Optimal Monetary and Fiscal Policies to Maximise Non-Parallel Risk Premia in Sovereign Bond Markets

Abstract

In this paper, we analysed several emerging market (EM) and developed market (DM) sovereign yield curves to identify the proportion of parallel and non-parallel shifts over time. We found that non-parallel shifts are more prevalent in EM due to higher political and economic risks. Key drivers include systemic risk events like wars, debt distress, and pandemics. By backtesting a long butterfly strategy to extract non-parallel risk premia from June 2007 to March 2024, we observed that steeper slopes and greater curvature result in higher returns. We also quantified monetary and fiscal regimes to determine what types of policies are required to extract non-parallel risk premia from these sovereign yield curves. Our research suggests that countries with opposing monetary and fiscal policies possess higher return opportunities whilst countries with complementing policies require tactical butterfly strategies to optimise returns.

1. Introduction and Literature Review

The abandonment of the gold standard in the early 1970s marked a pivotal shift in global economic policy, with profound implications for monetary and fiscal policy, as well as bond markets. The gold standard tied a nation’s currency value directly to a specific amount of gold, effectively limiting the supply of money to the amount of gold reserves a country held. This system, initially meant to promote stability and prevent excessive inflation, eventually constrained governments during economic crises, as they could not freely expand the money supply.

The final abandonment of the gold standard occurred on 15 August 1971, when President Richard Nixon announced that the US would no longer convert dollars into gold for foreign governments. This decision effectively ended the Bretton Woods system and marked a complete transition to fiat currency systems globally. As described by Bordo (1984), abandoning the gold standard allowed countries to gain greater flexibility in monetary policy and economic management, which allowed for more responsive measures in economic downturns, for example. Inflation spikes were a concern, but impressive growth and productivity gains were assumed to offset these inflationary risks.

Freed from the gold standard, central banks gained greater control over monetary policy, primarily through interest rate adjustments and open market operations. In a fiat currency system, central banks can create new money or contract the money supply as needed, without the constraint of gold reserves. See, for example, Autor (2021) and Cachanosky (2021). This change allowed policymakers to directly combat inflation and stimulate the economy in ways that had been impossible under the gold standard. The role of government spending as a fiscal policy tool also expanded, as governments could now run larger deficits without immediate concern for maintaining a gold reserve ratio. This flexibility provided a powerful tool to manage the business cycle, allowing for greater stimulus spending during recessions and more efficient control of inflationary pressures during expansions.

The effects of abandoning the gold standard on bond markets have been substantial. In a fiat currency system, inflationary expectations play a critical role in bond yields. When investors anticipate higher inflation due to expansive monetary or fiscal policies, bond yields typically rise as investors demand higher returns to offset the erosion of purchasing power. This relationship was particularly evident during periods of high inflation, such as the 1970s, when bond yields surged. Conversely, in periods of low inflation, as seen in recent decades, bond yields have been relatively low, even as governments have run large deficits.

Additionally, the removal of the gold standard has allowed central banks to use quantitative easing (QE) in recent years, by directly purchasing government bonds and other assets to lower interest rates and stimulate the economy. This policy would not have been feasible under a gold-backed system, as it relies on the ability to create money freely. QE has significantly impacted bond markets by keeping yields lower than they might otherwise be, encouraging investment and consumption by making borrowing cheaper. However, it also raises concerns about debt sustainability, as long-term reliance on QE could lead to inflationary pressures and reduce the value of bonds over time.

The fiat system therefore allows governments and central banks to respond to economic needs more fluidly, but the influence of inflationary expectations on bond yields means that bond markets are now closely tied to both fiscal discipline and monetary policy confidence; this leads to higher price volatility and creates opportunities across the yield curve in the form of risk premia. See, Cochrane (2017) and Cochrane and Piazzesi (2005).

Research by Nelson and Siegel (1987) and subsequent studies have shown that yield curve movements are not always parallel, meaning different parts of the yield curve can shift by different amounts. This phenomenon is often observed during periods of economic uncertainty or significant market events. Examples of such events are the 9/11 terrorist attacks, the 2008 financial crisis, and the COVID-19 pandemic. Other instances such as central bank intervention, and monetary and/or fiscal stimulus can also impact non-parallel shifts.

Ang and Piazzesi (2003) demonstrated that non-parallel yield curve shifts are more common during times of heightened uncertainty, as investors reassess their expectations about future economic conditions and risk premiums. Domestic macroeconomic factors, such as inflation and real activity, were found to be linked to yield curve levels and slopes, respectively. Liu et al. (2022) further confirmed this by using several economic variables in the Chinese bond market to identify early warning indicators of financial crisis. They found that the real effective exchange rate contributed most to the slope and curvature factors, as monetary policy would likely intervene to adjust short-term rates to appropriate levels. They also found that the M2 to M1 money supply ratio, which likely increased inflation expectations, contributed most to the level of long-term interest rates. Lu and Wu (2009) assessed the impact of economic factors on the US yield curve, they found that inflation-related shocks led to parallel curve shifts whilst output-related shocks (i.e., growth, capacity utilisation, retail sales, orders, spending, and inventories) generated a slope effect with greater sensitivity on short-dated yields. Positive output shocks resulted in curve flattening (improved productivity and lower risk premiums), whilst negative shocks led to steepening (deteriorating productivity and higher risk premiums). Liao et al. (2024) examine US bond returns from 1980 to 2022 and find that the trend in US debt holdings (debt held by the public) has strong predictability in outperforming US bonds (either short- or long-dated bonds, implying a slope effect). The trend in inflation demonstrated strong predictive power for both outperforming and underperforming US bonds across all maturities, which suggests the presence of a parallel effect.

Diebold and Li (2003) found evidence of significant non-parallel shifts in yield curves during periods of financial distress, indicating that market participants adjust their yield curve expectations differently across maturities in response to changing economic conditions. Diebold et al. (2007) build on Diebold and Li’s (2003) work by applying a dynamic Nelson–Siegel approach to yield curves in Japan, the UK, the US and Germany. Data from 1985 to 2005 were used, which correlated to the findings of Ang and Piazzesi (2003) in that global yield factors are linked to macroeconomic fundamentals (inflation and real activity), especially during the 1985 to 1995 sub-period. Across various countries and bond maturity periods, global factors contributed significantly to yield fluctuations (between a third and a half of the variation). The US market exhibited relatively lower dependence on these global factors but as bond maturity increased, the importance of global factors, especially inflation expectations, played a crucial role in pricing long-term bonds. Deguillaume et al. (2013) analyse data spanning almost 50 years from the US, Japan, the UK, and Switzerland, as well as UK Consol yields dating back to the 19th century. They find that rates behave differently depending on their ranges. When rates were below 1.5% or above 5%, the magnitude of changes were proportional to the level of rates with different sensitivity above 5% and displayed lognormal behaviour. When rates were between 1.5% and 5%, the magnitude of changes was independent of the level of rates; however, rates behaved in accordance with a normal distribution.

Studies by Adrian et al. (2015) and Kim and Orphanides (2005) suggest that periods of market volatility or risk-off sentiment are often characterised by non-parallel yield curve shifts. During such periods, investors may seek safe-haven assets, causing yields on certain maturities to decline more than others. This can result in steeper movements in certain parts of the curve compared to others, causing non-parallel shifts.

The research of D’Amico et al. (2014) indicates that non-parallel yield curve movements tend to be more pronounced during episodes of financial market stress, such as the global financial crisis of 2008 or sovereign debt crises. Their research focuses on the US TIPS (treasury insurance protection securities) curve and highlights how the US inflation risk premium changes during market stresses. Low or negative inflation risk premiums (low real yields) are experienced during market stresses and high inflation risk premiums (high real yields) during normal conditions. These inflation risk premiums are exaggerated at longer TIPS maturities given the heightened uncertainty and lower liquidity relative to US nominal treasuries.

Gürkaynak et al. (2005) argue that during times of heightened uncertainty, central bank actions and changes in market expectations can lead to asymmetric movements in different parts of the yield curve. The research suggests that non-parallel yield curve shifts, driven by the path factor, have a substantial impact on longer-term Treasury yields, showcasing the complexity of the relationship between monetary policy actions/statements and asset prices.

As described above, a non-parallel risk premium lends itself to a particular monetary and fiscal policy regime. Our research aims to identify which monetary and fiscal policy regimes are required to extract non-parallel risk premia from sovereign bond markets. Section 2 uses a principal component analysis (PCA) method to explain the proportion of parallel shifts across several emerging and developed sovereign bond markets. We describe what risk-off events coincide during an increased occurrence of non-parallel shifts. Section 3 analyses the types of yield curve behaviour (first, second, third, and interest rate cycles) for each sovereign bond market. Section 4 defines a long butterfly investment strategy to compare returns for the various sovereign bond markets. Section 5 quantifies monetary and fiscal policy in the selected markets and compares the types of policies to long butterfly returns. From our analysis, we conclude the type of butterfly strategy that is suitable for each monetary and fiscal policy regime.

Our paper uses three methodologies to convey our final analysis:

• the first methodology is provided in Section 2, where we describe a principal component analysis of sovereign yield curves, which highlights the extent of non-parallel curve shifts;
• the second methodology is provided in Section 4, where we define a long butterfly strategy on several EM and DM sovereign bond markets to determine suitable monetary and fiscal policy regimes for a profitable butterfly strategy;
• the third methodology is found in Section 5, which ranks and scores several monetary and fiscal indicators to confirm appropriate sovereign bond markets for profitable butterfly strategies.

2. Methodology and Risk-Off Events

In this section, we use principal component analysis on several emerging and developed sovereign bond curves to determine the proportion of non-parallel curve shifts, and analyse and identify reasons for the occurrences of non-parallel curve shifts.

The developed markets (DM) that we compare are the United States (US), United Kingdom (UK), Germany (GER), France (FRA), Canada (CAN), Italy (ITL), Japan (JPN), and Australia (AUS). The emerging markets (EM) that we analyse consist of South Africa (SA), Brazil (BRA), Turkey (TRL), Mexico (MEX), Poland (POL), Indonesia (IDR), India (IND), and China (CNY). We obtain generic sovereign yields (i.e., generic 3-month, 2-, 3-, 5-, 10-, 15-, and 30-year yields) for each sovereign curve. For some countries, generic yields did not exist for the above seed points so we linearly interpolated for those points. If no 30-year generic yield existed, we assumed the curve was flat from the previous closest generic point (i.e., the 15-year to 30-year yield curve is flat if the 15-year yield was the longest maturity) to reduce extrapolation error and extreme values. From this, we fitted a Nelson–Siegel–Svensson curve, adapted from Nelson and Siegel (1987), so that smooth approximations were created, and we could obtain yields for all points on the sovereign curve. The generic yield curve data were obtained from Bloomberg for all countries except SA as we were able to obtain a longer history from IRESS. Rebonato (2015) expands on the Diebold and Rudebusch (2013) dynamic Nelson–Siegel approach with stochastic, mean-reverting parameters providing statistical and no-arbitrage models. The dynamic Nelson–Siegel model identified and interpreted state variables relatively better than the Nelson–Siegel–Svensson model, but we preferred to use a simplified version of the Nelson–Siegel– Svensson model given that it is tractable without loss of generality.

Once we obtained smooth yield curves for all the EM and DM countries, we calculated the average yields for the 0–3 year, 3–7 year, 7–12 year, 12–20 year, and 20+ year maturity buckets. From this, monthly yield changes for each of the five maturity buckets were calculated such that each maturity bucket represented a fixed-income asset class. We then calculated a rolling one-year PCA by using the last 11-monthly yield curve changes for each maturity bucket. PCA is a fundamental technique in statistical analysis and machine learning used for dimensionality reduction. Abdi and Williams (2010) and Jolliffe and Cadima (2016) describe PCA as a statistical technique to transform a large set of correlated variables into a smaller set of uncorrelated variables called principal components, which capture the most significant variance in a dataset. PCA identifies patterns and relationships more discernibly, helps reduce noise, recognises key variables, and reduces overfitting risk.

PCA is applied to each of the smooth EM and DM sovereign yield changes using a rolling one-year period so that the variation explained by the first moment (known as duration or parallel shifts) can be determined. The remaining variations (second, third, fourth, and so on) are known as non-parallel shifts (e.g., slope, curvature, and other higher-order curve changes). We track the proportion of parallel and non-parallel shifts for each EM and DM sovereign yield curve and assess our findings.

Figure 1 and Figure 2 illustrate the proportion of EM and DM parallel curve shifts, respectively, with averages plotted in Figure 3. When the proportion of parallel shifts decreases below its long-term average of 90% it is likely that this was during a risk-off period.

A summary of the prominent global risk-off events is given below:

• 1991—Gulf war;
• 1992/3—End of the Cold War, splitting of Soviet states and the formation of the Euro;
• 1997/8—Asian financial crisis and Russian debt default;
• 2000—Dotcom bubble burst;
• 2001—9/11 attacks;
• 2008/9—Global Financial crisis;
• 2010/12—European Debt crisis;
• 2015—Greek debt default and systemic risk to other European nations;
• 2017—Brexit negotiations begin;
• 2019/20—COVID pandemic and supply chain disruptions;
• 2022/23—Ukraine/Russia conflict and cost of living crisis.

The prominent EM and DM idiosyncratic crises are described below with a more detailed summary provided in Appendix A:

(a)

Idiosyncratic events for emerging markets

• Indonesia (2006/07)—Commodity price volatility, natural disasters, and political instability;
• South Africa—End of Apartheid (1992), ANC political party winning majority 70% of national vote, Black Economic Empowerment, mishandling of HIV/AIDS (2003/04). Jacob Zuma elected as South African president after Arms deal and financial corruption charges were withdrawn (2009). Cyril Ramaphosa elected ANC leader and incoming South African president (2017);
• Mexico—Drug-rated violence (2010), Energy and telecom sector reforms (2014), political corruption scandals and instability, fiscal policy reforms, and NAFTA renegotiations (2016/17);
• India—Kargil conflict with Pakistan (2001), weak banking sector (2003), corruption scandals (e.g., Commonwealth Games) (2010), GST implemented and increased non-performing assets in banking sector (2018);
• China—Overheating housing market (2010), economic slowdown, US-China trade wars and increased industry regulation (2016–2018);
• Turkey—Political instability about government policies (2008), high inflation and government intervention (2010–2012), failed coup attempt and economic mismanagement (2015–2019);
• Brazil—Corruption scandals, economic slowdown, high inflation, political instability (2012–2014), political uncertainty from elections, corruption investigations, and economic mismanagement (2018);
• Poland—Leadership changes, new economic reforms, and EU ascension (2001–2006), slow growth prompted policy adjustments impacting the rule of law and causing economic disruptions (2010–2017).

(b)

Idiosyncratic events for developed markets

• France—Strikes and labour protests over pension reform (1998), yellow vest protests (2018–19), Eurozone debt crisis impacting bank sector (2010–2014);
• Germany—Reunification impacting fiscal policies (1997–1998), German banks under financial strain from global financial and Eurozone debt crises (2008–2014), Volkswagen emission scandal impacting corporate profits;
• Japan—Domestic banking sector crises (1993–1997), deflation and continued banking sector concerns (2000–03), Abenomic policies to stimulate growth (2014–2016);
• United Kingdom—Maastricht Treaty aimed at European integration and a unified currency (1993), BOE granted operational independence in 1997 impacting monetary policies and business confidence, pension fund deficits (1998–2001), austerity measures resulting in economic stagnation and double-dip recession fears (2010–2012), Scottish independence and Brexit uncertainty (2014–2015), 2019 elections, cost of living crisis and Brexit transitions (2018–2023);
• Canada—Economic policy adjustments, volatile currency and managing public debt (1999–2001), Energy exports suffered from strong currency (2004–2005), housing market bubble, fiscal austerity, and volatile commodity prices (2011), new government under Justin Trudeau and commodity price decline (2015), cost of living crisis, extreme weather and green energy transition (2021–2022);
• United States—President Clinton’s administration pushing for healthcare reforms following election victory over President Bush, high fiscal deficits (1991–1993), corporate scandals and LTCM failure affecting market confidence (1997–1998), 9/11 attacks and dotcom bubble (2000–2002), housing market collapse and banking failures (2008–2010), budgetary and fiscal concerns (2012), Obamacare and affordable healthcare act (2014), US-China trade tensions, Donald Trump’s victory at 2020 elections creating political uncertainty, supply chain disruptions (2019–2023);
• Australia—GST introduction and large spending for Sydney Olympics (2000), severe drought and housing affordability issues (2003–2005), severe natural disasters, reduced exports caused by Eurozone debt crisis and the introduction of a carbon tax (2011), frequent political changes, economic reforms and diversification away from resources (2013–2014), increased immigration, housing affordability and energy reliability concerns (2016–2017), COVID-19 pandemic induced recession and renewable energy debates;
• Italy—Corporate scandals, banking sector vulnerabilities, weak regulation and transition to Euro (2000–2002), high debt levels, contentious labour and pension reforms (2004–2005), severe recession and banking stress from global financial crisis, austerity and political stability (2008–2010), constitutional referendum and continued banking sector stress (2016), new government and EU budget disputes (2018), cost of living crisis, EU recovery fund assistance and fragmented government policies (2022–2023).

To classify the risk-off events, we followed non-asset market indices created by Baker et al. (2016), namely the economic policy uncertainty (EPU) index, a monetary policy uncertainty (MPU) index from Husted et al. (2017) that used Baker et al.’s methodology, a geopolitical risk (GPR) index developed by Caldara and Iacoviello (2022), and the IMF’s Financial Stress Index for several emerging and developed economies.

In constructing the US EPU index, Baker et al. (2016) count articles from ten major US newspapers containing specific terms.1 This method is adapted for other countries using analogous criteria. Due to the volume of newspapers and articles over time, monthly counts are scaled by each newspaper’s total article count for that month. Each newspaper series is adjusted to have a unit standard deviation for the period, and the average of these ten series is then normalised to a mean of 100 for that same period. This standardisation process is applied to each country’s series. The US EPU index exhibits significant spikes corresponding to major events likely to impact uncertainty, such as the Gulf wars, the US presidential elections, the 9/11 terrorist attacks, the 2008 stimulus debate, the Lehman Brothers bankruptcy, and TARP legislation. Additional peaks are observed during the 2011 US debt ceiling crisis and the 2012 “fiscal cliff” standoff.

For the MPU, Husted et al. (2017) apply the same text-based methodology of Baker et al. by referencing keywords2 from historical archives and newspapers. Having a narrower word search for the MPU isolates monetary policy events relative to economic events found in the EPU index. Husted et al. (2017) also show that declines in US output and inflation and tighter credit conditions coincide with increases in the US MPU index. The US MPU index showed notable spikes during key monetary events, such as the 2013 taper tantrum and just prior to the Federal Reserve’s 2015 interest rate “lift-off”. These spikes, aligned with Federal Open Market Committee (FOMC) decisions and reflect the index’s ability to capture both anticipated (ex ante) and actual (ex post) uncertainty around policy changes. The index also responded to significant macroeconomic events, like the 2003 Iraq invasion, highlighting its responsiveness to factors that influence monetary policy.

The GPR index developed by Caldara and Iacoviello (2022) measures adverse geopolitical events by quantifying newspaper coverage of geopolitical tensions and analysing its trends and economic impacts from 1900 onwards. The GPR index is derived from automated text searches within the digital archives of ten major newspapers, including The Chicago Tribune, The Daily Telegraph, Financial Times, The Globe and Mail, The Guardian, The Los Angeles Times, The New York Times, USA Today, The Wall Street Journal, and The Washington Post. Caldara and Iacoviello (2022) construct the index by calculating the monthly count of articles on adverse geopolitical events, expressed as a share of the total articles published. The search is organised across eight categories: War Threats, Peace Threats, Military Buildups, Nuclear Threats, Terror Threats, Beginning of War, Escalation of War, and Terror Acts.

Another risk classification index that we employ is the IMF’s Financial Stress Index (FSI) developed by Ahir et al. (2023) that also searches keywords to assess risk sentiment but analyses detailed reports from the Economist Intelligence Unit (EIU) instead of newspapers. The EIU uses an extensive network of experts located both in the field and at key global hubs. Country-specific experts prepare draft reports, drawing on input from field specialists, public sources, and in-house models. These drafts then undergo peer review, subediting, and data-quality checks to ensure standardisation and consistency across reports. This thorough process is designed to ensure transparency, accuracy, and reliability. The FSI was found to produce some false positives and true negatives (i.e., risk-off signals when none occurred and no signals when risk-off incidents did occur) which led to human intervention and search adjustments to improve the signal accuracy. The FSI measures financial stress in banking, equity, and exchange rate markets, covering various economies and often spikes during periods of market stress and risk aversion, making it a useful proxy for identifying risk-off conditions.

For guidance, a systemic risk-off event would cause a sell-off in asset classes and financial markets in its domestic market and a large proportion of other major markets. On the other hand, an idiosyncratic risk-off event would largely cause a negative event in its domestic market and possibly some negative spillovers into neighbouring markets. As developed economies have large asset bases and capital, reserve currencies and connected financial systems, risk-off events in these markets are likely to transform into systemic risk-off events, whilst risk-off events in emerging economies will likely be idiosyncratic if large DM capital is not at risk (if large DM capital is involved, an exodus will likely lead to global panic, forced selling, and increased systemic risk). Differentiating between systematic and idiosyncratic risk-off events can be subjective but, by using the above four risk indices (EPU, MPU, GPR, and FSI), we were able to provide some objectivity. If these global risk indices coincided with a spike above their long-term averages and a non-parallel shift occurred in a particular country, it provided an indication that a systemic risk-off event occurred during this period. If, for a country, we identified a period of non-parallel shifts but no elevated increase in the above risk indices, then we classified the risk-off event as idiosyncratic for that particular country.

Analysing the proportion of parallel curve shifts through time we notice the following:

• On average, parallel shifts account for 80–90% of DM sovereign curve variations and 70–90% of EM sovereign curve variations. DM in comparison to EM has a narrower dispersion of parallel curve shifts due to relatively lower inflation volatility. Lower, absolute inflation levels and inflation volatility are consequences of credible central bank and fiscal policies in keeping to primary mandates of price stability and secondary objectives of economic and employment growth;
• Table 1. Illustration of the 1st order PCA correlations (or relationship of parallel shifts) of the various EM and DM countries from 2009 as this is when all countries had congruent data. For the EM countries, we see the largest positive correlations exist between SA, IDR and IND, with the largest negative correlations existing between IDR and BRA, IND and BRA, and SA and CNY. Amongst DM countries, the highest positive correlations exist between GER, FRA, US and UK, and the lowest amongst JPN, CAN, and AUS.

  		EM								DM
  		IDR	SA	MEX	IND	CNY	TRL	BRA	PLN	FRA	GER	JPN	UK	CAN	US	AUS	ITL	EM	DM
  EM	IDR
  	SA	57%
  	MEX	−1%	26%
  	IND	62%	57%	34%
  	CNY	−1%	−29%	14%	20%
  	TRL	19%	−9%	−13%	12%	0%
  	BRA	−32%	−19%	−14%	−31%	−20%	−16%
  	PLN	−25%	4%	26%	−3%	−7%	−19%	5%
  DM	FRA	−4%	4%	−9%	−13%	11%	−23%	−6%	20%
  	GER	−30%	−23%	−1%	−20%	1%	1%	−22%	29%	62%
  	JPN	−1%	−20%	11%	−14%	6%	9%	−10%	18%	12%	17%
  	UK	14%	12%	−3%	0%	−9%	−24%	32%	25%	39%	10%	2%
  	CAN	19%	37%	35%	48%	−6%	−3%	−13%	16%	−3%	0%	−16%	11%
  	US	16%	24%	14%	10%	−10%	−29%	24%	31%	39%	12%	14%	84%	21%
  	AUS	−20%	7%	23%	8%	−11%	8%	24%	3%	−21%	−18%	−23%	15%	23%	0%
  	ITL	−22%	0%	17%	−11%	14%	−42%	6%	33%	48%	20%	7%	10%	−6%	32%	−13%
  	EM	55%	57%	52%	78%	26%	21%	−4%	28%	−5%	−21%	−1%	17%	41%	27%	13%	0%
  	DM	−9%	8%	25%	−1%	0%	−28%	13%	45%	64%	41%	38%	67%	26%	76%	21%	56%	18%

  shows the 1st order PCA correlations (or relationship of parallel shifts between two countries) of the various EM and DM countries from 2009 as this is when all countries had congruent data. We see that there is a slight +18% correlation between EM and DM, suggesting that parallel shifts in DM regions have some carryover to EM regions;
• If we look between the EM countries, we see the largest positive correlations exist between SA, IDR and IND, with the largest negative correlations existing between IDR and BRA, IND and BRA, and SA and CNY. A possible reason could be the resource-heavy SA economy that is dependent on CNY. A CNY slowdown will result in accommodative monetary policy and lower interest rates with increased fiscal risks in SA due to reduced exports to CNY. BRA has the least correlation with all EM regions (−4%) given its relatively low domestic debt compared to offshore debt resulting in a muted domestic yield curve. TRY has a −28% correlation to DM countries given its unorthodox economic and political policies. PLN has a +45% correlation to DM countries given its EU proximity;
• Amongst DM countries the highest positive correlations exist between GER, FRA, US and UK, and the lowest between JPN, CAN and AUS. For the most part, parallel shifts in DM regions occur in unison which could be because of their highly integrated economies and policy objectives. The US, UK, FRA, and ITL are the most synchronised given their large bond markets;
• Amongst EM and DM regions, the highest correlations are between CAN, SA, MEX and IND due to their commodity exports, UK and BRA, and US and PLN. The lowest correlations are between GER, IDR, SA, IND and BRA, US and TRY, IDR and AUS, and JPN and IND. Overall, concurrent parallel shifts between EM and DM regions are relatively distinct but can occur with leads or lags;
• Key characteristics of DM relative to EM are strong governance and institutions, stable politics, sound economic policies, reserve currency status, developed infrastructure, quality education and healthcare, innovation and technological advancements, open and competitive markets, social inclusion and equity, and a sustainable environment. EM countries can have vastly different characteristics. These are key characteristics cited by Khanna and Palepu (2010), Roberts et al. (2015), and the Investopedia Staff (2024).

During risk-off periods, we see an increase in non-parallel shifts due to increased volatility and investor uncertainty. Risk-off periods can be systematic or idiosyncratic.

Table A1. Summary of the calendar years of major idiosyncratic and systemic events of emerging markets where non-parallel shifts increased in frequency relative to their historic norms.

Emerging Market	Year	Idiosyncratic Risks	Systemic Risks
Indonesia	2006	Political uncertainty and corruption issues, such as scandals involving government officials.	Rising global commodity prices, particularly oil, creating inflationary pressures and tightening monetary policies globally.
	2007	Political instability due to regional conflicts and changes in regulatory frameworks affecting investment sentiment.	Early signs of global financial turmoil, increased volatility in capital flows.
	2011	Localised natural disasters impacting agriculture and infrastructure, such as earthquakes and volcanic eruptions.	Eurozone crisis impacting global markets.
	2018/19	Trade tensions with major partners, currency depreciation, and domestic political uncertainties ahead of elections.	Global trade wars, particularly between the US and China, and a slowing Chinese economy impacting global trade flows and market sentiment.
	2020	COVID-19 Response: Lockdowns, reduced consumer spending, and tourism decline.	Pandemic: Global economic shutdown, capital outflows, and recession.
	2021	Vaccination Rollout: Slow pace impacting recovery. Domestic Policies: Ongoing fiscal and monetary measures.	Pandemic: Continued impact and global supply chain issues.
	2022	Economic Recovery: Inflation pressures, balancing growth and stability. Pre-election uncertainties.	Global Inflation: Rising prices globally. Geopolitical: Ukraine–Russia conflict.
	2023	Political Dynamics: Approaching elections, structural reform challenges.	Global Economic Uncertainty: Slowdown risks, tightening financial conditions.
South Africa	1992	End of apartheid leading to significant political and economic restructuring and uncertainty.	Global recession and high global interest rates affecting emerging markets.
	1994	First South African democratic elections creating uncertainty and market volatility.	Emerging market crises affecting investor sentiment globally.
	2000	Political uncertainties, economic policy changes.	Dot-com bubble burst, global economic impact.
	2004	Political stability, economic reform measures.	Global economic recovery post-2001 recession but rising oil prices affecting emerging markets.
	2009	Domestic economic recovery efforts, Jacob Zuma elected president after Arms deal and financial corruption charges withdrawn.	Global financial crisis aftermath, global recession.
	2010	Labour strikes, particularly in the mining sector, and ongoing political instability.	Global economic recovery, European debt crisis.
	2017	Cyril Ramaphosa elected ANC leader and incoming South African president.	UK snap election and initiation of Brexit. Donald Trump elected US president.
	2021	COVID-19 vaccination efforts, civil unrest and riots, particularly in July, along with ongoing energy supply issues and political uncertainties.	Ongoing pandemic impact, global supply chain issues causing inflationary pressures.
	2022	High inflation, economic policy uncertainty, and concerns about government fiscal stability.	Global inflation, geopolitical tensions (Ukraine–Russia conflict), tightening global financial conditions.
Mexico	2010	Escalating drug-related violence, political uncertainty, and economic reforms.	Uneven global economic recovery, the European debt crisis, and volatility in commodity prices.
	2014	Reforms in energy and telecommunications sectors causing short-term uncertainties and adjustments.	Global oil price decline affecting revenues and economic stability, emerging market volatility.
	2016	Corruption scandals involving high-level government officials and political instability.	US election impact, heightened trade tensions, global economic uncertainty.
	2017	Impact of a significant earthquake, NAFTA renegotiation concerns affecting trade relations with the US and Canada.	Continued global trade tensions and vulnerabilities in emerging markets affecting investor sentiment.
	2020–22	The COVID-19 pandemic causing economic recession, health crises, and policy changes impacting business environments.	The global pandemic leading to economic shutdowns, supply chain disruptions, and geopolitical tensions affecting global markets.
India	2000/01	Slow economic reforms, political instability, and the Kargil conflict with Pakistan creating uncertainty.	The dot-com bubble burst leading to a global economic slowdown and market volatility.
	2003	Banking sector weaknesses and slow industrial growth impacting investor confidence.	Global economic recovery concerns and the impact of the SARS outbreak on markets.
	2006	High inflation, political corruption, and controversies such as the telecom scandal affecting market stability.	Rising global commodity prices and monetary tightening policies globally impacting markets.
	2010	High inflation, numerous corruption scandals (e.g., Commonwealth Games scam), and policy paralysis affecting economic growth.	The Eurozone crisis causing global market volatility and economic uncertainty.
	2018	Non-performing assets in the banking sector, political instability, and policy changes such as the implementation of GST.	Trade wars and global economic slowdown affecting markets and investment flows.
	2020–23	COVID-19 pandemic impact causing economic disruptions, health crises, and policy uncertainties.	The global pandemic leading to economic shutdowns, supply chain disruptions, rising inflation, and geopolitical tensions affecting global markets.
China	2007	Stock market bubble and subsequent crash, concerns about the overheating of the economy.	Global financial instability and the beginning of the global financial crisis impacting markets worldwide.
	2010	Housing market concerns, tightening of monetary policy to curb inflation, and regulatory crackdowns.	Global economic recovery uncertainty and the Eurozone crisis impacting global trade and investment flows.
	2016–18	Economic slowdown, trade war with the US leading to tariffs and trade barriers, and regulatory crackdowns on industries.	Global trade tensions (US and China), economic slowdown, and uncertainties affecting global markets.
	2020	COVID-19 impact, domestic lockdown measures.	Global COVID-19 pandemic, global recession.
	2023	Regulatory changes affecting technology and education sectors, geopolitical tensions with the US and other countries.	Global inflation, economic slowdown, and geopolitical tensions like the Ukraine-Russia conflict impacting markets.
Turkey	2008	Political instability, economic imbalances, and concerns about government policies.	The global financial crisis leading to economic downturns and market volatility worldwide.
	2010–12	High inflation, political instability, and concerns about government intervention in the economy.	The Eurozone crisis and global economic uncertainty impacting investor sentiment and capital flows.
	2015–19	Political instability, a failed coup attempt in 2016, economic mismanagement, and high inflation.	Global economic slowdown, regional geopolitical tensions, and emerging market vulnerabilities.
	2020–23	COVID-19 pandemic causing economic disruptions, high inflation, currency depreciation, and political instability.	The global pandemic causing economic shutdowns, supply chain disruptions, rising inflation, and geopolitical tensions affecting global markets.
Brazil	2012–14	Corruption scandals, economic slowdown, high inflation, and political instability affecting investor confidence.	Decline in global commodity prices impacting export revenues and economic stability.
	2018	Political uncertainty due to elections and corruption investigations, economic mismanagement.	Global trade tensions and vulnerabilities in emerging markets impacting investment flows.
	2020	COVID-19 pandemic causing severe economic recession, health crisis, and policy uncertainty.	The global pandemic leading to economic shutdowns and a severe global recession.
Poland	2001	Shifts in political leadership and new economic policies created uncertainty among investors.	The global economy slowed down following the dot-com bubble burst, impacting Poland’s economic growth.
	2002	Continued economic reforms and political instability led to market concerns.	The global economic environment remained unstable after the 9/11 attacks, affecting investor confidence.
	2004	Poland’s accession to the EU brought significant economic adjustments and policy changes, causing initial uncertainty.	Rising oil prices and geopolitical tensions affected global inflation and economic stability.
	2005	Ongoing political instability and uncertain economic policies created a volatile market environment.	Continued global economic concerns, including rising oil prices, influenced market sentiment.
	2006	Economic reforms and political instability continued to affect investor confidence.	A period of global economic growth driven by increased trade and investment influenced Poland’s economy positively.
	2009	The global financial crisis led to economic slowdown and necessary policy adjustments in Poland.	The aftermath of the global financial crisis and the European debt crisis created widespread economic instability.
	2010	Poland focused on policy adjustments to sustain economic growth amid a challenging environment.	The European debt crisis raised concerns about financial stability in the region.
	2011	Policy changes and political uncertainties influenced market dynamics.	The global economic environment slowed, with the Eurozone crisis impacting markets.
	2012	Poland faced economic slowdown and implemented policy responses to maintain growth.	Ongoing global economic uncertainty, particularly due to the Eurozone crisis, affected market sentiment.
	2014	Political changes and new economic policies created a challenging market environment.	The recovery from the European debt crisis and geopolitical tensions, notably in Ukraine, influenced market stability.
	2016–17	Political instability, judicial reforms causing concerns about the rule of law, and economic policy shifts.	Global economic slowdown, trade tensions, and uncertainties affecting emerging markets.
	2020	COVID-19 Pandemic Impact: The pandemic led to domestic lockdowns and significant economic disruptions.	The COVID-19 pandemic caused widespread economic disruptions and supply chain issues globally.
	2022	Poland faced challenges in economic recovery and inflation pressures.	Rising global inflation and geopolitical tensions, particularly the Ukraine–Russia conflict, caused market volatility.
	2024	Ongoing economic policy changes and political uncertainties affected market conditions.	A global economic slowdown and tightening financial conditions due to rising interest rates influenced markets.

and

Table A2. Summary of the calendar years of major idiosyncratic and systemic events of developed markets where non-parallel shifts increased in frequency relative to their historic norms.

Developed Market	Year	Idiosyncratic Risks	Systemic Risks
France	1998	Domestic political instability, strikes, and labour protests over pension reforms.	Asian financial crisis leading to global market volatility, Russian debt default impacting emerging markets.
	2000–01	Economic policy adjustments, domestic reforms creating uncertainty and an economic slowdown.	Dot-com bubble burst, causing significant declines in technology stocks and broader market turbulence. 9/11 attacks causing global shock, subsequent global economic slowdown.
	2009–10	Economic recession due to global financial crisis, domestic policy measures to combat downturn, pension reform protests leading to public unrest.	Global financial crisis aftermath, European debt crisis causing widespread economic instability.
	2014	Economic stagnation, high unemployment affecting consumer spending and business investments.	European recovery from debt crisis, geopolitical tensions influencing market sentiment.
	2018–19	Yellow vest protests, economic reforms creating domestic instability and market volatility.	Global economic slowdown, trade tensions between US and China impacting global trade.
	2021	COVID-19 recovery efforts, vaccination rollout challenges, policy adjustments.	Ongoing pandemic impact, global supply chain disruptions causing economic uncertainty.
Germany	1997–98	Domestic political and economic challenges, reunification impact on fiscal policies.	Asian financial crisis causing global economic instability, Russian debt default, LTCM crisis causing global market turbulence.
	2000–01	Economic slowdown, policy reforms impacting business confidence.	Dot-com bubble burst leading to significant declines in technology stocks. 9/11 attacks causing global economic shock and market volatility.
	2005	Political instability, economic reforms causing uncertainty in business environment.	Global economic uncertainty, rising oil prices impacting global inflation.
	2008–09	German banks faced significant challenges during the global financial crisis, leading to a domestic recession.	Global financial crisis causing severe economic downturn, European debt crisis causing widespread economic instability.
	2015	Volkswagen emissions scandal affecting corporate confidence, economic policy adjustments.	Global economic slowdown, Greek debt crisis impacting European financial stability.
	2019	Economic slowdown, manufacturing sector downturn impacting overall economic growth.	Global economic slowdown, trade tensions between US and China.
Japan	1993	Economic stagnation, banking sector issues leading to financial instability.	Global economic slowdown following Gulf War and oil price spike, affecting export-driven economies.
	1996–97	Banking crisis, domestic economic policies aimed at recovery.	Asian financial crisis causing regional economic instability.
	2000	Economic policy adjustments, banking sector restructuring affecting financial stability.	Dot-com bubble burst causing global market turbulence.
	2002–03	Deflation, continued banking sector problems leading to financial instability.	Global economic uncertainty, recovery from dot-com bubble burst. SARS outbreak impacting global economic activity.
	2006–07	Economic recovery, structural reforms improving domestic economic conditions. Political instability, economic policy concerns leading to market uncertainty.	Global economic boom driving increased trade and investment. Early signs of global financial turmoil, US subprime mortgage crisis beginning to unfold.
	2010–12	Economic stagnation, policy adjustments aimed at stimulating growth and combating deflation.	Global economic recovery, European debt crisis causing concerns about financial stability.
	2014–16	Abenomics, economic policy adjustments aimed at stimulating growth.	Global economic uncertainty, oil price volatility impacting global markets.
	2018–20	Trade tensions, economic slowdown due to global trade conflicts.	US-China trade war, global economic slowdown, COVID-19 pandemic causing significant market disruptions.
	2022–23	COVID-19 impact, supply chain issues leading to economic challenges, political stability concerns.	Global inflation, geopolitical tensions (Ukraine–Russia conflict) causing market volatility, tightening global financial conditions due to rising interest rates.
UK	1993	Maastricht Treaty aimed at European integration and a unified currency, welfare reforms, labour disputes in transport and public services sectors.	Global economic slowdown affecting domestic economy.
	1998–2001	Strong pound depressed UK exports specially manufacturing, BOE granted operational independence in 1997 impacting monetary policies and business confidence. Pension fund deficits, foot and month disease impacting agriculture and election uncertainty.	Asian financial crisis, Russian debt default, Dot-com bubble burst, 9/11 attacks causing global instability.
	2007	The onset of the global financial crisis hit UK banks hard, leading to economic policy challenges.	The global financial crisis began to spread globally, affecting the UK.
	2010–12	Economic recovery, austerity measures affecting public spending, economic stagnation and double-dip recession fears.	Global economic recovery, European debt crisis impacting financial stability and creating volatility.
	2014–15	Scottish independence referendum creating political uncertainty, economic policy concerns, Brexit uncertainties causing market instability.	European recovery, geopolitical tensions (Ukraine crisis) influencing market sentiment. Global economic slowdown, Greek debt crisis impacting European financial stability.
	2018–23	Brexit transitions, leadership concerns with Conservative Party, 2019 elections, cost of living crisis, economic policy adjustments creating uncertainty in business environment.	US-China trade war, global economic slowdown, COVID-19 pandemic, global inflation, geopolitical tensions.
Canada	1999–2001	Economic policy adjustments, volatile currency and managing public debt.	9/11 attacks, dot-com bubble burst, global economic slowdown causing market instability.
	2004–05	High dependence on the energy sector whilst manufacturing exports struggled from a strong currency.	Global economic uncertainty, rising oil prices impacting global inflation.
	2008	Economic recession due to global financial crisis, policy responses to combat downturn.	Global financial crisis causing widespread economic instability.
	2011	The European debt crisis affected global demand, impacting Canada’s export-driven economy. Housing market bubble, fiscal austerity, fluctuating commodity prices.	Global economic uncertainty, Eurozone crisis impacting global markets.
	2015	Commodity price decline affecting resource-dependent economy, diversifying into technology and manufacturing, new government under Justin Trudeau.	Global economic slowdown, oil price volatility impacting global markets.
	2021–22	COVID-19 recovery efforts, vaccination rollout challenges impacting economic recovery, inflation pressures due to supply chain disruptions, extreme weather and green energy transition.	Ongoing pandemic impact, global supply chain disruptions causing economic uncertainty, geopolitical tensions (Ukraine–Russia conflict) causing market volatility.
US	1991–93	Economic recession, President Bush ousted by President Clinton, President Clinton’s administration pushing for healthcare reforms, high fiscal deficits.	Gulf War causing global economic uncertainty and slowdown.
	1997–98	LTCM crisis required federal intervention, policy adjustments aimed at controlling inflation. Corporate scandals affecting market confidence.	Asian financial crisis causing global market volatility. Russian debt default, LTCM crisis causing global market turbulence.
	2000–02	9/11 attacks, dot-com bubble burst causing recession and loose monetary and fiscal policies.	9/11 attacks, dot-com bubble burst causing significant declines in technology stocks.
	2008–10	The housing market collapse and banking sector failures led to a severe economic downturn.	Global financial crisis, European debt crisis impacting financial stability.
	2012	Political changes, concerns over budgetary and fiscal issues created significant market uncertainty.	Global economic uncertainty, Eurozone crisis causing market volatility.
	2014	Obamacare, Affordable Care Act, widening income inequality.	Global economic recovery, geopolitical tensions (Ukraine crisis) influencing market sentiment.
	2019–23	Trade policy uncertainties between the US and China affecting business confidence, supply disruptions elevating inflation, political instability during 2020 elections following President Trump’s victory.	COVID-19, global economic slowdown, trade tensions between major economies, supply chain disruptions, geopolitical tensions (Ukraine–Russia conflict), tightening global financial conditions due to rising interest rates.
Australia	2000	GST introduction caused confusion, high spending for Sydney 2000 Olympics and long-term financial impact.	Dot-com bubble burst causing global market turbulence, Asian financial crisis effects.
	2003–05	Severe drought impacting agriculture and water supply, housing affordability issues given rising prices.	Global economic recovery driving increased trade and investment.
	2008	The global financial crisis led to significant challenges for Australian banks and a recession.	Global financial crisis causing widespread economic instability.
	2011	The European debt crisis affected global demand, impacting Australia’s export-driven economy. Severe natural disasters required significant government expenditure, introduction of carbon tax.	Global economic uncertainty, Eurozone crisis impacting global markets.
	2013–14	Frequent political changes, economic reforms to diversify economy away from resources, housing affordability challenges.	Global economic uncertainty and trade tensions impacting business confidence.
	2016–17	Housing affordability concerns and speculation, immigration growth increasing infrastructure and social costs, energy grid reliability.	Global economic uncertainty, oil price volatility impacting market stability, trade tensions between major economies.
	2019–21	Economic slowdown/recession due to global trade conflicts and COVID-19 pandemic, renewable energy debates.	Global economic slowdown, trade tensions, COVID-19 pandemic causing significant market disruptions.
Italy	2000–02	Several corporate scandals that undermined investor confidence. Banking sector vulnerabilities due to slow economic growth and weak regulatory oversight. Transition to Euro with new monetary and fiscal policy adjustments.	The aftermath of the dot-com bubble burst and the economic shock from the 9/11 attacks led to a global economic slowdown, affecting Italy’s export-driven economy.
	2004–05	Frequent changes in government and contentious labour and pension reforms, political instability, and high debt levels.	Rising oil prices and geopolitical tensions contributed to global inflationary pressures and economic uncertainty.
	2008–10	Italy faced a severe recession, significant stress in the banking sector from non-performing loans and declining asset values. High sovereign debt levels, austerity measures and political instability.	The global financial crisis led to widespread economic downturns, significantly impacting European economies, including Italy.
	2014	Prolonged economic stagnation and high unemployment rates eroded consumer confidence and domestic demand.	The slow recovery from the European debt crisis and geopolitical tensions, particularly the Ukraine crisis, influenced market sentiment.
	2016	Italy’s banking sector faced significant challenges, and political instability, highlighted by the constitutional referendum, created uncertainty.	The Brexit vote led to market volatility, and a global economic slowdown exacerbated uncertainties.
	2018	Sergio Mattarella taking presidency from Giorgio Napolitano, ongoing banking sector problems, budget disputes with EU as Italy wanted to increase spending and reduce taxes.	Trade conflicts (US and China), and a slowing European economy affected global and local markets.
	2022–23	Cost of living crisis, EU recovery fund assistance, fragmented government and unclear economic policies created an uncertain investment climate.	Rising global inflation and geopolitical conflicts, notably the Ukraine–Russia conflict, contributed to market volatility.

in Appendix A summarise the calendar years of major idiosyncratic and systemic events of each EM and DM, where non-parallel shifts increased in frequency.

In the modern age, world trade and financial systems are well integrated. Thus, economic risk-off events in major DM countries have a greater impact on other economies, specifically EM (e.g., the US global financial crisis, Eurozone debt crisis or unified currency, monetary/fiscal policy tightening or the US dotcom bubble). There are also instances such as natural disasters, contagious diseases, supply chain issues or wars that create systemic risk throughout the globe (e.g., Japanese earthquakes and tsunamis, Australian wildfires, US hurricanes, US-China trade tensions, Gulf, Russian–Ukraine or Middle East wars, HIV/AIDS or COVID-19 pandemic).

Reinhart and Rogoff (2009) who studied financial crises over the past 800 years conclude that financial crises are a persistent and recurring phenomenon throughout history. They argue that the same types of financial vulnerabilities and policy mistakes that led to past crises continue today. The authors cite typical warning signs such as rapid credit expansion, asset price bubbles, and rising debt levels as a precursor to financial crises. These crises have severe economic consequences including deep recessions, prolonged recoveries, and long-lasting effects on public debt and unemployment. They stress that the aftermath of crises often involves significant social and political upheaval. Reinhart and Rogoff (2009) recommend prudent fiscal policies, robust financial regulation, international co-operation to address financial vulnerabilities and transparent financial markets to reduce the fallout from financial crises.

Obstfeld (2012) concludes that financial globalisation has significantly increased the volume and volatility of cross-border capital flows, which enhances global growth and development, but also increases the risk of financial crises. Volatile current account balances reflect underlying structural issues that can spread across countries and regions given the interconnection of financial markets. Obstfeld (2012) advocates for macroprudential policies that can address systemic risks and the resilience of financial systems. These policies include measures to monitor and control credit growth, leverage, and other financial vulnerabilities.

During the above risk-off periods, we see an increased occurrence of non-parallel shifts on global yield curves due to amplified monetary and fiscal frameworks, and volatile risk premiums. Rakotondratsimba and Jaffal (2012) observe that the frequency of non-parallel shifts increased following the global financial crisis. Caldara and Iacoviello (2022) identify that heightened geopolitical risks tend to induce financial market volatility, create uncertainty, and delay investment decisions. Their custom geopolitical index reveals that geopolitical risk surged dramatically during both World Wars, remained high in the early 1980s, and has been rising since the start of the 21st century, thereby increasing the likelihood of future, negative macroeconomic events.

The IMF’s Global Financial Stability Report by Catalán et al. (2023) raises alarms about escalating geopolitical tensions among major nations. These tensions are expected to trigger a reversal of capital flows towards safer assets, leading to higher funding costs, decreased profitability, and elevated default risks. Emerging markets (especially small, open economies) are likely to be severely impacted. World Economic Forum (2024), based on a survey conducted in September 2023, revealed that 54% of respondents foresee instability and moderate global catastrophes within the next two years, and 63% anticipate a turbulent outlook for the next decade. Key risks include extreme weather events, AI-driven misinformation, social and political polarisation, cost-of-living crises, economic downturns, supply chain disruptions, and interstate armed conflict. Predicting these high-risk macroeconomic events is a formidable challenge. However, it is evident that they are rising in frequency and breadth due to rising geopolitical tensions between the East and West, uncoordinated monetary and fiscal policies (or modern monetary theory), mounting debt issuances and fiscal deficits, uncensored media and sensationalism, and a widening wealth inequality gap, leading to social unrest. These unpredictable trends are likely to persist, increasing the likelihood of non-parallel sovereign bond curve movements relative to their historical norms. Next, we analyse what EM and DM yield curve movements have been most prevalent throughout our historic period.

3. Yield Curve Behaviour

In this section, we compare the frequency of interest rate cycles, including 1st, 2nd, and 3rd order curve changes for emerging and developed markets from June 2007 to March 2024, these are shown in

Table 2. Summary of the frequency of interest rate cycles, including 1st, 2nd, and 3rd order curve changes for emerging markets from June 2007 to March 2024.

EM Scenarios	IDR	SA	MEX	IND	CNY	TRL	BRA	PLN
Rates Cycle
Hiking	34%	48%	44%	43%	17%	36%	48%	30%
Cutting	66%	52%	56%	57%	83%	64%	52%	70%
1st Order
Parallel Up	44%	51%	52%	47%	48%	48%	49%	47%
Parallel Down	56%	49%	48%	53%	52%	52%	51%	53%
2nd Order
Bull Steep	20%	12%	11%	20%	20%	14%	14%	15%
Bull Flat	23%	25%	25%	17%	19%	13%	27%	23%
Bear Steep	18%	25%	26%	14%	14%	13%	23%	19%
Bear Flat	15%	12%	15%	23%	16%	16%	15%	14%
Flat Twist	15%	15%	12%	12%	11%	24%	11%	16%
Steep Twist	7%	11%	10%	13%	19%	19%	9%	13%
3rd Order
Pos Convex	49%	54%	51%	55%	50%	49%	49%	50%
Neg Convex	51%	46%	49%	45%	50%	51%	51%	50%

and

Table 3. Summary of the frequency of interest rate cycles, including 1st, 2nd, and 3rd order curve changes for developed markets from June 2007 to March 2024.

DM Scenarios	FRA	GER	JPN	UK	CAN	US	AUS	ITL
Rates Cycle
Hike	21%	21%	8%	30%	58%	34%	31%	21%
Cut	79%	79%	92%	70%	42%	66%	69%	79%
1st Order
Parallel Up	46%	44%	44%	45%	50%	51%	46%	45%
Parallel Down	54%	56%	56%	55%	50%	49%	54%	55%
2nd Order
Bull Steep	12%	11%	6%	26%	12%	11%	15%	16%
Bull Flat	33%	30%	32%	22%	24%	28%	30%	30%
Bear Steep	24%	22%	22%	21%	25%	24%	19%	17%
Bear Flat	13%	11%	8%	19%	15%	15%	17%	17%
Flat Twist	9%	12%	17%	6%	9%	11%	11%	11%
Steep Twist	9%	13%	15%	4%	13%	10%	7%	8%
3rd Order
Pos Convex	52%	56%	55%	51%	51%	54%	52%	54%
Neg Convex	48%	44%	45%	49%	49%	46%	48%	46%

, respectively. EM countries have experienced more cutting cycles than hiking cycles over the period, with IDR, PLN and CNY experiencing the most accommodative interest rate cycle with cuts occurring 66%, 70% and 83% of the time, respectively. We define first, second, and third order curve changes according to Hariparsad and Maré (2023). First order changes, such as parallel up-and-down scenarios, affect the average yield level and are explained by a single point on the curve. Second order changes, such as steep/flat twists and bull/bear steepening/flattening focus on two points on the curve whilst third order changes, such as positive and negative twists compare three points on the curve. Looking at first order changes, there have been more parallel down shifts compared to parallel up shifts as inflation has drifted lower for most EM countries. Bull flattening and bear steepening have been the most common second order shifts for SA, MEX, BRA and POL. IDR, IND, and CNY have experienced more bull steepening. TRL experienced more flat and steep twists (24% and 19%, respectively), whilst IND realised more bull steepening and bear flattening (20% and 23%, respectively). Third order shifts are generally evenly split between positive and negative convexity, with SA and IND having slightly more positive than negative convexity shifts.

For DM countries there have been substantially more cutting cycles than hiking cycles over the period, with JPN experiencing accommodative policies 92% of the time, European nations between 70 and 79%, and the US and AUS at 66% and 69%, respectively. Canada has experienced more hiking than cutting cycles (58% vs. 42%). Looking at 1st order changes, parallel down shifts have been a common occurrence throughout the DM countries with the US and CAN being balanced between parallel up and down. Similar to EM, bull flattening and bear steepening have been the most common second order shifts with the UK undergoing more bull steepening. Positive convexity has been the common third order scenario amongst DM countries.

The key takeaway over the period is that inflation has drifted lower, resulting in a greater proportion of bullish interest rate scenarios for both emerging and developed markets. There have been several steepening and flattening occurrences so in the next section we quantify the effects of slope and curvature changes on a long butterfly return strategy.

4. Butterfly Strategy Analysis

In this section, we assess the return prospects of a long butterfly strategy on each of the EM and DM countries. A butterfly strategy consists of a short-, medium- and long-dated sovereign bond. The long butterfly strategy purchases the medium-dated sovereign bond and sells the short- and long-dated sovereign bonds in a duration and cash-neutral manner. As an example, a 2v5v10 long butterfly strategy would buy the 5-year bond and sell the 2-year and 10-year bonds in a duration and cash-neutral manner. The selling weights of the 2-year and 10-year bonds will be rebalanced and calculated each month to maintain the duration and cash neutrality to the long position in the 5-year bond. Being duration neutral allows the strategy to be immunised against parallel shifts but exposed to non-parallel shifts (such as slope and curvature changes). Cash neutrality is employed to allow for operational efficiency, so no cash surpluses/shortfalls are invested or borrowed. Trade costs are ignored for now as we want to determine the pure effects of slope and curvature changes on a long butterfly strategy. In reality, trade costs from rebalancing frequencies are an important consideration and must be managed to ensure a profitable butterfly strategy.

As we do not have the actual sovereign bonds, we use generic zero-coupon sovereign bonds with maturity sectors: 1–3 years, 3–7 years, 7–12 years, and 12+ years. Each of these maturity sectors contains an equally weighted amount of zero-coupon sovereign bonds, e.g., the 3–7 year maturity bucket will contain equal amounts of the 4-,5-,6-, and 7-year zero-coupon sovereign bonds. Each month we assume new zero-coupon sovereign bonds are issued. The long butterfly strategy purchases the 3–7 year maturity bucket, and sells the 1–3 year and 7–12 year maturity buckets in a cash and duration neutral manner. This mimics a 2v5v10 long butterfly that purchases the 5-year bond and sells the 2-year and 10-year bonds (cash and duration neutral). We opted to use the maturity buckets rather than individual sovereign bonds to eliminate concentration risk by diversifying amongst several sovereign bonds. The maturity bucket (diversified) approach is much stricter than the individual (concentrated) approach, so if positive returns emerge, we have greater confidence that the long butterfly strategy is profitable.

The long butterfly strategy invests in the maturity buckets (cash and duration neutral) at the beginning of the month and closes the positions at month-end. New maturity buckets are invested at the beginning of the following month and closed at month-end. This monthly rebalancing process is continued from June 2007 to March 2024 with zero trade costs assumed so that we can determine the strategy’s effectiveness for each country.

Table 4. Summary of the performance statistics of the EM long butterfly strategy from June 2007 to March 2024. SA has the highest returns due to its steep slope, whilst TRY has the lowest returns from an inverted/flat slope.

EM Long Butterfly	IDR	SA	MEX	IND	CNY	TRL	BRA	PLN
Index (Start = 100)	100.82	106.14	100.16	102.77	102.11	92.44	101.65	100.71
Tot Ret (pa)	0.05%	0.36%	0.01%	0.16%	0.12%	−0.47%	0.10%	0.04%
Ret SD (pa)	1.2%	1.4%	1.3%	1.1%	1.3%	4.6%	2.5%	1.4%
Avg Spread Dur	4.1	4.1	4.2	4.1	4.6	3.6	3.8	4.5
Spread Vol (pa)	39%	48%	48%	38%	57%	161%	54%	59%

and

Table 5. Summary of the performance statistics of the DM long butterfly strategy from June 2007 to March 2024. ITL has the highest returns due to a relatively steep slope, followed by the US and GER, whilst JPN has zero returns due to a flat slope and low volatility.

DM Long Butterfly	FRA	GER	JPN	UK	CAN	US	AUS	ITL
Index (Start = 100)	102.72	103.26	99.99	102.37	101.75	103.21	101.71	104.94
Tot Ret (pa)	0.16%	0.19%	0.00%	0.14%	0.10%	0.19%	0.10%	0.29%
Ret SD (pa)	0.8%	1.0%	0.3%	0.4%	0.7%	1.1%	0.8%	1.2%
Avg Spread Dur	4.8	4.8	5.0	4.7	4.7	4.7	4.6	4.7
Spread Vol (pa)	21%	31%	8%	7%	20%	36%	26%	29%

highlight the performance statistics of the EM and DM long butterfly strategies. Amongst the EM countries, SA has the highest performance at 0.36% p.a. followed by IND, CNY and BRA at 0.16%, 0.12%, and 0.1% p.a. TRL is the underperformer at −0.47% p.a., given its volatile yield environment. Out of the DM countries, ITL is the outperformer at 0.29% p.a., followed by the US, GER, FRA, and UK between 0.14% and 0.19%. JPN has zero performance, given its relatively flat yield curve and low yield volatility market. To understand the performance of these long butterfly strategies, we will compare the long butterfly returns to the level of slope/curvature and the volatility of slope/curvature. The slope is defined as the 7–12 year yield less the 1–3 year yield, and the curvature is defined as the 3–7 year yield less the average of the 1–3 year yield and 7–12 year yield.

Figure 4 and Figure 5 show the average EM and DM slope level, curvature level, slope volatility and curvature volatility relative to the long butterfly returns, respectively (we will refer to long butterfly returns as returns for ease of reference). There is a positive relationship between EM slopes/curvature and returns in that steeper slopes and/or increased curvature imply higher returns. SA has a relatively steep slope and positive curvature resulting in high returns, conversely, TRL has an inverted slope and negative curvature leading to negative returns. We also find that increased slope and curvature volatility leads to lower returns, this is demonstrated by TRL who have succumbed to political interference in their central banking policies leading to extreme moves in their exchange rate, inflation and interest rate levels. Thus, a short butterfly strategy (selling the 3–7 year maturity bucket and purchasing the 1–3 year and 7–12 year maturity buckets in a cash and duration neutral manner), which is the opposite of the long butterfly strategy, will be profitable in a volatile interest rate environment with inverted curves and low curvature as in TRL.

SA has experienced similar slope and curvature volatility to the other EM countries but has relatively higher returns due to steeper slopes and increased curvature. This is because SA has undergone a decade of below trend growth due to poor infrastructure investment, reduced power generation, rising unemployment and social inequality. Thus, the government has had to increase its debt levels and fiscal deficit to maintain spending levels. Investors require higher risk premiums for increased debt loads, resulting in a steeper slope and curvature.

According to Figure 5, a similar pattern transpires for the DM long butterfly strategies, in that steeper slopes and/or increased curvature imply higher returns. Of the DM countries, ITL on average has the steepest slope and greatest curvature, translating into the greatest returns. JPN has the flattest slope and lowest curvature leading to the lowest returns at zero. This is because the Japanese government incorporates large stimulus measures to suppress long-term bond yields whilst the Bank of Japan has, for many years, maintained an accommodative monetary policy stance, resulting in a flat government yield curve with reduced volatility.

In the DM space, we see that volatile slope and curvature changes imply greater returns which is the opposite of what occurs with EM countries in that increased volatility results in lower returns. A possible reason is that with increased volatility in DM countries, we have increased opportunities to capture non-parallel risk premia with the added insurance of DM fiscal stimulus which can control yield curve shapes. This is evident with ITL, US, and GER who have increased volatility and high returns due to their ability to control yield curves by utilising fiscal stimulus measures. JPN has relatively muted slope and curvature changes resulting in fewer return opportunities and lower returns. The UK is interesting in that it also has relatively muted slope and curvature volatility, but steeper slopes and positive curvature allow for increased return potential.

Figure 6 illustrates the long butterfly returns versus inflation volatility in both EM and DM countries. If we exclude the EM outliers of SA (high slope and curvature levels) and TRL (low slope and curvature levels), we can see that increased inflation volatility leads to higher returns. This pattern continues for the DM countries with JPN being a slight outlier (flat slope and low curvature) but still following this relationship. Volatile inflation requires extreme monetary policy and possible fiscal intervention to moderate current and future inflation expectations within central bank targets. Increased inflation volatility translates into an increased occurrence of non-parallel curve changes, risk premia and amplified returns.

This means that long butterfly strategies are advantageous in countries with credible central banks that are disciplined at managing inflation volatility and expectations, but also have above-average fiscal risk or term premia resulting in steep yields and increased curvature like SA and ITL. Short butterfly strategies are profitable when countries experience inverted curves with low curvature and increased inflation volatility which could occur when unconventional monetary and fiscal policies are applied as in the case of TRL. When we have loose monetary and fiscal policy like JPN, where flat curves with low curvature and inflation volatility are evident then neither a long or short butterfly strategy will be profitable. During tight monetary and loose fiscal policy, as is common in many DM countries (like the US, UK, GER, FRA, AUS and CAN due to a large amount of quantitative easing and stimulus programmes), long butterfly strategies are still profitable (albeit to a lesser degree) but tactically switching between long and short butterflies during curve normalisations and inversions would be beneficial to maximise returns. See

Table 6. Summary of the findings of which monetary and fiscal policy regime is profitable for a given long or short butterfly strategy and the countries in our analysis that possess these policies.

	Monetary Policy
Fiscal Policy	Loose	Tight
Loose	JPN	SA, ITL
Optimal Strategy	None	Long Butterfly
Tight	TRL	US, UK, GER, FRA, AUS, CAN
Optimal Strategy	Short Butterfly	Tactical Long/Short Butterfly

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In the next section, we use a quantitative approach to determine the type of monetary and fiscal policy of each EM and DM country.

5. Quantifying Monetary and Fiscal Policies

To quantify the extent of monetary and fiscal policies in each country, we used several indicators to determine the extent of policy tightness or looseness. Data were obtained from Bloomberg and the World Bank. The indicators are given in

Table 7. Ranks and scores monetary and fiscal policies of EM and DM countries on a scale of −1 (very loose policy) to +1 (very tight policy) with 0 being neutral policy, on a relative basis. The rationale for using them and the data frequency is also provided.

	Variable	Rational	Data Frequency
Fiscal Policy Measures	Budget to GDP3 ratio	Greater budget deficit = increased funding and bond supply = increased term premia and steeper curves	Annual data from January 2007 to December 2023
	Volatility of budget to GDP ratio	Increased budget volatility = uncertainty in government finances = increased term premia and steeper curves	Annual data from January 2007 to December 2023
	Average gross debt to GDP	High debt to GDP = leveraged economy that is dependent on investor demand for debt and susceptible to high interest rates.	Annual data from January 2007 to December 2023
	Gross debt to GDP volatility	Increased debt volatility = uncertainty in government finances and susceptibility to global growth cycle = increased term premia and steeper curves	Annual data from January 2007 to December 2023
	Average net borrowing requirement to GDP	Increased borrowing requirements = increased bond supply = increased term premia and steeper curves	Annual data from January 2007 to December 2023
	Volatility of average net borrowing requirement to GDP	Increased volatility of borrowing requirements = uncertainty in bond supply, financing costs and susceptibility to global growth cycle = increased term premia and steeper curves	Annual data from January 2007 to December 2023
	Average difference between real GDP and the long-term real yield	Smaller difference = negative impact on government finances as will find it difficult to service debt, not generating sufficient growth to repay debt = increased term premia and steeper curves	Quarterly data from January 2007 to March 2024
	Variable	Rational	Data Frequency
Monetary Policy Measures	Inflation volatility	Greater inflation volatility = increased central bank intervention and volatile central bank rates = volatile short-term rates with extreme steepening and flattening.	Monthly data from June 2007 to March 2024
	Real effective exchange rate volatility	Greater currency volatility = increased inflation passthrough and volatility = greater central bank intervention required = volatile short-term rates with extreme steepening and flattening.	Monthly data from June 2007 to March 2024
	Average real central bank rate	Higher real central bank rates = greater incentive to save and invest rather than spend and consume = lower demand-pull inflation and inflation volatility.	Monthly data from June 2007 to March 2024
	Average long-term real yields	Higher long-term real rates = greater incentive to invest, attracting foreign investment flows, capital flows > consumption flows = increased productivity = lower structural inflation and volatility.	Monthly data from June 2007 to March 2024

together with the rationale for using them and the data frequency used. We ranked and scored monetary and fiscal policies on a scale of −1 (very loose policy) to +1 (very tight policy) with 0 being neutral policy, for all the DM and EM countries on a relative basis. The rank and scoring methodology entailed finding the minimum and maximum values of each indicator so we could rescale the indicator data from −1 to +1. This provided a simple and effective way to quantify the relative value of each indicator and compare the score for each country. As an example, if we have the following list of indicator values [−3, −1, +4, +7, +11] and we want to rescale between −1 and +1, we would take each list value, subtract the minimum list value, and divide by the difference between the maximum and minimum list value. The first list value would be transformed as (−3–(−3))/(11–(−3)) = 0, and the second list value would be transformed as (−1–(−3))/(11–(−3)) = 0.14, and so on. We would then rescale these list values between −1 and +1 by subtracting 0.5 and multiplying the result by 2, e.g., the first transformed value would be (0–0.5) ∗ 2 = −1, the second transformed value would be (0.14–0.5) * 2 = −0.7, and so on. This is continued for each indicator so that we can find an average score for each country for relative comparison purposes.

The 45-degree dotted line in Figure 7, Figure 8, Figure 9 and Figure 10 represents a country that has relatively balanced monetary and fiscal policy. Using data from 2007, we see that TRL had a very loose monetary policy caused by volatile inflation, currency, and relatively low real central bank rates and real yields. On the contrary, this translated into a weak currency and increased TRL exports which helped fund the fiscal deficit resulting in a tighter fiscal position. Of the DM countries, we saw that the UK, US, JPN, CAN, and ITL had loose fiscal policies due to their large stimulus and quantitative easing programmes. These stimulus programmes aim to suppress long-dated interest rates and term premia, resulting in flatter yield curves that would otherwise occur. Term premia is the excess yield that investors demand for holding a longer-term bond compared to a series of shorter-term bonds. Term premia compensate investors for risks (such as interest rate, reinvestment and inflation risk) associated with investing in long-term bonds rather than investing in a series of short-term bonds for the entire holding period. Term premia vary over time based on economic conditions; for example, during severe risk-off events like the great financial crisis and COVID-19 pandemic, many DM countries experienced negative term premia due to the large stimulus programmes implemented in their domestic bond markets, whilst EM countries had increased term premia due to heightened fiscal risk. With a negative term premium, investors are not compensated for holding long-dated government bonds, this was intentional as DM governments encouraged businesses and consumers to spend rather than save.

FRA had neutral fiscal policies and relatively tight monetary policies brought about by a stable Euro currency and inflation environment. Out of the DM countries, GER and AUS had the tightest fiscal policies, as they controlled their budget deficits and did not allow them to get out of hand with excessive borrowing.

Since 2007, EM on average has relatively tighter fiscal policies than DM; however, DM has marginally tighter monetary policy relative to EM (mainly due to the extremely loose TRY monetary policy). If we remove the TRY outlier, we can see that EM has tighter monetary and fiscal policies relative to DM, as represented in Figure 8. MEX, IDR and CNY have the tightest fiscal and monetary policies, as they maintain high real central bank rates. IND and PLN have similar monetary and fiscal policies whilst BRA has relatively tight monetary policy but loose fiscal policy. SA and FRA have similar monetary policies with SA having slightly tighter fiscal policy due to lower overall debt levels. GER and AUS have the tightest fiscal policies out of the DM countries owing to their lower debt levels and budget deficits. The UK, US, and JPN have loose monetary and fiscal policies caused by large budget deficits, borrowing requirements and low real central bank rates. Despite utilising their reserve currency statuses to increase government debt at low interest rates, DM countries still have relatively loose fiscal policies. If it were not for the stimulus measures to suppress long-dated interest rates, DM countries would have much steeper yield curves leading to greater long butterfly returns. Since the GFC, term premia in the US and Europe have declined and become negative in some instances. This trend is attributed to shifts in expected short-term rates rather than changes in term premia themselves and can be observed using the Board of Governors of the Federal Reserve System (US) (2024) who apply the Kim and Wright (2005) term premium approach. Cohen et al. (2018) also find that the term premia in the US and Europe has been negative post the GFC. A Barclays insights paper from Vernier (2024) describes how the US Federal Reserve utilised its System Open Market Account to absorb five trillion dollars of US treasury bills and bonds, which suppressed long-term treasury yields and resulted in a negative term premium post the GFC. The term premia used was the Adrian, Crump, and Moench 10-year term premium developed by Adrian et al. (2013). Vernier (2024) cautions against rising term premia from further US fiscal slippage and bond supply; however, this would likely be temporary as the path of US policy rates and cycles remains the dominant driver of yields. A PIMCO perspectives paper by Seidner and Dhawan (2024) discusses the US leveraging its privilege as the world’s reserve currency but warning against this privilege turning into profligacy if bond vigilantes (who demand higher yields given increased deficits) are not satisfied. This prudence was last observed in the 1980s and 1990s; however, they conclude that current political will is unlikely to mirror those austere years, suggesting that US fiscal deficits are here to stay.

The same chart from December 2019 to March 2024 (which can be described as the coincidental and post-COVID-19 era) illustrates similar fiscal policies but tighter monetary policies for both EM and DM. If we exclude TRY as seen in Figure 10, we can see that EM has a tighter monetary policy relative to DM countries, even tighter than using data from June 2007. Inflation surged following the COVID-19 pandemic period as massive stimulus was introduced by DM countries. The rebound in growth and consumer demand, together with supply chain disruptions were underestimated. EM central banks responded quickly to the sharp inflation increase by hiking interest rates relatively earlier than DM central banks. Thus, cost-push inflation in DM countries far exceeded their inflation targets requiring aggressive interest rate increases which disrupted financial markets, especially long-term interest rates. Once again MEX, IDR, and CNY had the tightest fiscal and monetary policies given their high real central bank rates, low debt levels and borrowing requirements. SA and IND had a tight monetary policy, POL had a much looser monetary policy but a tighter fiscal policy, and BRA had a tight monetary policy with a loose fiscal policy. Out of the DM countries, AUS and ITL had relatively looser monetary and fiscal policies post December 2019 compared to the whole period. Tighter monetary and fiscal policies were observed in FRA, GER, JPN, CAN, UK and the US post December 2019 relative to the whole period.

From the above, we see that large stimulus measures from DM countries suppress long-term interest rates resulting in flat or inverted yield curves and lower long butterfly returns. Thus, we find that the appropriate policies to increase long butterfly returns are countries that have relatively tight monetary policies and neutral to slightly loose fiscal policies. From our analysis, countries that fall into this category are SA, BRA, ITL, CAN, US, and FRA, but ITL, CAN, US, and FRA are DM countries that can stimulate and artificially suppress long-term interest rates. Therefore, SA and BRA have the most appropriate monetary and fiscal policies to maximise long butterfly returns. If we reverse this argument, we find that TRY which has a loose monetary policy and tight fiscal policy favours a short butterfly strategy due to its volatile inflation and currency regime. Countries with relatively balanced monetary and fiscal policies will still be able to generate attractive butterfly returns but will require tactical switches between long and short butterfly strategies for significant returns.

6. Conclusions

In this paper, we analysed several EM and DM sovereign yield curves to detect the proportion of parallel and non-parallel shifts that occur through time. We identified the idiosyncratic and systemic events that caused the increased occurrence of non-parallel shifts. These were primarily systemic, risk-off events commonly associated with acts of war and terrorism, sovereign, corporate and/or household debt distresses, political agendas and factions, and infectious diseases/pandemics. We found that non-parallel shifts are relatively more prevalent in EM than in DM countries due to increased political and economic risks, higher risk-off betas and volatile interest rates. Parallel curve shifts between EM and DM countries do coincide but there is only a slight positive correlation of 18%. This is largely due to MEX and POL being included in our EM group and being in close proximity to the DM economic hubs of the US and Europe, respectively. Since 2009, rate-cutting cycles have frequently occurred for both EM and DM countries, with bull flattening and bear steepening being the most common second order curve scenario whilst positive convexity is the most prevalent third order curve scenario for DM countries.

To determine what curve properties are beneficial for extracting non-parallel risk premia, we backtested a long butterfly strategy on EM and DM countries of each country to mimic a 2v5v10 long butterfly strategy using data from June 2007 to March 2024. We found that there is a positive relationship between slopes/curvature and the long butterfly returns in that steeper slopes and/or increased curvature imply higher returns. Amongst the EM countries, this is well demonstrated by SA, which had a relatively steep slope and positive curvature resulting in high returns. For the DM countries, ITL had the steepest slope and greatest curvature, which translated into the highest DM returns. TRL had an inverted slope and negative curvature caused by inconsistent monetary policy which led to negative returns. JPN had the flattest slope and lowest curvature due to loose monetary and fiscal policy which resulted in the lowest DM returns. We also found that volatile slope and curvature changes amplify returns as there are increased opportunities (positive and negative) to capture non-parallel risk premia. ITL, US, GER, SA, POL and BRA are positive examples of this, whilst TRL has greater negative shocks due to its extreme monetary policies and heightened political risk.

Another interesting aspect is that increased inflation volatility leads to higher returns for most EM and DM countries. Volatile inflation requires extreme monetary and fiscal policies to moderate current and future inflation expectations towards central bank targets. Outliers to this are SA (high slope and curvature levels) and TRL (low slope and curvature levels). SA has high, positive returns from the long butterfly strategy due to a credible central bank reducing inflation volatility and a steep slope due to increased fiscal risk. TRL has negative, long butterfly returns due to unconventional monetary and fiscal policies with inverted curves and increased inflation volatility.

To identify the relevant extent of tight or loose monetary and fiscal policies, several variables were combined to generate a policy score (TRY was excluded due to its extreme policies). We found that EM countries generally had tighter monetary and fiscal policies relative to DM countries owing to relatively higher real central bank rates to curb volatile inflation and lower debt levels due to the high EM cost of funding. DM countries had the privilege of their reserve currencies to stimulate economic growth by increasing debt at relatively cheap levels which resulted in loose fiscal policies. After the COVID-19 pandemic, global inflation and growth rebounded strongly, which, after the initial loose policies to support economies, required much tighter monetary and fiscal policies in both EM and DM, which was evident. Our research suggests that countries with contrary monetary and fiscal policies possess higher return opportunities whilst countries with complementing policies require tactical butterfly strategies to optimise returns. For the EM countries, we see that SA and BRA have the most appropriate monetary and fiscal policies to maximise long butterfly returns whilst TRY has loose monetary policy and tight fiscal policy to maximise short butterfly returns. Amongst the DM countries ITL offers attractive long butterfly returns but, generally speaking, DM countries will likely require tactical allocations to short and long butterfly strategies to generate significant returns.

In summary, we have described the types of monetary and fiscal policies that are required to extract non-parallel risk premia from yield curves. Passive long or short butterfly strategies can be profitable under certain monetary and fiscal policy regimes, whilst tactical butterfly strategies (switching between long and short butterflies) are essential in others. Successfully identifying monetary and fiscal policy regimes will lead to beneficial butterfly strategies; however, trading costs will have to be pragmatically managed to ensure meaningful after-cost returns.