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Macro factors of the risk-parity trade

Risk-parity positioning in equity and (fixed income) duration has been a popular and successful investment strategy in past decades. However, part of that success is owed to a supportive macro environment, with accommodative refinancing conditions and slow, disinflationary, or even deflationary economies. Financial and economic shocks, as opposed to inflation shocks, dominated markets, leading to a negative equity-duration correlation. The macro environment is changeable, however, and a strong theoretical case can be made for managing risk-parity strategies based on economic trends and risk-adjusted carry. We propose simple strategies based on macro-quantamental indicators of economic overheating. Overheating scores have been strongly correlated with risk parity performance and macro-based management would have even benefited risk parity performance even during the past two “golden decades” of risk parity.

The below post is based on proprietary research of Macrosynergy. 

A Jupyter notebook for audit and replication of the research results can be downloaded here. The notebook operation requires access to J.P. Morgan DataQuery to download data from JPMaQS, a premium service of quantamental indicators. J.P. Morgan offers free trials for institutional clients.

The post ties in with the SRSV summary on implicit market subsidies.

Understanding the equity-duration risk parity trade

Risk-parity means equal exposure to different investment positions in terms of risk metrics, such as expected return volatility. Risk-parity equity-duration positions refer to equal exposure to broad equity risk, for example through an equity index futures contract, and to duration risk, for example through a fixed receiver position in an interest rate swap (IRS). These types of positions are also called “long-long” and have delivered formidable risk-adjusted returns since the turn of the century (view section below).

There have been three major forces behind the popularity and success of the equity-duration risk-parity trade: undiversifiable risk premia, generous funding by central banks, and great diversification benefits from predominant negative return correlations between equity and duration exposure (view post here).

  • Both equity and longer-maturity duration exposure typically pay risk premia since the market cannot diversify away corporate earnings risk and the dangers of inflation and interest rate shocks, given that governments and non-financial corporates are the main obligors in bond markets.
  • In the 2000s and 2010s, refinancing conditions were very accommodative, with negative and fairly stable real interest rates across the developed world. This increased carry and made it cheaper for leveraged investors to extract risk premia from equity and fixed-income term exposure.
  • In the 2000s and 2010s, the correlation between equity and duration returns has predominantly been negative. In an environment of low inflation and real interest rates financial and growth shocks dominate inflation shocks, and the former drive returns in different directions (view post here). For example, a positive growth shock pushes equity prices up but high-grade bond prices down. A negative equity-duration correlation means that volatility-adjusted carry and returns on risk parity conditions are elevated.

Importantly, neither risk premia nor the relevant macroeconomic conditions are structural and stable. A strong case can be made for tracking both through proper quantamental indicators and managing risk parity exposure in accordance.

20-year performance of the equity-duration risk parity trade

We calculate simple equity-duration positions for all eight major developed market currency areas.  The currency areas are in alphabetical order: AUD (Australian dollar), CAD (Canadian dollar), CHF (Swiss franc), EUR (euro), GBP (British pound), JPY (Japanese yen), SEK (Swedish krona) and USD (U.S. dollar).

An equity position is taken in the main equity index future, recalibrated at the beginning of each month to observe an annualized volatility target of 10% annualized. A duration position is taken as a 5-year fixed receiver in the local-currency interest rate swap market, again recalibrated at the beginning of reach to pursue an annualized volatility target of 10% of the allocated risk capital. Then the composite risk-parity position is again volatility targeted to 10%. In all cases, positions are scaled to the volatility target based on the historic standard deviation for an exponential moving average with a half-time of 11 days.

Across currency areas, total cumulative returns (non-compounding) have been between 100% and almost 300%. A simple equally weighted “constant long-long” portfolio of risk parity long-long positions across all eight developed countries since 2002 would have earned an average Sharpe ratio of 0.8-0.9 and a Sortino ratio of 1.2, with a 36% correlation with the S&P500.

The relation between the economy and long-long returns

In a nutshell, there are three prominent perils for constant long-long risk parity positions that caution against perpetual constant exposure:

  • Risk premia paid by the calibrated positions can be eroded, which would be indicated by low earnings yields and duration premia.
  • Funding conditions can deteriorate, which would typically happen in association with overheating economies, rising inflation, and tightening monetary conditions.
  • The correlation between equity and duration exposure can turn positive. This would slash diversification benefits and might even become a new structural feature as was the case from the 1970s to the mid-1990s. A structural correlation shift could happen in association with a more inflationary environment and more alert central banks when shocks to inflation push equity and bond prices in the same direction. A positive correlation means much higher risk metrics per notional.

Since both funding costs and the correlation between the inflationary environment, metrics of overheating and inflation are plausible indicators of the macro conditions of risk-parity trades. Empirically there has been a strong negative correlation (of more than 40%) between a simple composite overheating score, based on growth, labour market conditions, inflation and credit growth (explained below) and concurrent equity duration returns over the past 20 years across all major developed markets.

Quantamental macro factors

Economic performance trends

As indicators of economic overheating or underperformance are of critical importance, we consider four types that typically matter for monetary conditions and the balance of risk of macro development: economic growth versus a normal rate, unemployment and employment growth versus neutral levels, core inflation trends versus effective target, and price credit growth versus estimated medium-term GDP growth.

Data are taken from the JPMorgan Macrosynergy Quantamental System (JPMaQS). JPMaQS indicators use for each point in time the actual or approximate latest time series that the market could have observed at that time. This means that the data consider release dates and revisions and do so consistently across a range of currency areas. These economic “information states” are suitable for backtesting and for assessing the predictive power on publicly available macro information. View further information here (with J.P. Morgan credentials) or a shortened summary here (no credentials required).

Excess economic growth trends

This quantamental indicator uses real-time information in the latest estimable GDP growth trend (% over a year ago, 3-month moving average) based on actual national accounts and monthly activity data, based on sets of regressions that replicate conventional charting methods in markets (view detailed notes here). The excess growth trend subtracts the previous five-year moving average of published GDP growth rates, based on national accounts, as a rough estimate of what people may people consider as “normal” or a long-term growth trend.

Positive excess growth has been modest over the past 20 years and concentrated on the recoveries that followed the financial crisis and the COVID pandemic. In all developed countries economic growth has on average underperformed its trailing moving average over the sample period.

Labour market tightness

This indicator is a composite of real-time information on two labour market indicators:

  • The difference between a 5-year moving average and the latest value of the unemployment rate (seasonally adjusted, 3-month average) is a measure of labour market state relative to what one might consider as normal. See documentation of this quantamental indicator here.
  • Employment growth (% over a year ago, 3-month moving average) minus an approximate workforce growth is a measure of labour market tightening. See documentation here.

Both metrics are z-scored on a panel basis to a maximum value of 2.5 standard deviations and out-of-sample, so they can be added up to a composite measure.

The composite labour market tightness score shows pronounced cyclical fluctuations and little short-term volatility when compared to standard output-based business cycles or overheating indicators.

Excess inflation

As inflation trend, we use for each day the real-time information on the latest headline consumer price index values, seasonally- and jump-adjusted % of the latest 6 months over the previous 6 months at an annualized rate. Jump-adjustment means that CPI data are adjusted for large spikes and one-off jumps. Both seasonal and jump adjustment factors are sequentially re-estimated always based on concurrent data vintages. This inflation metric is one of the most reliable real-time price indicators. See the documentation of the full methodology here.

Excess inflation refers to the above inflation trend minus an effective inflation target. The effective inflation target is the estimated official inflation target plus an adjustment for past “target misses”. This adjustment is the last 3 years’ average gap between actual inflation and the estimated official target mean. See the documentation here.

Excess inflation has been more volatile than output- and labour market-based overheating indicators. For most countries, core inflation indicators (excluding food and energy) may actually be more indicative of sustained consumer price trends.

Excess private credit growth

Credit growth here means real-time information on private bank credit at the end of the latest reported month, % change over a year ago, seasonal and jump-adjusted. See the documentation here. Excess price growth subtracts an estimate of medium-term nominal GDP growth, based on the last 5-year’s real GDP performance and the effective inflation target of the currency area.

Excess private credit growth has been far more idiosyncratic and diverse across currency areas than other overheating indicators, reflecting both cyclical and structural influences.

Composite excess macro trend score

A composite overheating score is calculated in a most simple (not optimized) way: all four sectoral overheating metrics are z-scored (standardized by out-of-sample panel standard deviations) around their natural zero values and with a cap of 2.5. Then they are just averaged. There is no claim that this is the best way to aggregate overheating performance, but the method’s simplicity makes it suitable for a proof of concept, i.e. a test if a simple overheating score has predicted equity-duration risk-parity returns.

The composite overheating score is a slow-moving indicator that is clearly associated with the cyclical state of developed economies. It is positively correlated across all eight countries, albeit the timing and amplitudes of fluctuations of economic trends have been different.

Equity-duration risk parity carry

The basis for carry calculation is risk-parity equity duration positions that are calibrated in the same as those underlying the target returns and there we explained above. Both the equity index future and IRS fixed receiver legs are equalized in terms of expected volatility and the overall position is calibrated to a 10% annualized volatility target. The carry values for both legs of the position are taken from JPMaQS and the documentation can be found here and here. We further define access carry as carry for a 10% vol position minus 2%, as a minimum requirement for carry with such volatility to look attractive.

The carry metrics reflect secular trends, medium-term cycles and ample short-term volatility, in accordance with the plausible drivers of such carry: funding conditions, economic performance and short-term return volatility and correlation.

Managed equity-duration risk-parity strategies

Two value checks

Based on sample periods of 2002 or 2004 to 2022 (October) and for all eight developed markets we test two basic propositions:

  • A simple composite overheating score predicts returns of equity-duration risk parity positions and can be used to manage the standard “constant long-long” exposure (“macro trends overlay”).
  • A combination of equity-duration carry and composite overheating score serves as long-short signal for equity-duration risk parity exposure.

Macro trends overlay

We first test the correlation between monthly overheating scores and subsequent monthly risk-parity returns. If markets are not fully information efficient, excess growth, inflation and so forth should herald low or negative long-long returns. Indeed, overheating has been significantly and negatively related to subsequent risk-parity returns, in the overall panel, in each and every country, and across decades (see chart below).

As a trading signal, overheating scores do not conceptually imply a long bias for risk-parity positions. Indeed, over the past 20 years, they implied a small short bias. Hence, on its own, the overheating score would not have been suitable for extracting the equity and term risk premia. Still, it delivered 52.9% accuracy (ratio of correctly predicted monthly return directions) and 53.5% balanced accuracy (average of the ratios of correctly detected positive returns and correctly detected negative returns). This means that the overheating score has meaningfully helped predict market direction.

We calculate naïve PnLs based on the following assumptions. First, positions are taken based on z-scores of the overheating score. The z-scores are winsorized at 2 standard deviations to mitigate data outliers and to avoid excessive risk-taking in any single market or period. Second, positions are rebalanced monthly with a one-day slippage for trading. And third, the long-term volatility of the PnL for positions across all currency areas has been set to 10%. These are standard procedures that we have been using in previously published proof-of-concept analyses. Note that this PnL is called “naïve” because it does not consider transaction costs and realistic risk management rules.

Value generation of the overheating score has naturally focussed on periods when the economy was significantly overheating or underperforming, such as the great financial crisis and the COVID pandemic (see chart below). Notwithstanding its pronounced seasonality, the overheating-based PnL has produced roughly the same Sharpe ratio (0.9) as the constant long-long portfolio, but without any long bias and without any correlation to market benchmarks.

To test the proposition of a “macro overlay” of the long-long portfolio we set the normal position value for each country to 1 and then subtract the overheating z-score. This means that in the absence of significant excess macro trends positions will be equal to the constant long-long, in case of overheating scores in excess of 1 standard deviation positions will be negative, and in case of negative overheating scores, positions will be larger than for the standard long-long.

The monthly accuracy of the macro overlay signal has been near 60% and even the balanced accuracy, which is not affected by the long bias, has been above 55%. Furthermore, accuracies have been above 50% in all countries and only the balanced accuracy in Canada has been slightly below that threshold.

The Sharpe ratio of the managed long-long portfolio has been 1.4 since 2002 with 26% correlation to the S&P500 return, compared to 0.9 and 36% for the constant long-long. Such outperformance is significant, albeit – naturally – focussed on periods where actual economic overheating occurred.

Carry-overheating strategy

The long bias of the managed equity-duration parity strategy described above was set arbitrarily to a unit standard deviation of the overlay signal. This simply equalized the influence of the long bias and the influence of the overheating z-score. The underlying assumption is that risk premia are approximately stable.

However, one can use the carry on risk-parity positions to assess the fluctuations in risk premia. Since the purpose of the long bias is to extract risk premia and since these premia are often related to carry an alternative is to manage that long bias through excess carry on the risk-parity position as explained above. Here we simply average a carry z-score and the negative of the overheating z-score. As before, this is the simplest aggregation, not the most plausible or optimized one. High carry and negative economic trends give strong positive position signals, low or negative carry with overheating signs give negative position signals.

As expected the carry-overheating score has been positively correlated to subsequent monthly equity-duration risk parity returns and a little more strongly so than the overheating signal alone.

Balanced accuracy of hitting the right direction of subsequent monthly returns has been almost exactly the same as for the overheating-managed long-long signal.

Also, naïve PnL performance of the overheating-carry signal has been quite similar to the managed long-long with a slightly lower Sharpe ratio (1.3) but less than half of the S%P correlation (16%).  Note that the sample period of the overheating-carry signal has been 2 years shorter, as quantamental equity carry signals have not been available for all countries prior to 2004.

The above empirical analysis relies on only two business cycles and, therefore, may not satisfy all empirical criteria. However, it does support basic common sense: risk-parity does not give positive returns unconditionally and is more likely to generate value if risk premia seem high and economies warrant monetary policy support.


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