Equity index future volatility #

This category group includes measures of realized return volatility for major developed and emerging countries’ local-currency equity index futures. It also includes related generic leverage ratios for volatility targets.

Equity index future volatility #

Ticker : EQXRxEASD_NSA

Label : Estimated annualized standard deviation of equity index future return.

Definition : Annualized standard deviation of equity index future return, % of notional, based on exponential moving average of daily returns.

Notes :

  • The standard deviation is calculated based on an exponential moving average of daily returns with a half-life of 11 active trading days.

  • The return is the % change in 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.

Leverage ratio of vol-targeted equity future position #

Ticker : EQXRxLEV10_NSA

Label : Leverage ratio of equity index future position for 10% annualized vol target.

Definition : Equity index future leverage for a 10% annualized vol target, as a ratio of contract notional relative to risk capital on which the return is calculated.

Notes :

  • This serves as the leverage ratio for a 10% annualized vol target and is inversely proportional to the estimated annualized standard deviation of the return on a USD1 notional position. The leverage can viewed as indicative for positioning and endogenous market risk.

  • See further the notes for “Equity index future volatility” ( EQXRxEASD_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 = cids_dmeq + cids_eueq + cids_aseq + cids_exeq + cids_nueq
main = ["EQXRxEASD_NSA", "EQXRxLEV10_NSA"]
econ = ["RIR_NSA", "CABGDPRATIO_NSA_12MMA"]  # economic context
mark = ["EQCRR_NSA", "EQCRR_VT10", "EQXR_NSA", "EQXR_VT10"]  # 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 208
Downloading data from JPMaQS.
Timestamp UTC:  2023-07-04 14:47:37
Connection successful!
Number of expressions requested: 832
Requesting data: 100%|█████████████████████████████████████████████████████████████████| 42/42 [00:13<00:00,  3.21it/s]
Downloading data: 100%|████████████████████████████████████████████████████████████████| 42/42 [00:27<00:00,  1.50it/s]
Download time from DQ: 0:00:51.770545

Availability #

cids_exp = cids  # cids expected in category panels
msm.missing_in_df(dfd, xcats=main, cids=cids_exp)
Missing xcats across df:  set()
Missing cids for EQXRxEASD_NSA:  set()
Missing cids for EQXRxLEV10_NSA:  set()

For most currencies, quantamental indicators for equity index future volatility are available by 2000. Notable late-starters are Brazil and Turkey.

For the explanation of currency symbols, which are related to currency areas or countries for which categories are available, please view Appendix 2 .

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())
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/14d9941b056f9d22954da162e8355e3a14f8d97e8324151372065b744eeddd27.png
Last updated: 2023-07-04
xcatx = main
cidx = cids_exp

plot = msm.check_availability(
    dfd, xcats=xcatx, cids=cidx, start_size=(18, 2), start_years=False
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/631b0eb90502a8db0c4b2e08f1b208546a1194ea71d0049a56095157cc5c72ca.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",
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/53b67ea96c68035906d2a5fc162166a0ac44c69314c7cf059692fdedeb77d525.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),
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/3f44cf47eaa4489861fe92841f4536e0f7ac23c18d8ff56d141aa38607ba7c45.png https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/d345f3059cc198434fe18b3932d367016e46a09b243d2a500710b059a25bf5bf.png

History #

Equity index future volatility #

Historically, volatilities of equity index future returns have not been as diverse across countries as those of currency or interest rate swap positions. The long term averages of countries ranged from less than 15% (annualized) for FTSE Bursa Malaysia KLCI to over 30% for the Hang Seng China Enterprises index.

xcatx = ["EQXRxEASD_NSA"]
cidx = cids_exp

msp.view_ranges(
    dfd,
    xcats=xcatx,
    cids=cidx,
    sort_cids_by="mean",
    start=start_date,
    kind="bar",
    title="Means and standard deviations of equity index future return standard deviations, exponential lookback, % ar, since 2000",
    xcat_labels=["Equity index future volatility"],
    size=(16, 8),
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/ba0be72a5f9d2bff75fab03f00c27017f418a71f516e97d145c21e9ed5e12b62.png

Peak values in crisis episodes post-2000 exceeded 120% (Brazil Bovespa, Nikkei 225 and Hang Seng)!

xcatx = ["EQXRxEASD_NSA"]
cidx = cids_exp

msp.view_timelines(
    dfd,
    xcats=xcatx,
    cids=cidx,
    start=start_date,
    title="Equity index future volatility, exponential lookback, 11-day half-time, % ar",
    title_fontsize=27,
    title_adj=1.02,
    title_xadj=0.5,
    cumsum=False,
    ncol=4,
    same_y=True,
    size=(12, 7),
    aspect=1.7,
    all_xticks=True,
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/f55f19f1407709301cf3692a8b9508b8b7241b9342045db7d603e7649b521b14.png

Unsurprisingly, cross-country correlations of equity volatilities have been strongly positive. China’s Shanghai Shenzhen CSI 300 and Poland’s Warsaw General Index 20 have displayed the most idiosyncratic dynamics.

xcatx = "EQXRxEASD_NSA"
cidx = cids_exp

msp.correl_matrix(
    dfd,
    xcats=xcatx,
    cids=cidx,
    title="Cross-sectional correlations of equity index future volatilities",
    size=(20, 14),
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/b836c2632243e72bbf3335ea2cb51c919e65ec980ee152401936ab098cd1f18e.png

Leverage ratio of vol-targeted equity future position #

Leverage differences for equal volatility targets across markets have been modest, between 0.4 and 0.9.

xcatx = ["EQXRxLEV10_NSA"]
cidx = cids_exp

msp.view_ranges(
    dfd,
    xcats=xcatx,
    cids=cidx,
    sort_cids_by="mean",
    start=start_date,
    kind="bar",
    title="Means and standard deviations of equity index future leverage ratios, 10% annualized vol target, since 2000",
    xcat_labels=["Leverage ratios of vol-targeted equity future positions"],
    size=(16, 8),
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/e1a09c4037e2f6523a9b6027b236e1cda849c062f5555aca14e8feaf9454f028.png

Fluctuations across time have been more sizeable, with leverages ratios in many countries ranging from 0.2 to over 2.

xcatx = ["EQXRxLEV10_NSA"]
cidx = cids_exp

msp.view_timelines(
    dfd,
    xcats=xcatx,
    cids=cidx,
    start=start_date,
    title="Leverage ratios of vol-targeted equity index futures positions",
    title_adj=1.02,
    title_fontsize=27,
    title_xadj=0.5,
    cumsum=False,
    ncol=4,
    same_y=True,
    size=(12, 7),
    aspect=1.7,
    all_xticks=True,
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/210f35602847298995a091d4703b47dcda07a30e7420d08ffac1cec2fab1afa3.png

Importance #

Empirical Clues #

Historically, the correlation between realized equity volatility and subsequent quarterly index future returns has been positive.

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

cr = msp.CategoryRelations(
    dfd,
    xcats=xcatx,
    cids=cidx,
    freq="Q",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="2000-01-01",
)
cr.reg_scatter(
    title="Equity futures volatility and subsequent quarterly returns (global panel)",
    labels=False,
    coef_box="upper right",
    xlab="Historic equity futures return volatility (11-day half-life, end of quarter)",
    ylab="Equity index future return (next quarter)",
)
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/80db0831009d0de7ba68ad26fc6314c006d0efed1859232ac78c9c028b8dd49f.png

Countries and episodes with higher real interest rates typically coincided with higher equity volatility.

xcatx = ["RIR_NSA", "EQXRxEASD_NSA"]
cidx = cids_exp

cr = msp.CategoryRelations(
    dfd,
    xcats=xcatx,
    cids=cidx,
    freq="M",
    lag=0,
    xcat_aggs=["mean", "mean"],
    start="2000-01-01",
    years=3,
)
cr.reg_scatter(
    title="Short-term real interest rate and concurrent equity volatility, since 2000",
    labels=True,
    xlab="Real short-term interest rate",
    ylab="Equity index futures volatility, % ar",
)
RIR_NSA misses: ['DEM', 'ESP', 'FRF', 'HKD', 'ITL', 'NLG'].
https://macrosynergy.com/notebooks.build/themes/shock-and-risk-measures/_images/7b48f3aef1be8228b44281bfe1ebf4b4e21c7484a11e61e142b18e558483c121.png

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).