aggfunc="max"))
    .reset_index()
)
dfba["xcat"] = "FXBLACK"
fxblack = msp.make_blacklist(dfba, "FXBLACK")
fxblack
{'BRL': (Timestamp('2012-12-03 00:00:00'), Timestamp('2013-09-30 00:00:00')),
 'CHF': (Timestamp('2011-05-02 00:00:00'), Timestamp('2016-06-30 00:00:00')),
 'CNY': (Timestamp('2000-01-03 00:00:00'), Timestamp('2023-09-05 00:00:00')),
 'HKD': (Timestamp('2000-01-03 00:00:00'), Timestamp('2023-09-05 00:00:00')),
 'INR': (Timestamp('2000-01-03 00:00:00'), Timestamp('2004-12-31 00:00:00')),
 'MYR_1': (Timestamp('2000-01-03 00:00:00'), Timestamp('2007-11-30 00:00:00')),
 'MYR_2': (Timestamp('2018-07-02 00:00:00'), Timestamp('2023-09-05 00:00:00')),
 'SGD': (Timestamp('2000-01-03 00:00:00'), Timestamp('2023-09-05 00:00:00')),
 'THB': (Timestamp('2007-01-01 00:00:00'), Timestamp('2008-11-28 00:00:00')),
 'TRY_1': (Timestamp('2000-01-03 00:00:00'), Timestamp('2003-09-30 00:00:00')),
 'TRY_2': (Timestamp('2020-01-01 00:00:00'), Timestamp('2023-09-05 00:00:00'))}
xcatx = ["FXXR_NSA", "EQXR_NSA"]
cidx = cids_exp

cr = msp.CategoryRelations(
    dfd,
    xcats=xcatx,
    cids=cidx,
    blacklist=fxblack,
    freq="A",
    lag=0,
    xcat_aggs=["sum", "sum"],
    start="2000-01-01",
    years=None,
)
FXXR_NSA misses: ['DEM', 'ESP', 'FRF', 'HKD', 'ITL', 'NLG', 'USD'].
cr.reg_scatter(
    title="Annual cumulative local-currency equity index and FX forward returns since 2000",
    labels=True,
    coef_box="lower left",
    xlab="FX forward returns",
    ylab="Equity index futures returns",
)
../_images/Equity index future returns_39_0.png

OLS regression reveals a highly significant positive intercept, implying that on average, the FX forward returns need to be quite negative to result in negative equity index futures.

cr.ols_table()
                            OLS Regression Results                            
==============================================================================
Dep. Variable:               EQXR_NSA   R-squared:                       0.103
Model:                            OLS   Adj. R-squared:                  0.100
Method:                 Least Squares   F-statistic:                     39.86
Date:                Wed, 06 Sep 2023   Prob (F-statistic):           8.28e-10
Time:                        14:23:47   Log-Likelihood:                -1550.7
No. Observations:                 351   AIC:                             3105.
Df Residuals:                     349   BIC:                             3113.
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          6.7064      1.078      6.220      0.000       4.586       8.827
FXXR_NSA       0.6054      0.096      6.314      0.000       0.417       0.794
==============================================================================
Omnibus:                       20.111   Durbin-Watson:                   2.311
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               33.792
Skew:                          -0.372   Prob(JB):                     4.59e-08
Kurtosis:                       4.326   Cond. No.                         11.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Appendices#

Appendix 1: Equity index specification#

The following equity indices have been used for futures return calculations in each currency area:

  • AUD: Standard and Poor’s / Australian Stock Exchange 200

  • BRL: Brazil Bovespa

  • CAD: Standard and Poor’s / Toronto Stock Exchange 60 Index

  • CHF: Swiss Market (SMI)

  • CNY: Shanghai Shenzhen CSI 300

  • DEM: DAX 30 Performance (Xetra)

  • ESP: IBEX 35

  • EUR: EURO STOXX 50

  • FRF: CAC 40

  • GBP: FTSE 100

  • HKD: Hang Seng China Enterprises

  • INR: CNX Nifty (50)

  • ITL: FTSE MIB Index

  • JPY: Nikkei 225 Stock Average

  • KRW: Korea Stock Exchange KOSPI 200

  • MXN: Mexico IPC (Bolsa)

  • MYR: FTSE Bursa Malaysia KLCI

  • NLG: AEX Index (AEX)

  • PLN: Warsaw General Index 20

  • SEK: OMX Stockholm 30 (OMXS30)

  • SGD: MSCI Singapore (Free)

  • THB: Bangkok S.E.T. 50

  • TRY: Bist National 30

  • TWD: Taiwan Stock Exchange Weighed TAIEX

  • USD: Standard and Poor’s 500 Composite

  • ZAR: FTSE / JSE Top 40

See Appendix 2 for the list of currency symbols used to represent each cross-section.

Appendix 2: Currency symbols#

The word ‘cross-section’ refers to currencies, currency areas or economic areas. In alphabetical order, these are AUD (Australian dollar), BRL (Brazilian real), CAD (Canadian dollar), CHF (Swiss franc), CLP (Chilean peso), CNY (Chinese yuan renminbi), COP (Colombian peso), CZK (Czech Republic koruna), DEM (German mark), ESP (Spanish peseta), EUR (Euro), FRF (French franc), GBP (British pound), HKD (Hong Kong dollar), HUF (Hungarian forint), IDR (Indonesian rupiah), ITL (Italian lira), JPY (Japanese yen), KRW (Korean won), MXN (Mexican peso), MYR (Malaysian ringgit), NLG (Dutch guilder), NOK (Norwegian krone), NZD (New Zealand dollar), PEN (Peruvian sol), PHP (Phillipine peso), PLN (Polish zloty), RON (Romanian leu), RUB (Russian ruble), SEK (Swedish krona), SGD (Singaporean dollar), THB (Thai baht), TRY (Turkish lira), TWD (Taiwanese dollar), USD (U.S. dollar), ZAR (South African rand).