Foreign Exchange Intervention with UIP and CIP Deviations

Whether the cost of holding reserves is governed by UIP wedges or by CIP deviations — and the paper argues the distinction is “particularly relevant for safe haven countries such as Switzerland and Japan, since these deviations may be of different sign.” One strand focuses on UIP wedges (Cavallino 2019; Basu et al. 2020; Fang and Liu 2021; Maggiori 2021; Itskhoki and Mukhin 2022); another argues that CIP deviations are what matter (Amador et al. 2020; Fanelli and Straub 2021). The empirical tension the paper points to is concrete: hedged returns in these currencies, equal to CIP deviations, “have been positive since the GFC,” while investors accept lower unhedged excess returns on safe-haven currencies given their hedging properties in bad times, so UIP deviations measured with survey exchange-rate expectations “show systematic negative expected excess returns for these currencies.” The paper notes many papers analysing interest-rate differentials assume complete markets, so that either UIP deviations vanish or CIP and UIP deviations coincide — and states flatly, “This is not consistent with the data.”

A two-period small open economy receiving capital flows through risk-averse international financial intermediaries who are the marginal investors and set both deviations through their hedged and unhedged portfolio choices. The structure follows recent work on reserves, but “financial intermediaries are risk averse,” and markets are incomplete. The central relation is devUIP = devCIP − cov(m*, X*)/E m*, where m* is the intermediaries’ stochastic discount factor and X* the foreign-currency excess return from their perspective. The covariance term “represents the risk premium for a UIP, or carry-trade, investment strategy, which involves exchange-rate risk in contrast with a CIP strategy,” and it arises precisely because intermediaries are risk averse: “they could hedge exchange-rate risk on the forward market, but it may not be optimal to fully hedge.” For a safe-haven currency, cov(m*, X*) > 0 — “the safe-haven currency yields a higher return in bad times” — so “it is possible to have a positive CIP deviation with a negative UIP deviation.” CIP deviations themselves come from two intermediation frictions in the model: a participation/collateral constraint parameter Γ and a foreign-currency convenience yield χ.

Whenever the combined supply of government bonds and reserves is below households’ desired gross foreign liabilities, because households cannot short domestic-currency bonds; this is stated as Proposition 1. The paper defines interventions to be “effective” only if they change the gross foreign liabilities of the economy, bH*, in equilibrium. Under the Wallace (1978) irrelevance proposition, if households can freely adjust their portfolio they can undo any open-market operation; here they face short-selling constraints, “which breaks the Wallace Irrelevance under some conditions.” Specifically, if bG + bCBF < bmax, then bH* = bG + bCBF, “FX interventions that increase bCBF increase gross foreign liabilities bH* one-for-one, and increase EX* and Z*” — because “offsetting would require households to issue domestic currency bonds, which they cannot.” The excess supply of domestic bonds must then be absorbed by intermediaries through higher excess returns. The paper summarises: “FX interventions are effective when they do not satiate the households’ need for gross foreign liabilities.” Three conditions are maintained throughout: a safe-haven economy (ρ > 0 and 0 ≤ α < 1/(1+bG)); a “risky environment” in which Γ and χ are small relative to σ², so that “CIP deviations will be smaller in magnitude than UIP deviations”; and a technical condition ensuring a unique, well-behaved solution with small net foreign positions and excess returns.

It is the expected product of the excess return X and the households’ SDF, divided by the expected discount factor — a certainty-equivalent version of the traditional monetary cost of reserves.* In the traditional sense used by Frenkel and Jovanovic (1981), Jeanne and Rancière (2011) and Adler and Mano (2021), the cost is the foregone earnings on reserves; here that corresponds to X* directly, since central bank profits are τ = −X*·bCBF. But since central bank profits are eventually distributed to households, “the question is whether this could increase households’ utility,” and holding more reserves also raises the exchange-rate risk the central bank bears. Normalising by the expected discount factor means the new measure “coincides with the traditional monetary cost X* in the absence of risk.” The paper also notes it “can be seen as a measure of the deviation from portfolio optimality… evaluated in units of future goods.”

UCFX = Z − ΔCov: the CIP deviation, which is an intermediation wedge, minus the difference between the intermediaries’ and the households’ currency risk premia, which is a risk-sharing wedge.* The two risk-premium terms “enter UCFX for very different reasons”: the intermediaries’ premium “affects the pricing of the excess return, since international financial intermediaries are the marginal investors,” while the households’ premium “only affects its welfare valuation.” Proposition 2 states the two limiting cases exactly: the utility cost equals the CIP deviation Z* when cov(m, X*)/Em = cov(m*, X*)/Em*, and equals the UIP deviation EX* when cov(m, X*) = 0. The first case obtains “in the absence of risk, as in Amador et al. (2020), or when financial intermediaries have the same discount factor as households.” The second is the limit “where domestic agents have negligible risk aversion compared to financial intermediaries,” which the paper identifies as what Itskhoki and Mukhin (2021) implicitly assume by rescaling intermediary risk aversion but not that of households. In general “the sum of the two wedges does not coincide with either the CIP or the UIP deviations,” and if a safe-haven currency is more valuable as a hedge to foreign investors than to domestic ones, so that ΔCov > 0 and the difference is large enough, “there may be a utility gain from accumulating reserves, rather than a cost.”

A non-zero utility cost is an arbitrage opportunity, so it requires a binding short-selling constraint; Proposition 3 states that if bCBF + bG < bmax then UCFX < 0 and is increasing in bCBF. From the households’ first-order condition, −UCFX = (λH − λF)/Em, so “a necessary condition for a negative UCFX is λH > 0, that is, a binding domestic currency bond short-selling constraint.” A negative UCFX means households “would be willing to engage in a domestic currency carry trade: go short in domestic currency and long in foreign currency”; that opportunity survives in equilibrium “only if households are prevented from going short in domestic currency.” If they were unconstrained, both wedges would adjust until UCFX = 0 — more domestic bonds absorbed by intermediaries raises Z*, and more household exposure to currency risk raises the household covariance and shrinks ΔCov, which the paper shows depends negatively on bH* in a linear approximation. The gains are bounded: “as the central bank accumulates reserves, UCFX becomes less negative, until UCFX = 0 when bCBF = bmax − bG.” The paper is careful about which friction does what: households’ limited bond-market participation is what makes UCFX non-zero, but “for households to face an arbitrage opportunity, it must be that financial intermediaries do not fully exhaust it” — which requires either intermediation frictions (Γ > 0 or χ > 0) or a risky environment, since ΔCov = 0 if σ = 0.

Shocks to the intermediation frictions Γ and χ move the CIP and UIP deviations “in the same direction and with the same magnitude,” whereas shocks to global risk σ move only the UIP deviation. Under the conditions of Proposition 1, bH* depends only on bCBF and bG, so an increase in collateral requirements Γ or in the convenience yield χ “generate a more positive CIP deviation,” and since cov(m*, X*)/Em* depends only on ρ and σ, the UIP deviation shifts identically. “Shocks to global risk σ, in contrast, only move the UIP deviation: an increase in global risk makes the UIP deviation more negative, while the CIP deviation remains the same.” This is the sense in which the two objects are informative about different things.

With parameters β = 0.98, σ² = 1, χ = 0.002, Γ = 0.5, α = 0.6, ρ = 0.2, g = 0.05 and bG = 0.01, and a policy rule where the nominal rate targets a fixed exchange rate subject to a zero lower bound, the UIP deviation is negative and the CIP deviation positive, and accumulating reserves pushes both toward zero cost. As bCBF rises, “the CIP deviation becomes more positive (and the UIP less negative), as the excess supply of domestic bonds arising from FX interventions is absorbed by an increase in the real interest rate,” achieved through exchange-rate depreciation because the interest rate is at the ZLB. A negative UCFX “represents a carry-trade arbitrage opportunity for households,” but households cannot issue domestic bonds, so interventions are effective. UCFX becomes less negative both because Z* rises and because “households become more exposed to currency risk,” reaching zero at bCBF = bmax − bG. In this specification interventions remain effective beyond that point too, because UCFX turns positive — households would want to run the opposite carry trade but are constrained in issuing foreign bonds. With a larger bG this changes: households then hold positive foreign bonds and can partially offset interventions by liquidating them, “but only up to the point where it exhausts their stock of foreign bonds.”

Households’ SDF is a standard consumption-based m = β(c′/c)^(−γ); the intermediaries’ SDF follows the intermediary asset-pricing literature and is proportional to the growth in their net worth, constructed as a capital ratio times aggregate wealth as in He, Kelly and Manela (2017). The paper is explicit about why the two are treated differently: the households’ SDF “is not reflected in asset prices, while the latter is.” Net worth is the product of a capital ratio η and aggregate wealth W, so that “the financial intermediaries’ marginal utility of wealth rises when either the aggregate wealth in the economy or the equity capital ratio is low” — the first capturing weaker fundamentals, the second the idea that “the intermediaries’ risk-bearing capacity is impaired when the capital ratio is low.” Four specifications are used, combining two capital-ratio measures — the He, Kelly and Manela primary-dealer equity capital ratio and the Adrian, Etula and Muir inverse book leverage of security brokers and dealers — with two wealth measures, US GDP and the MSCI World Equity Index. The capital-ratio risk factor is the residual from regressing the capital ratio on its lag, divided by the lagged ratio. The exercise sets β = 0.99 and γ = 10, uses log excess returns of CHF and JPY against USD, and splits the sample at 2010 with Newey-West standard errors.

Since 2010 the intermediaries’ covariance term is positive and statistically significant in most specifications — up to 5.3% for Switzerland and 6.4% for Japan — while the households’ covariance is small and insignificant; before 2010 the intermediary term is “generally an order of magnitude smaller (or negative).” For the CHF the post-2010 estimates are 5.3% and 5.0% under the two MSCI-based specifications and 0.96% and 0.8% under the GDP-based ones, all significant, against a household covariance of 0.01 (insignificant). For the JPY they are 6.4% and 6.2% (MSCI) and 1.02% and 1.01% (GDP), against a household covariance of 0.33 (insignificant). The 1999–2010 subsample shows near-zero or negative values for the intermediary term, while the household term is significant in that earlier period (0.25 for Switzerland, 0.7 for Japan) — the insignificance the paper leans on is a post-2010 feature. The reading offered: “being long in CHF or JPY tends to provide higher returns when the marginal utility of the wealth of financial intermediaries is high, which indicates that the CHF and the JPY behave as a hedge for international intermediaries,” and the post-2010 magnitudes are “quantitatively in line with the UIP deviations depicted in Figure A.1.” Applying Proposition 2, “for Switzerland and Japan… it is not CIP but UIP deviations that should matter for FX interventions since cov(m, x*)/Em is not significantly different from zero.”

Adler and Mano (2021) estimate a negative ex-ante quasi-fiscal cost of intervention for Japan and Switzerland over 2002–2013 using UIP deviations; this paper reaches a negative cost too, but from a welfare rather than a quasi-fiscal standpoint, and stresses the two need not coincide. Adler and Mano cover 73 countries and find the cost positive for most of them. The paper’s own contribution is stated carefully: “we examine the cost of intervention from the welfare point of view, and find that it is also negative for Japan and Switzerland, but that it is not equal to UIP deviations in general” — the equality holds only under the condition in Proposition 2(ii), which is what the empirical section tests.

The central bank, treated as a constrained planner maximising household welfare, sets reserves so that the marginal benefit of intervention is zero, where that benefit is the utility gain minus a dynamic terms-of-trade externality. The planner’s first-order conditions yield MBFX = −UCFX − μ = 0, where μ is “a dynamic terms-of-trade externality (as in Costinot et al., 2014)” arising because interventions distort the interest rate and exchange rate. μ depends on Γ, since “FX interventions have an impact on equilibrium prices only if Γ > 0”; when the country is short in domestic currency, reducing the excess return on foreign currency is costly, so μ > 0. Two consequences follow: “the social benefit of FX interventions MBFX is strictly higher than the private benefit −UCFX,” and “the central bank has an incentive not to fully shut down its risk-adjusted foreign currency excess return in order to maximize its profit,” a term the paper describes as “the central bank’s rent as a monopolistic issuer of domestic bonds.” Because MBFX > −UCFX, the central bank’s desired level of gross foreign liabilities is below what households want, so optimal gross liabilities b̂ < bmax whenever Γ > 0, with equality when Γ = 0; optimal reserves are then b̂CBF = b̂ − bG.

Proposition 4: optimal FX interventions are increasing in global risk σ, and decreasing in the intermediation frictions Γ and χ, in the domestic output exposure to global risk α, and in the supply of government bonds bG. The economics offered: “risk tends to increase the covariance differential ΔCov, which generates an excess benefit of FX interventions, while the intermediation frictions generate a cost,” and greater exposure of domestic output to global risk “decreases the covariance differential and generates a cost.” The government-bond result follows from substitutability: “if the government issues more bonds, then this reduces the need for the central bank to issue liabilities through FX interventions.” A caveat is stated for the risk result — the derivative sign requires Γ small, which holds under the paper’s technical condition.

Proposition 5: as global risk rises, the CIP deviation becomes more positive, the UIP deviation more negative, and the utility cost more negative. Higher risk “affects positively the foreigners risk premium,” making the UIP deviation more negative and the utility gain of reserves larger, so the planner accumulates more reserves; but “it is not in the planner’s interest to completely offset the impact of risk on UCFX, because the monopoly rent increases with risk as the foreign intermediaries have more appetite for the domestic currency.” The CIP deviation rises “as financial intermediaries need to absorb more capital inflows to finance the excess domestic liabilities bH* resulting from the interventions.” The second numerical illustration confirms this and adds that a higher level of public debt bG “reduces the domestic currency excess return… through a lower interest rate or an appreciated currency,” because higher net foreign liabilities raise households’ period-2 marginal utility, making them more risk averse and reducing the benefit of the carry trade. In that exercise the ZLB binds for σ² ≥ 0.62, and optimal reserves are positive only in the low-public-debt case (bG = 0.5); with bG = 1.1 the central bank would want to be long domestic and short foreign bonds, “however, this is possible only if the central bank is allowed to be short in foreign currency.”

Both countries show domestic households valuing their currency’s hedging property less than international investors do, but “the incentives for intervention are stronger for Switzerland as its public debt is much smaller than in Japan.” This follows from Proposition 4(iv). The conclusion also situates the exercise in the post-GFC environment: “systematic deviations from CIP, an increased demand for safe assets, and an expansion in central banks balance sheets,” alongside “a stronger demand for safe-haven currencies and more FX intervention by these countries’ central banks” — noting that “the spectacular increase in the balance sheet of the Swiss National Bank has occurred exclusively through the purchase of foreign assets.”

The two-period horizon, and the fact that sterilised interventions cannot address intertemporal distortions. On the horizon: the two-period assumption “allows us to assume that the period-2 exchange rate is exogenous and its correlation with the global factor is given.” With more periods, “anticipated future FX interventions could affect the exchange rate dynamics and its stochastic properties,” and the safe-haven status of a currency would itself become endogenous; the authors state Proposition 2 and the UCFX equations “would remain unchanged” because the exchange-rate process is taken as given by households and intermediaries, and flag “a comprehensive dynamic extension, in which a safe-haven currency emerges endogenously” as future research. On the instrument: “sterilized FX interventions cannot address intertemporal optimality,” because the foreign-currency no-borrowing constraint “cannot be relaxed by sterilized FX intervention since changes in bH* are offset by changes in bCBF.” An appendix extension in which the central bank performs fiscally-backed unsterilised interventions achieves both intertemporal optimality and MBFX = 0.