A Nash Equilibrium

By Peter De Coensel,
CIO Fixed Income at DPAM



    • Today we discuss the Nash Equilibrium and apply the concept to central bank strategies. The Nash equilibrium exists in the realm of game theory.

    • Game theory sits at the core of financial market functioning and applies seamlessly to investment management. Over long horizons speculative investment management resembles a zero-sum game. Proper investment management can be considered a positively skewed game in which investment managers vie for an increase in wallet share by convincing institutional and retail investors that a consistent investment process edge leads to above average results. After costs. The Nash equilibrium, named after the mathematician John Nash Jr., defines the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is supposed to know the equilibrium strategies of the other players and no player has anything to gain by changing only their own strategy. Effectively most developed market (DM) central banks have chosen and communicated at length on their strategies. The common trait of these strategies builds on enforced forward guidance in policy rate setting next to sustained asset purchase programs that absorb duration, contain rate volatility and keep funding level for governments at bay. Over the past weeks, a lot of ink has flown on potential lift-off moments for policy rates next to assessments on the impact of asset purchase tapering. I would use the word tinkering instead of tapering. The previous episode, 2015- 2018, has shown that aggressive tapering by the FED quickly delivered unintended consequences. Unintended consequences known under the label of tightening of financial conditions. Tightening of financial conditions leads to market instability. With higher levels of leverage and margin debt currently visible in the financial system, the point of instability might come even faster today than was the case over H2 2018. Back then, the rules of the Nash equilibrium were trespassed giving rise to negative externalities. Fact is that financial market instability quickly spills over into negative real economic impact. Negative main street impact that requires central bank intervention or another round of fiscal support. And the whole cycle can start once more, leading to ever more central bank control on the price (read rates) formation mechanics across markets. We will make a quick tour that unveils the presence of Nash equilibrium awareness across central bankers. It’s a fragile equilibrium but one that maintains cost of funding for indebted DM governments well below levels that would ensue in a world without QE and enforced forward guidance.

    • On April 21, the Bank of Canada (BoC) announced that it would trim its asset purchase program to CAD 3 billion a week from CAD 4 billion and advance the timing for a possible interest rate hike – from 0.25% – to 2022 from 2023. Tapering is tinkering. Moving the lift-off marker is playing games with markets in a way to assess its vulnerability. The Canadian rates market did not really budge, the yield curve embraces the status quo. Thumbs up for the BoC. On March 19, the Bank of Japan (BoJ) decided to maintain its QQE (qualitative and quantitative easing) framework with yield curve control, but to enlarge the band to 25bp from 20bp around the 0.00% target level for the 10-year JGB rate. They also tinkered regarding ETF purchases, moving from Nikkei trackers towards TOPIX ETF’s. The TOPIX index has the largest number of component stocks and would better contain the shareholding ratio of the BoJ. Over the past week, the Bank of England has informed the public that they will tinker QE towards GBP 3.5 billion a week from GBP 4.5 billion. Martin Kazaks, the Bank of Latvia governor and ECB council member, was eager to announce this week that the ECB would review asset purchases in June. He added as well that winding down PEPP (that will be fully depleted and run till March 2022) might make room to increase the old APP program. We can expect that, within the FED, such announcements might be scheduled during the end of August Jackson Hole central bank ‘Hohe Messe’. Throughout all the noise delivered by the central bank community, we observe a well-orchestrated, officially non-cooperative, solution/outcome that pleases all central banks: We observe orderly moves across government bond markets. The timing for lift-off stretches from Q4 2022 to Q1 2023 for early flyers like the BoC, Reserve Bank of Australia or New Zealand Central Bank. Traditionally, these central banks test the waters. The FED might come into action over H2 2023. At best, we expect the ECB to start tinkering with policy rates by Q4 2024. Whether the Bank of Japan might lift policy rates ever again remains a key question that deserves an answer. The Bank of Japan has experimented the most with the use of unconventional instruments. As such it will take a lot of time to reverse course, leading to a rise in policy rates which have sat at -0.10% since 2016, before a long stint at +0.10% between end of 2008 till end of 2015. At best, expect a move towards +0.10% between 2025 and 2030. Before the pandemic, during an episode of accelerating globalisation between 2001 up to 2018, a Nash equilibrium state among central banks was less evident. The ECB policy rate mistakes of 2008 and 2011 come to mind. The FED mid-cycle hiking cycle between end of 2015 till end of 2018 has probably been a bit of an aberration. The prevailing tendency over the next decade might become a more orchestrated withdrawal of accommodative policy across central banks. By now, the players in the game have reached a higher level of understanding. So instead of focusing on the question of what is the terminal rate for the FED, we should answer the question what is the optimal terminal rate for the FED in this game? An optimal rate that will not disturb the Nash equilibrium allowing for steady, redistributive and climate oriented fiscal policy to unfold across DM, and by extension Emerging Market (EM) economies. The market has a terminal rate FED policy rate priced at 2.25%-2.50% today. However, that would read as a repeat of the ‘2015-2018’ mistake. Maybe, the moment the hot US economy debate loses some steam, the market might shift towards a lower end state for FED policy rates….1.50% anyone? This scenario would have a highly consolidating effect on current US long rates.

    • If a Nash equilibrium is in place and we account for the interconnectedness of international fixed income flows, I become more convinced that long term rates among OECD countries have entered an era of convergence. Surplus regions like the EU and Japan will perpetuate a solid interest towards US bond products. A positive windfall might also befall some EM economies as they get pulled into the gravity field of DM long rates and profit from lower funding levels. Countries like Romania, Czech Republic, Serbia across Eastern Europe or Mexico as main contender in Latam spring to mind. Central banks that apply Nash equilibrium principles in the conduct of their strategy might also have a compressing impact on term premium that market participants levy on various point of respective yield curves.


    • The Non-Farm Payroll and Unemployment Rate numbers send some shivers through global bond markets on Friday, May 7. Both missed expectations by a margin that requires much to explain about. The sell-side was quick in pointing to measurement problems, promising strong numbers ahead. The sell-side also finds each other in pointing to an overheating US economy followed by a potential for inflation unanchoring. Time will tell. The FED sticks to their plan not to run policy based on forecasts. I believe that forecasts and soft economic indicators will succumb to more of the past week’s disappointments. Effectively, the pandemic uncertainty remains high. The US Treasury bull steepened over the week. The 5-year to 7-year maturity bracket posted the best results, as both reference rates dropped by 7.5bp to 0.774% and 1.236% respectively. The 10-year and 30-year dropped a more modest 5bp and 2.5bp towards 1.57% and 2.28%. US inflation expectations continue to trend higher, mostly through an aggressive push downward of real rates. 10-year breakeven rates closed at 2.51%, an 8-year high. 10-year real rates closed at -0.93%: A solid 15bp lower over the week!

    • The bleeding for European Government Bonds (EGB’s) came to a halt. EGB’s sector shed a small 6bp. Year-to-date the sector goes into the red by 3.55%. As we wrote last week, market participants feel uncomfortable with EGB’s. Italian 10-year spreads to Germany spiked to 118bp. The more aggressive PEPP purchases over Q2 decided about a month ago has been an invitation to reduce BTP exposure. On February 22, we reached a low of 97bp in 10-year Bund-BTP spreads. Nothing to worry about, but more fragmentation is truly unwelcome for an Italian economy that really should be shielded from tightening financial conditions. Spanish and Portuguese 10-year spreads to Bunds closed at 3-month wides just above 70bp. The sticky 10-year French OAT-Bund spread is closing in on 40bp! Tensions are building. Again. The June 10 ECB meeting carries a lot weight.

    • European investment grade and high yield bond sectors locked in positive weekly returns at 12bp and 3bp respectively. The smaller corporate sector purchase program (CSPP is achieving its stated objectives more effectively than the larger APP/PEPP government bond programs. Whenever discussions on tapering (tinkering!) start, reducing CSPP might be least damaging. The European HY sector is still not ‘tainted’. Let’s leave it so.

    • A decent week for EM LC debt with 0.76% total return in EUR terms. The yield of the GBI EM GD index fell 3bp to 4.90% while the EMBI GD spread ticked up by 1bp to 310bp. EM currencies gained 1.50% in USD terms as disappointing US data and falling US real yields weighed on the dollar.

    • On the topic of inflation, we had a few CPI prints in EM this week and they were all on the rise and above expectations. Mexican CPI increased from 4.67% to 6.12% YoY, Chilean CPI increased from 2.9% to 3.3%; South Korean CPI rose from 1.5% to 2.3% and Turkey from 16.19% to 17.14%. On the monetary policy front, Poland, Czech Republic, Turkey, Malaysia and Thailand all left their policy rates on hold while the Brazilian central bank raised rates by 75bp as expected. While inflation is clearly bouncing off from the lows, due to base effects and elevated energy and food prices (which account for a higher part of CPI in developing countries), those effects are expected to be transitory and should fade in the summer. For instance, the BoK does not expect inflation to exceed the 2% target over the medium term, and some of its members stressed that inflationary pressures should not change the picture on the rate outlook given the weak job market in the country. Also, a resurgence of COVID cases like the one observed in some South-East Asian countries are likely to cap demand-pull inflationary pressures for now.

    • Unless we observe an exceptional spike in US rates volatility like in Q1, we think in this context local rates exhibit an attractive carry to the yield-hungry investor. They also offer an interesting valuation compared to USD-denominated bonds. Some countries even have a potential for duration gains, but here we also reaffirm the importance of selection in the investments, as economic trajectories are widely diverging. Countries with less macro imbalances and stronger institutional frameworks are likely to outperform.

    • Speaking of imbalances, Colombia was the cliff-hanger of the week, with a sharp sell-off across its bonds and currency the moment Carasquilla, the Minister of Finance, resigned. The long-awaited (from rating agencies at least) tax reform in the country is on its way out. This reform, opposed by a majority of parliament, sparked days of popular street revolt. The plan consisted of an increase in the wealth tax, a middle-income tax rise, while increasing redistributions, at the margin, for lower-income classes. It was designed to increase revenues by 1.6% of GDP until 2031. Rating agencies are considering a reform as a key element to retain the Investment Grade rating. The bond sell-off was sharp but a floor is in the making. The government has reaffirmed its willingness to keep its rating and to reach a consensus to increase fiscal revenues. As a reminder, the central bank, BanRep, left its key interest rate last month at a record low of 1.75% but warned that a loss of investor confidence over the deficit could weigh on the ability to maintain an expansionary monetary policy. On top, this week’s CPI print showed an acceleration in headline inflation from 1.51% to 1.95% YoY (consensus was 1.69%). While it remains below the 2%-4% target range, it could complicate things further for the BanRep. Local swap markets have reacted by pricing a more aggressive hiking cycle of +75bps over the next 6 months.


In a post-COVID world, fiscal and monetary authorities have entered a collaborative regime. We have observed such a model across DM as well as EM economies. In that context, the applied monetary strategies might have the optimal and most sustainable outcomes if these are following Nash equilibrium behaviour.

The episode between the GFC of 2008-2009 and the start of the pandemic was littered with central banks trying to go at it alone, expecting better outcomes at home. We know by now that such solo policies are prone to run into trouble once confronted by a globalised financial system. A system that stretched the definitions of leverage and margin debt.

It’s time to accept that, given the rampant financialisation over the past 40 years, markets cannot return towards policy rate conditions that were present when central bankers were still by-standers. Today, central banking sits at the center of financial markets. Central banking works best when applying paths of conduct that deliver a series of states mimicking a Nash equilibrium. Open to discussion, because the implications are far reaching… maybe even beyond imagination.


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