The average annualized return of local-currency index futures for 25 international markets has been 6% with a standard deviation of just under 20%. All markets recorded much fatter tails of returns than should be expected for normal distributions. Autocorrelation has predominantly been positive in the 2000s but decayed in the 2010s consistent with declining returns on trend following. Correlation of international equity returns across countries has been high, suggesting that global factors dominate performance, diversification is limited and country-specific views should best be implemented in form of relative positions. For smaller countries equity returns have mostly been positively correlated with FX returns, underscoring the power of international financial flows. Volatility targeting has been successful in reducing the fat tails of returns and in enhancing absolute performance. Relative volatility scaling is essential for setting up relative cross-market trades. The performance of relative positions has displayed multi-year trends in the past.
The post is based on proprietary research of Macrosynergy Partners and SRSV Ltd.
Scope of the empirical review
The subject matter of this research is returns on equity index futures. Index futures contracts commit buyers to purchasing the underlying index at a particular price at a specified date in the future. If on that future date the price of the index is higher than the agreed-upon price the buyer makes a profit. If the index is lower than the agreed price the buyer suffers a loss. Through index future contracts investors can take long or short positions in the underlying equity market. The futures do not stipulate delivery of the stocks in the index. Instead, they are settled daily on a “mark-to-market” basis. Counterparties pay losses or collect profits daily in cash. Market participants use daily settlement information to manage daily profit and loss, as well as to adjust margin levels with their clearing firms.
The theoretical price of an equity index future is calculated by adding to the spot price of the index the cost of carry of holding a long position in the constituent parts of the index. That cost of carry is roughly the difference between the relevant funding interest rate and the expected dividend yield. The actual futures price will not necessarily trade at the theoretical price, and is ultimately determined by demand and supply. Note that equity futures contracts exclude expected dividends over the life of the contract from the futures price because one would not receive these if one bought the index on the future date.
Here we look at liquid equity index futures for 25 international markets, both developed and emerging. Futures positions represent equity exposure in local currency term, not in USD terms, as would be the case with many ETFs. The list of the 25 equity indices can be found in the annex at the end of this post. Labels in the charts below use currency symbols related to the local indices.
Equity index return distribution
Monthly equity index returns across all 25 countries have averaged 0.5% ,with a standard deviation of 5.6% across countries. The average Sharpe ratio has been 0.3 The largest return variations (more than 7%) were recorded for the emerging markets of Brazil, China A-shares and Turkey, the lowest (4% or less) for the mature markets of Australia and Canada. On average the skew of returns has been negative and has been particularly pronounced for developed and lower-volatility markets. Returns have been balanced or even positively skewed for the higher-volatility Emerging Markets. India’s CNX Nifty has produced the largest positive (27.9%) monthly return, whereas Thailand has produced the largest monthly drawdown (-30%).
All equity index futures have posted positive long-term returns, as far as meaningful data are available for this study. The pattern for most countries has been similar: a secular upward drift with at least two pronounced crisis setbacks. The cumulative long-term local currency return has been highest in India and Mexico (near 300% and 200% respectively) and lowest in Brazil and some European countries.
The heatmap of annual equity index returns illustrates that in times of pronounced global financial cycles country equity index futures offer rather limited diversification: they tend post positive and negative returns in the same years. However, there can also be years with significant shares of both positive and negative country performances, such as 2002, 2011, 2015 and 2016.
All countries except Poland (short history) have displayed a fat-tailed distribution of monthly equity index future returns. On a panel basis monthly returns in an inner range of -3% to +5% and those outside a wide +/- 15% band have been overrepresented relative to a normal distribution.
Daily returns have displayed much fatter tails than monthly returns. The below quantile-quantile plot shows that for all countries the outliers on both the negative and positive sides have recorded more extreme values than should be expected in a normal distribution. On a panel basis daily returns inside the +/-1.5% range and outside the +/-7% range have been overrepresented.
Autocorrelation and cross-correlation of returns
Monthly returns have been predominantly positively autocorrelated in the first order and for the overall sample period, i.e. there has been a tendency of returns in adjacent months to deviate from mean in the same direction. However, the positive autocorrelation coefficient has been significant only for 5 countries. More importantly, positive autocorrelation was mainly a phenomenon of the 2000s and did not prevail in the 2010s, coinciding with the declining success of trend following.
Monthly equity index future returns are much more correlated across countries than currency and fixed income returns. All markets have been positively correlated with all other markets. Many developed market pairs posted correlation coefficients of over 80%, within the euro area even over 90%. This plausibly reflects that local shares are effectively a payout from global business activity and that differentiation comes mainly from global financial conditions that also have large communal global factors. The consequence of high correlation for trading are:  country-specific factors should always be expressed through hedged or relative trades, even over short horizons, since the global equity “factor” usually dominates the PnL,  the border between relative and hedged positions is blurred due to high “beta” of almost all markets and  precision of calibration of relative trades is particularly important.
The correlation between monthly equity and local-currency FX forward returns for smaller markets (ex U.S., euro area, and China) has been positive, but not uniformly so. For most smaller (non-U.S./euro area/China) countries FX-equity correlation has been positive on average, between 30 and 60%, possibly because both currencies and stocks benefit from international funding. This means currencies and equity markets had a slight tendency to perform in the same direction. However, for Japan, Switzerland and the UK the correlation has been negative, presumably because the JPY is a funding currency that tends to appreciate in equity drawdowns. Across decades, correlation between FX and equity returns was more clearly positive in the 2000s, probably reflecting pronounced fluctuations in USD funding conditions.
The principal purpose of volatility targeting is to scale positions such that the expected variation of their PnL accords with a target. The aim is to keep the actual volatility close to that target. Here, we consider 10% annualized volatility-targeting based on monthly rebalancing. Volatility is predicted by the annualized realized standard deviations of an exponential lookback window of returns with 11-days half-time.
Realized volatility has indeed fluctuated greatly across time. For most markets it averaged between 10% and 25%. On the low end it could slip below 10%. On the high end, outliers soared to a 60-90% range. Correlation of realized volatility has generally been strongly positive across markets.
To assess the potential benefits of volatility targeting of equity index future positions we compare actively targeted positions with those that are sluggishly calibrated by using a 3-year half-time exponential average. The below charts illustrate that the latter calibration is very smooth over time and only accounts for secular drifts in volatility.
Successful volatility targeting should keep actively targeted returns closer to target than sluggishly calibrated positions and reduce fat tails. Indeed, kurtosis (measure of fat tails) has been reduced through active targeting from 1.5 to 0.5. Successful volatility targeting should also make return variances more similar across sections. The max-min standard deviation ratio between the most and least volatile cross section has been lowered through active targeting, but not much from 1.6 to 1.5.
Vol-targeted positions have also a slightly different long-term performance profile that the sluggishly calibrated positions. For most countries the long-term absolute return of an actively vol-targeted position has been higher. The performance improvement seems to have come from both containment of drawdowns in crises (see Canada and the U.S.) and larger returns in lower-vol periods (India and China).
The case for relative volatility calibration
Plausibly, there should be both structural and temporary differences in equity index volatility. Structural differences could arise from the business of the underlying constituents and the local macro and political risks. Temporary differences could arise from local financial turbulences. Both should be partly predictable. If this is the case, relative trades between countries should be based on positions that adjust for expected volatility differences.
Here we calculated relative standard deviations for each market as ratio of the local standard deviation to the standard deviation of the S&P500. The two equally-weighted lookback windows have been exponential with 21-days and 24-months respectively to strike a plausible balance between structural and short-term factors.
Indeed, there is clear evidence of long-term differences in relative standard deviations. Thus, volatility in Brazil, China, India and Turkey has consistently been on above the S&P500. In Australia, Canada and the UK it has mostly been below.
Here, normalized returns are returns on positions scaled by relative (past) standard deviations. The below chart shows that return distribution has been a lot more similar for normalized positions than for outright position (see chart at top of the post). Indeed, the ratio of largest to smallest cross-sectional standard deviation drops from 2.2 to 1.3.
Differences in distribution across relative returns have been modest across primary markets. The difference between largest and smallest mean return has been 0.4 standard deviations. The ratio between most and least volatile market has been 2. Note that, for example, a relative position with China A-shares as primary leg is naturally more volatile than one with the S&P500, since the latter is more closely aligned with global (basket) trends. Put simply, the range of idiosyncratic fluctuations naturally varies across markets.
Since 2000 the best relative performance would have been delivered by primary longs in India, Mexico and Malaysia and primary shorts in Brazil, Japan and the Netherlands.
Importantly, relative performance of equity index futures has on numerous occasions displayed multi-year trends, probably reflecting the power of medium-term macro factors. For example, the long-term relative performance of the S&P500 since 2000 can be summarized in just two trends: underperformance in the 2000s and similar outperformance in the 2010s.
Annex: The 25 markets of the empirical analysis
Futures contracts have been chosen for the following local indices (alphabetically by currency symbol):
AUD: Australian Stock Exchange (ASX) 200 or ASX 200 (200 constituents as of August 2018).
BRL: Brazil Bovespa (67 constituents).
CAD: Toronto Stock Exchange 60 Index (60 constituents).
CHF: Swiss Market or SMI (20 constituents).
CNH: Hang Seng China Enterprises (50 constituents, “H-shares”, actually quoted in HKD).
CNY: Shanghai Shenzhen CSI 300 (300 constituents, “A-shares”).
DEM: Germany DAX 30 Performance/ Xetra (30 constituents, actually quoted in EUR).
ESP: Spain IBEX 35 (35 constituents, actually quoted in EUR).
FRF: France CAC 40 (40 constituents, actually quoted in EUR).
GBP: UK FTSE 100 (101 constituents).
INR: India CNX Nifty (50 constituents).
ITL: Italy FTSE MIB Index (40 constituents).
JPY: Nikkei 225 Stock Average (225 constituents).
KRW: Korea Stock Exchange KOSPI 200 (201 constituents).
MXN: Mexico IPC (35 constituents).
MYR: FTSE Bursa Malaysia KLCI (30 constituents).
NLG: Netherlands AEX Index (25 constituents, actually quoted in EUR).
PLN: Warsaw General Index 20 (20 constituents).
SEK: OMX Stockholm 30 (30 constituents).
SGD: MSCI Singapore Free (25 constituents).
THB: Bangkok SET 50 (50 constituents).
TRY: Turkey Bist National 30 (30 constituents).
TWD: MSCI Taiwan (89 constituents).
USD: Standard and Poor’s 500 Composite (500 constituents).
ZAR: South africa FTSE / JSE Top 40 (42 constituents).
Return data for most countries start in 2000-2002, with the following exceptions, due mostly to limited availability: Poland has only been considered from 2014. China A-shares have been considered from 2011. Thailand has been considered from 2007, Sweden and Turkey from 2006, China H-shares from 2005, India and Singapore from 2003.