The impossible trinity, yet again

Stephen Grenville 26 November 2013



Starting point of the impossible trinity

The variety of interpretations surrounding the impossible trinity (Aizenmann et al 2010, Rey 2013, and Klein and Shambaugh 2013) can be put in perspective if we go back to Mundell’s(1963) starting point. His central insight came from thinking in terms of different currencies being close substitutes. He might have had in mind, say, the US dollar and the sterling.

Two operational characteristics define this substitutability.

  • First, there are a significant number of portfolio managers who can – and do – readily switch between currencies in response to changes in expected returns. These potential arbitrageurs maintain the discipline implied by the impossible trinity.
  • Second, expected portfolio returns are well defined in terms of a tight relationship between two of the three impossible trinity’s variables – interest differentials and expected exchange-rate movements. The short-hand for these well-defined expectations is uncovered interest parity (UIP) – if there is an interest differential between the two currencies, this has to be balanced by a widely-held expectation of offsetting exchange-rate change. Any departure from this interest rate/exchange rate nexus would set-off powerful arbitrage flows. This ties the three corners of the triangle together.

Could the impossible trinity operate today?

Today’s reality, however, looks more complicated.

  • First, it is now well established that uncovered interest parity does not hold with any consistency (Engel 1996).

Portfolio managers no longer have a clear view of where the exchange rate will be when their investment ends. The less certain they are, the more risk they take in arbitraging an interest differential.1

  • Second, this exchange rate risk is not the only uncertainty. Financial instruments in different currencies will have different attributes.

Transactions affecting the balance of payments (i.e. involving non-residents) will involve foreign laws, regulations, procedures, payments/settlements systems, taxation, and a myriad other specific issues, often unfamiliar to the investor. Each of these adds to the uncertainty, and makes financial instruments less substitutable.

  • Third, there is the arbitrage process itself.

Mundell thought of monetary policy in terms of the arbitrage inflows increasing base money, with the money/credit multiplier transmitting this to the domestic economy. However, central banks have not operated monetary policy like that for some decades. In practice, they set the short-term interest rate and have considerable operational capacity to sterilise inflows.

What happens to impossible trinity when it is not operating in Mundell’s world of close substitutes, UIP, and money multipliers, but instead – in a world where risk and unfamiliarity play a big role in portfolio decisions?

Moreover, what happens to the impossible trinity when capital flows are only modestly influenced by interest differentials? If interest differentials were the main driver, we would not expect to observe the huge two-way gross capital flows into and out of most advanced countries, vastly larger than the net flows.

Challenges for some of the theories on the impossible trinity

Capital flows are characterised by global surges and retreats, responding to volatile and subjective risk perceptions rather than interest differentials. This is Rey’s world, where the VIX (a measure of uncertainty and risk aversion) goes a long way to explaining the volatility of flows. For Rey, this intensifies the policy constraint, turning the trilemma into a dilemma – “an independent monetary policy is possible if and only if the capital account is managed, directly or indirectly”.

The presence of substantial risk, however, frees policy from the tight strictures of the impossible trinity. Once risk is added to the portfolio managers’ calculation, the firmly-based arbitrage process, envisaged by Mundell, is muted – or even absent. Interest rates can be held well above international levels without this either requiring a constant depreciation to retain portfolio balance, or resulting in a destabilising flood of foreign capital inflow.

This can be observed in the case of less-substitutable currencies such as those of the emerging Asian economies, for example, the Indonesian rupiah and the Thai baht. They have been able to maintain significantly higher interest rates for sustained periods while at the same time experiencing appreciating currencies (see Grenville 2011). Their monetary conditions were not largely set in world markets, as Rey suggests. They did, however, have important policy challenges imposed by the global surges and reflows of capital – their exchange rates came under strong pressure tending to push the rate away from underlying equilibrium. This presents a policy challenge, whether the country has a floating rate, or a managed float.

In the face of these volatile capital flows, how much capacity do countries have to keep their exchange rates close to underlying equilibrium through exchange-rate management? Their principal constraint is not that the impossible trinity’s arbitrage flows will nullify their intervention. Arbitraging speculators taking contrary positions are betting against reversion-to-equilibrium, and, in addition, have all the risk elements discussed above
That said, the capital surge may be too strong for intervention alone to offset the capital surge.2 Then policy should turn, in addition, to the range of measures (macroprudential, capital management) that Rey discusses.

Moreover, (perhaps it hardly needs emphasising), the policymakers do not have an open-ended ability to set the exchange rate whenever they like. Defending a non-equilibrium rate will fail, sooner or later.

This view of the world fits neatly into Williamson’s (2008) Band Basket Crawl (BBC) prescription. He acknowledges an element missing from Mundell – that the exchange rate will not always be at its equilibrium, perhaps because of volatile capital flows responding to Rey’s time-varying risk perceptions, reflected in the VIX. Of course, policymakers cannot know exactly where the fundamental equilibrium exchange rate is, but if the band is reasonably wide, and is crawling in response to underlying fundamentals, when the rate gets to the edge of the band the authorities can be fairly confident that intervention aimed at shifting the rate back towards the centre of the band will be a move in the right direction – towards equilibrium. Speculators who take them on cannot have a better view on where the rate ought to be. A determined defence of the edges of the band has a high probability of success. When it does, this will provide a more stable price signal to the real economy than is provided by a pure free float.

In short, adding risk to the impossible trinity’s story creates a band (rather than a single point) within which the exchange rate might move without the Mundell arbitrage forces coming into play. This is consistent with Rey’s view, but a much more positive message is indicated, because it suggests that intervention (supplemented if necessary by the other policy measures she discusses) has a high likelihood of delivering a stable exchange rate close to the fundamental equilibrium. It also easily accommodates Aizenmann’s view that the impossible trinity triangle has rounded corners.

Less easy to accommodate is the view of Klein and Shambaugh. Their approach does not provide the promised “better way to organise our thinking” in a world where capital flows are responding mainly to factors other than interest differentials. They group together countries, which have different experiences. Within this diversity their evidence seemingly confirming the impossible trinity is consistent with other explanations as well. Australia, for example, is among the countries which are said to have “focused monetary policy on conditions in their domestic economies while allowing their exchange rates to be determined by the market.” During this period its interest rate moved parallel with America’s. Superficially, this fits Rey’s view that policy is dictated from outside even for floating-rate countries, just as well as it fits the impossible trinity story. In fact, the real story fits neither view – a domestically oriented independent monetary policy moved in parallel with America because the global cycle was impinging on Australia. The substantial exchange rate movement was not related to interest differentials or capital flows, but to commodity prices.

Concluding remarks

In today’s world, volatile capital flows driven by risk-on/risk-off swings in sentiment are overwhelming the interest-driven flows that are central to the impossible trinity story. The implications are particularly serious for emerging economies with immature financial markets not able to buffer these flows smoothly. Of course, policy instruments are connected to each other (first lesson of macroeconomics – everything is connected to everything else). Naturally, interest differentials play a role in the policymakers’ response. However, the policy trilemma is not “all they need to know”. The rest is more than ‘commentary’ – it is the main game.

The impossible trinity may support the policy choices of the advanced economies. Open capital accounts and free-floating exchange rates have generally served these countries well. For the emerging economies, however, their shallow financial markets can’t readily absorb the risk-driven capital flows which characterise the international economy. At the same time, these underdeveloped financial markets free these economies from the rigid strictures of the trinity because their currencies are not close substitutes for other currencies. In normal times, they can maintain interest rate settings substantially different from other countries without this triggering nullifying capital flows. In the face of volatile capital inflows, they often have considerable capacity to constrain their currency appreciation through intervention. The Trinity is a reminder of the interconnectedness of policy instruments, but an inadequate guide to the range of policy options available.


Aizenmann, Joshua, Menzie D Chinn, and Hiro Ito (2010), “The Emerging Global Financial Architecture: Tracing and Evaluating the New Patterns of the Trilemma’s Configurations”, Journal of International Money and Finance 29(4): 615–641.

Engel, C (1996) “The forward discount anomaly and the risk premium: a survey of recent evidence”, Journal of Empirical Finance, vol 32: 305-319

Grenville, Stephen (2011) “How can the impossible trinity not apply to East Asia?”, 26 November. 

Klein, Michael W and Jay C. Shambaugh (2013), “Is there a dilemma with the Trilemma?”, 27 September.

Mundell, Robert A (1963). "Capital mobility and stabilization policy under fixed and flexible exchange rates", Canadian Journal of Economic and Political Science 29 (4): 475–485.

Rey, Hélène (2013b), “Dilemma not Trilemma: The global financial cycle and monetary policy independence”,, 31 August.

Williamson, John (2008) “Exchange rate economics” Peterson Institute working Paper 08/03, February

1 The conventional term ‘risk’ is used here, but ‘uncertainty’ would be a better description.

2 It is sometimes argued that official intervention will fail because it is tiny compared with the volume of transactions. This confuses stocks and flows. Intervention has to counter the position-taking, not the transaction volume. With this correct measure of scale, intervention may not be tiny.



Topics:  Macroeconomic policy Monetary policy

Tags:  capital flows, exchange rate, Impossible trinity, portfolios

Visiting Fellow, Lowy Institute for International Policy

CEPR Policy Research