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---

### Paper structure and empirical context
- Effects stronger before the Great Recession, likely related to the importance of shale oil production in the US since 2010 and the secular downtrend in North Sea oil production in the UK.
- Results align with Juvenal (2011) and contrast with Bergin (2006) and Lubik and Schorfeide (2006).
- Positive global uncertainty shocks generally lead to dollar appreciation.
- Paper organization:
  - Section II: theory for FX risk premiums and a small GE model showing importance of risk premiums and policy divergence for exchange rate dynamics.
  - Section III: measurement of the FX risk premium and empirical characteristics, and Consensus forecasts.
  - Section IV: SVAR analysis.
  - Section V: recent event studies.
  - Section VI: conclusion.

### Theory: FX risk premium and uncovered interest parity (UIP)
- No-arbitrage relation between domestic and foreign interest rates with foreign currency holds at all horizons (see Appendix A).
- UIP with FX risk premium term (in original notation):
  - Equation (1.2): i*_{t+j} - i_{t+j} = E_t Δs_{t+j} - rp_{t,j}
  - rp_{t,j} denotes the FX risk premium for horizon j.
- Interpretations and implications:
  - An increase in rp_t = increase in preferences for holding U.S. dollar-denominated assets vis a vis foreign-currency assets.
  - For given expected depreciation, a higher FX risk premium allows a lower US interest rate.
  - Risk premium determined by covariance between the pricing kernel and home currency depreciation (Appendix A).
  - Higher domestic uncertainty should lead to a decline in the risk premium.
  - Higher global uncertainty typically induces a “flight to safety” (increase in preferences for US assets).
  - Monetary policy shocks, policy uncertainty, and oil price movements can affect rp by altering exchange rate or SDF stochastic properties.

### Small two-country sticky-price model (role of rp and policy divergence)
- Model features:
  - Small two-country sticky-price model under perfect capital mobility and flexible exchange rates (building on Benigno and Benigno 2008).
  - Core element: UIP condition (equation 1.2).
  - Closure: monetary policy rule; backward-looking IS and Phillips curves; monetary rule reacts to inflation and output gaps; intercept captures neutral rate.
  - Shocks: three cyclical shocks (IS, Phillips, monetary rule), a 1-year ahead news shock to monetary policy (forward guidance), exogenous neutral rate process.
- Forward guidance specification:
  - υ_{t+1|t} = 0.5 υ_{t+2|t−1} (presented in original notation).
  - Deviations driven by current and past monetary policy announcements, θ_t, discounted geometrically.
- Modeling choice for FX risk premium:
  - Construct rp directly from survey data (Consensus) and estimate a stochastic process for the observed rp rather than pinning it to macro variables.

### Model equations, calibration, and parameters
- Model expressed in country differentials (˜x* = x* − x) with lag operator L.
- Calibration and numeric details:
  - Monthly frequency using U.S. and UK data from 1990 to 2015.
  - Standard deviations of monetary policy and forward guidance shocks set at 12.5 bps (Gertler and Karadi 2015).
  - Neutral rate differential process calibrated to roughly match evolution of U.S. and UK short-term rates.
  - τ_g = 0.25/3 and τ_p = 1/3 with φ = 3.
  - Persistence = 0.9; output sensitivity to the interest rate gap is unitary.
  - Long-term policy rate responses to inflation and output included (full parameterization in equation block 1.3 in source).

### Model results and mechanisms
- Exchange rate determined by cumulated expected future short-term rates and FX risk premiums (equation (1.4)).
- Impulse-response findings (Figures 2–3):
  - Idiosyncratic shocks raising home inflation and output → little and not very persistent home currency appreciation.
  - Monetary policy tightening → brief appreciation unwound as policy reacts to weaker inflation and output.
  - Risk premium shock → strong direct impact on exchange rate but not long lasting.
  - Neutral rate shock (policy divergence) → substantial and persistent exchange rate effects through future expected short-term rates.
  - US forward guidance shock announcing tighter policy 12 months ahead → appreciation of the U.S. dollar today despite small short-term differential move; later implementation can produce negative covariance between exchange rate and short-term differential.
- Variance decomposition (Table 1):
  - Cyclical and monetary policy shocks explain little of exchange rate forecast error variance at short and long horizons.
  - Neutral rate shocks can explain more than 2/3 of low frequency (level) movements of the exchange rate.
  - Risk premium shocks explain most short-term fluctuations (changes) in the exchange rate.

### Measurement and properties of the FX risk premium
- Measurement approach:
  - FX risk premium defined using UIP-based framework; constructed from Consensus Economics exchange rate forecasts matched to interest rates on the specific survey day.
  - Bilaterals: $/euro, $/sterling, $/yen, and $/can.
  - Data: Eurocurrency deposit rates where possible; Bloomberg government bond rates otherwise; sample constrained to start in 1989 for Consensus forecasts.
- Forecast and dispersion properties:
  - Consensus forecasts show significant cross-forecaster dispersion (Figure 4).
  - Forecast changes less volatile than actual changes; mean forecast error converges to zero with horizon.
  - Near-term Consensus forecasts do worse than random walk at the 3-month horizon in RMSFE; RMSFEs close at 1-year; Consensus forecasts have lower RMSFEs at 2-year horizon (1 percent significance for both all and dollar-only bilaterals).
- Exact dispersion and forecast statistics (Table 2 and Table 3; sample 1990–2016 monthly):
  - Table 2: Exchange Rate Changes (standard deviation; average across four bilaterals)
    - Expected 3-month: 9.42
    - Actual 3-month: 21.71
    - Expected 1-year: 4.31
    - Actual 1-year: 10.32
    - Expected 2-year: 2.86
    - Actual 2-year: 7.31
  - Table 3: Bilateral Forecast Errors (dollar bilaterals)
    - 3-Month: Mean -2.10; RMSFE 22.05; Kurtosis 1.49
    - 1-Year: Mean -0.46; RMSFE 9.83; Kurtosis -0.28
    - 2-Year: Mean -0.19; RMSFE 6.49; Kurtosis -0.55
  - Random walk comparison statistics (All bilaterals and Dollar bilaterals) reported as means, RMSFE ratios, and kurtosis in source.
  - Distributional feature: Consensus forecasts have smaller tails (lower kurtosis) than random walk forecasts.
- Risk premium estimates and stats (Consensus forecasts 1990–2016 at 1-year horizon; Table 4):
  - Standard dev.: GBP 2.5* ; EUR 4.5 ; CAD 2.43*** ; JPY 4.47*** ; Weighted 2.59**
  - Mean: GBP .23* ; EUR -.16 ; CAD 1.13*** ; JPY -3.13*** ; Weighted -.28**
  - Notes: For UK and euro the mean is not statistically different from zero at the 5 percent level; CAD mean positive; JPY mean negative.
- Spectral decomposition: substantial part of rp variance explained by cycles longer than 5 years (Figure 8).
- Historical patterns:
  - Euro, Sterling, and Loonie rp particularly high at turn of the century (preference for U.S. assets).
  - Yen rp negative following Asian crisis through mid-2000s.
  - Average FX premium across major dollar bilaterals declined before the GFC; preferences for US assets increased during the crisis except for Yen.

### SVAR analysis: identification, results, and role of rp
- SVAR setup:
  - Monthly SVAR for each dollar bilateral covering 1993:1–2016:3.
  - Variables: VIX, WTI, Consensus one-year GDP forecast differential (dY), Consensus one-year inflation forecast differential (dπ), one-year interest rate differential (di1), risk-premium (RP), 10-year interest rate differential (di10), nominal exchange rate (S). All variables in logs except interest rate differentials and risk premiums.
  - Dynamic ordering: VIX, WTI, expected GDP differential, expected inflation differential, short-rate differential, risk premium, long-rate differential, exchange rate.
  - Timing: rp and forecast differentials observable on survey day; other variables averaged over previous week.
- Identification of structural shocks:
  - Global risk sentiment shock = VIX equation innovation.
  - Oil price innovations = risk-preserving oil shocks (affect expected GDP and interest differentials but not VIX).
  - FX-specific rp shock = does not move contemporaneous VIX.
  - Policy divergence shock = innovations in long-term interest rate differentials that do not contemporaneously affect VIX, expected inflation differentials, and rp.
- Key impulse-response and variance decomposition findings (Figures 9A–9D):
  - Global risk sentiment shock:
    - Persistent U.S. dollar appreciation vs CAD, EUR, GBP; U.S. dollar depreciation vs JPY (flight-to-safety).
    - Increases FX risk premium (preference for U.S. assets), except for JPY which shows safe-haven behavior.
  - Oil price shock:
    - Depreciation of the U.S. dollar against all currencies; an 8 percent increase in oil price leads to U.S. dollar depreciation between 0.25 percent and 0.8 percent on impact.
    - CAD and JPY responses more persistent than EUR and GBP.
    - For Canada, WTI shocks explain significant share of rp dynamics.
  - Cyclical shocks and short-term rate differential shocks: transitory or minor effects on exchange rate and rp.
  - Policy divergence (neutral rate) shocks: larger role for Loonie and Euro; less so for Pound and Yen.
  - FX-specific rp shocks: explain almost half of exchange rate variations at short horizons and a significant part at longer horizons.
  - Global risk shocks: relevant both directly and indirectly (via rp).
- Monetary policy shocks and rp:
  - Identified SVAR shocks explain about 50 percent of forecast error variance of rp for most dollar bilaterals.
  - Empirical UIP failure induces positive covariance between UIP-based rp and interest rate differentials (monetary easing can be associated with higher rp in practice).

### Appendix A3, robustness, and alternative risk sentiment measures
- Appendix A3: exchange rate impulse responses using the excess bond premium instead of VIX; sample comparisons pre-Great Recession and full-sample.
- Differences in exchange rate responses to WTI shocks across samples suggest the impact has declined more recently, possibly due to shale oil and North Sea trends.
- VAR robustness checks: Figures A1–A4 present alternative impulse responses and variance decompositions (including excess bond premium as global risk factor) for time spans 1993M1 – 2016M03 and 1993M1 – 2007M12.

### CTW specification, proxy VAR, and monetary policy surprises
- CTW (Christiano, Trabandt and Walentin (2011)) specification posits risk assessment falls when domestic interest rate reduced; functional form presented in source.
- Paper’s rp measure allows direct testing of CTW and investigation of how rp responds to monetary policy shocks.
- Proxy VAR blending:
  - Monetary policy surprise measures (U.S. and UK) added to benchmark VAR; surprises ordered first.
- Findings on monetary policy surprises:
  - U.S. monetary policy shocks (Gertler and Karadi 2015 measures):
    - Short-lived negative impact on Euro area and Japan rp.
    - Positive effect on Canadian rp.
    - UK rp less significantly affected but moves with Euro and Japan directionally.
  - UK monetary policy shocks: small and generally insignificant effects on rp and Euro exchange rate.
  - Interpretation: results generally confirm CTW specification—positive monetary policy shock tends to increase perceived domestic risk (except Canada, reflecting trade links to U.S.).
  - Monetary policy shocks explain little of exchange rate variance (consistent with theoretical results).

### Event studies: taper tantrum and non-U.S. announcements
- Taper Tantrum (Bernanke May 2013):
  - Rally in U.S. 10-year yield; not universal dollar appreciation.
  - Much of rally reflected increase in U.S. term premium rather than expected future policy rates.
  - Bilateral highlights:
    - Euro: 10-year differential fell ~100 bps; euro appreciated as decline in rp (preference for euro assets) offset falling differential.
    - Yen: dollar appreciated somewhat post-speech but much sharper before speech; pre-speech rising rp and declining di10; post-speech decline in rp but larger decline in yen di10 (100 bps versus 60 bps) sustained dollar appreciation.
    - Loonie: depreciation began before taper tantrum along with declining di10; rp declined but volatile.
    - Pound: appreciated considerably post-speech; di10 dynamics showed rise in UK gilt yield relative to UST in subsequent months.
- Non-U.S. forward guidance and surprises (Draghi Jackson Hole Aug 22, 2014; ECB QE Jan 2015; BoC cut Jan 21, 2015):
  - Euro: di10 declining and rp rising pre-Draghi; depreciation accelerated after speech and QE; euro stabilized and appreciated in April 2015 as di10 rebounded and rp declined.
  - Loonie: after BoC cut Jan 21, 2015, di10 declined markedly; loonie depreciated tracking di10 with less monthly volatility; rp fell significantly in quarter following cut (preference for Canadian assets).
- Event-study conclusions:
  - Policy divergence (10-year differentials) important in recent dollar appreciation.
  - rp movements can offset or reinforce effects depending on shock source and bilateral.

### Overall conclusions and policy-relevant outlook
- Long-term interest rate differentials (policy divergence) are key drivers, especially for the euro and the loonie.
- Risk premiums play a major role in explaining dollar movements.
- Global risk sentiment shocks increase preference for the dollar (and the yen).
- Oil shocks are more relevant for commodity currencies such as the loonie, and to a smaller extent the British pound.
- Cyclical shocks (monetary policy shocks and output growth differential shocks) explain little of exchange rate movements.
- Looking ahead:
  - If monetary policy divergence persists it will continue to drive dollar movements.
  - This effect can be offset or reinforced by FX risk premium movements.
  - Oil price dynamics could play an important role depending on the bilateral.
  - An increase in global uncertainty will generally lead to appreciation of the U.S. dollar and Yen.

*Source: excerpt from the supplied IMF working paper content unit _wp16125 — Appendix 2 (Figures A3-4) and associated sections.*

### Appendix 2 (Figures A3-4), these results appear to be even stronger before the Great Recession, likely related to

### _wp16125 - Appendix 2 (Figures A3-4), these results appear to be even stronger before the Great Recession, likely related to

### Paper structure and key empirical context
- The paper finds that effects are stronger before the Great Recession, likely related to the importance of shale oil production in the US since 2010 and the secular downtrend in North Sea oil production in the UK.
- Results align with Juvenal (2011) (little role for monetary policy shocks in explaining exchange rate movements) and contrast with Bergin (2006) and Lubik and Schorfeide (2006) (which find a disproportionate role for monetary policy shocks).
- Positive global uncertainty shocks generally lead to dollar appreciation.
- The rest of the paper is organized as:
  - Section II: theory for FX risk premiums and a small GE model showing importance of risk premiums and policy divergence for exchange rate dynamics.
  - Section III: measurement of the FX risk premium and empirical characteristics, and Consensus forecasts.
  - Section IV: SVAR analysis.
  - Section V: recent event studies.
  - Section VI: conclusion.

### Theory: why FX risk premiums and long-term interest rates matter
- Fundamental no-arbitrage relation (absence of default risk, capital controls, transaction costs) between domestic and foreign interest rates with foreign currency must hold at all horizons (see Appendix A).
- Equation (1.1) (in original notation) links the spot exchange rate St, the pricing kernel m, and the foreign risk-free rate.
- Under log-normality and manipulation, relation becomes uncovered-interest-parity (UIP) with a FX risk premium term:
  - Equation (1.2): i*_{t+j} - i_{t+j} = E_t Δs_{t+j} - rp_{t,j}
  - rp_{t,j} denotes the foreign exchange (FX) risk premium for horizon j.
- Interpretations and implications:
  - An increase in rp_t can be interpreted as an increase in preferences for holding U.S. dollar-denominated assets vis a vis foreign-currency assets.
  - For given expected depreciation, a higher FX risk premium allows a lower US interest rate.
  - The risk premium is determined by changes in the covariance between the pricing kernel and home currency depreciation (see Appendix A).
  - Higher domestic uncertainty should lead to a decline in the risk premium.
  - Higher global uncertainty typically induces a relative increase in foreign investor perception of risk, inducing a “flight to safety” (increase in preferences for US assets).
  - Monetary policy shocks, policy uncertainty, and oil price movements can affect the FX risk premium by altering stochastic properties of the exchange rate or the SDF.

### Small illustrative macroeconomic model (setup and role of risk premium)
- The model is a small two-country sticky-price model under perfect capital mobility and flexible exchange rates (building on Benigno and Benigno 2008).
- Core element: UIP condition (equation 1.2) relating home and foreign interest rates.
- Model closure:
  - Monetary policy rule.
  - Backward-looking IS and Phillips curves for each country.
  - Monetary rule reacts to inflation and output gaps; intercept captures neutral rate.
  - Small feedback: exchange rate appreciation reduces both inflation and output, ceteris paribus.
- Shocks and additional features:
  - Three cyclical shocks affecting IS, Phillips, and monetary policy rule respectively.
  - A 1-year ahead news shock added to monetary policy rules to capture effects of central bank announcements (forward guidance).
  - Neutral rate modeled as an exogenous process.
- Modeling the FX risk premium:
  - Literature lacks consensus on microfoundations for the FX risk premium (Engel 2013 and 2015).
  - Many solution methods (low-order approximations) rule out movements in the risk premium by construction.
  - Authors construct the FX risk premium directly from survey data and estimate a stochastic process for the observed FX risk premium rather than pinning it to macro variables.

### Model equations and calibration
- Model expressed in country differentials (˜x* = x* − x) with lag operator L.
- Forward guidance specification:
  - Forward guidance, υ_t, reflects information on future (1-year ahead) policy rate deviations from systematic policy.
  - υ_{t+1|t} = 0.5 υ_{t+2|t−1} (presented as ߥ_{௧ାଵଶ = 0.5ߥ_{௧ାଵଵ} in original notation).
  - Deviations driven by current and past monetary policy announcements, θ_t, with past ones discounted geometrically.
- Calibration details:
  - Monthly frequency using U.S. and UK data from 1990 to 2015.
  - Standard deviations of the IS and Phillips’ curve and parameter κ set to match second moments of GDP and inflation differentials between U.S. and UK.
  - Exogenous risk premium process estimated based on constructed 1-year U.S. dollar-UKP risk premium measure (see Section III).
  - Neutral rate differential process calibrated to roughly match evolution of U.S. and UK short-term rates.
  - Standard deviations of monetary policy and forward guidance shocks set at 12.5 bps (Gertler and Karadi 2015).
  - In the monetary policy rule, the long-term policy rate responses to inflation and output are included (parameters and full equations in equation block 1.3).

### Conceptual implications and empirical strategy
- The model illustrates that FX risk premiums and policy divergences matter greatly for explaining exchange rate dynamics.
- Because macro models often exclude endogenous risk-premium movements, constructing rp from survey data allows empirical assessment of its stochastic behavior and role.
- Empirical analysis will include SVAR analysis and event studies to evaluate how monetary policy shocks, uncertainty, and oil price movements translate into exchange rate responses through the risk premium channel.

*Source: _wp16125 - Appendix 2 (Figures A3-4), these results appear to be even stronger before the Great Recession, likely related to*

### 1.5 and 0.5

### 1.5 and 0.5

### Model Results
- Model setup: persistence is 0.9; output sensitivity to the interest rate gap is unitary; τ_g = 0.25/3 and τ_p = 1/3 with φ = 3.  
- Key mechanisms:
  - Exchange rate is determined by the cumulated sum of expected future short-term rates and FX risk premiums as expressed in equation (1.4): s_t = sum_{i=0}^{∞} E_t ( ... ) — the model implies exchange rates respond to changes in long-term interest rate differentials once long-term rates are adjusted for the term premium.
- Impulse-response findings (Figures 2–3):
  - Idiosyncratic shocks that increase inflation and output of the home country (relative to foreign) produce little and not very persistent home currency appreciation.
  - A monetary policy tightening shock induces only a brief appreciation of the home currency that is unwound when systematic monetary policy reacts to weaker inflation and output.
  - A shock to the risk premium has a strong direct impact on the exchange rate but is not long lasting.
  - A neutral rate shock (policy divergence) produces substantial and persistent exchange rate effects, working mainly through future expected short-term rates and introducing longer-term predictability.
  - A US forward guidance shock announcing tighter policy 12 months ahead generates an appreciation of the U.S. dollar today even though the short-term interest rate differential barely moves; when policy is implemented the exchange rate and short-term differential can show negative covariance (dollar depreciates while US rates rise).
- Variance decomposition (Table 1):
  - Cyclical and monetary policy shocks explain little of the exchange rate forecast error variance at both short and long horizons.
  - Neutral rate shocks can explain more than 2/3 of low frequency movements (level) of the exchange rate.
  - Risk premium shocks explain most short-term fluctuations (changes) in the exchange rate.

### The FX Risk Premium: Measurement and Properties
- Measurement approach:
  - FX risk premium defined using UIP-based framework: rpi_{t,t+j} = E_t s_{t+j} + ... (as in source formula).
  - Focused bilaterals: $/euro, $/sterling, $/yen, and $/can.
  - Data: Eurocurrency deposit rates where possible and generic government bond rates from Bloomberg otherwise; exchange rate forecasts from Consensus Economics (sample constrained to start in 1989).
  - Consensus forecasts matched to exchange rates and interest rates prevailing on the specific survey day each month.
- Properties of Consensus forecasts:
  - Consensus forecasts exhibit significant cross-forecaster dispersion as shown by standard deviations across forecasts (Figure 4).
  - Forecast errors and volatility:
    - Forecast changes (expected changes) are less volatile than actual changes and do not have a significant bias over the whole sample, especially at longer horizons.
    - Mean forecast error converges towards zero as horizon increases (forecasters do better at longer horizons).
    - Near-term Consensus forecasts do worse than random walk at the 3-month horizon in RMSFE; RMSFEs are very close at 1-year; Consensus forecasts have lower RMSFEs at 2-year horizon (1 percent significance for both all and dollar-only bilaterals).
- Exact dispersion and forecast statistics reported:
  - Table 2: Exchange Rate Changes (standard deviation 1/; average across four bilaterals; sample 1990-2016 monthly)
    - Expected 3-month: 9.42
    - Actual 3-month: 21.71
    - Expected 1-year: 4.31
    - Actual 1-year: 10.32
    - Expected 2-year: 2.86
    - Actual 2-year: 7.31
  - Table 3: Bilateral Forecast Errors (sample 1990-2016; comparison against random walk R.W.)
    - Dollar bilaterals: Mean and RMSFE and Kurtosis
      - 3-Month: Mean -2.10; RMSFE 22.05; Kurtosis 1.49
      - 1-Year: Mean -0.46; RMSFE 9.83; Kurtosis -0.28
      - 2-Year: Mean -0.19; RMSFE 6.49; Kurtosis -0.55
    - Comparison with R.W. (All bilaterals): 3-Month Mean -0.01; RMSFE 1.10; Kurtosis -0.70; 1-Year Mean -0.13; RMSFE 1.05; Kurtosis -0.31; 2-Year Mean 0.03; RMSFE 0.95; Kurtosis -0.24
    - Comparison with R.W. (Dollar bilaterals): 3-Month Mean -0.32; RMSFE 1.09; Kurtosis -0.74; 1-Year Mean -0.30; RMSFE 1.01; Kurtosis -0.45; 2-Year Mean -0.08; RMSFE 0.93; Kurtosis -0.19
  - Distributional feature: Consensus forecasts have smaller tails (lower kurtosis) than random walk forecasts — many smaller misses drive forecast-error variance rather than few large misses.
- Risk premium estimates and historical evolution:
  - Risk premiums for the four major U.S. bilaterals show persistent dynamics and vary sign over time (Figure 7).
  - Table 4: Risk Premium Statistics (Consensus forecasts 1990–2016 at 1-year horizon)
    - Standard dev.: GBP 2.5* ; EUR 4.5 ; CAD 2.43*** ; JPY 4.47*** ; Weighted 2.59**
    - Mean: GBP .23* ; EUR -.16 ; CAD 1.13*** ; JPY -3.13*** ; Weighted -.28**
    - Note: For UK and euro the mean is not statistically different from zero at the 5 percent level; Loonie (CAD) mean positive and Yen mean negative (reflecting safe-haven status and low nominal rates).
  - Spectral decomposition: a substantial part of risk premium variance is explained by cycles longer than 5 years (Figure 8).
  - Historical notes:
    - Euro, Sterling, and Loonie risk premiums particularly high at the turn of the century (preference for U.S. assets).
    - Yen enjoyed negative risk premiums following the Asian crisis through mid-2000s.
    - Average FX premium across major dollar bilaterals declined before the GFC; preferences for US assets increased during the crisis except for Yen-denominated assets.

### VAR Analysis (SVAR) — Identification, Results, and Role of Risk Premiums
- Data and variables:
  - Monthly SVAR for each of 4 dollar bilaterals covering 1993:1–2016:3.
  - Variables included: VIX, WTI crude oil price (WTI), Consensus one-year-ahead GDP growth forecast differential (dY), Consensus one-year-ahead inflation forecast differential (dπ), one-year interest rate differential (di1), the risk-premium (RP), the 10-year interest rate differential (di10), and nominal exchange rate (S). All variables in logs except interest rate differentials and risk premiums.
  - Dynamic ordering used: VIX, WTI, expected GDP differential, expected inflation differential, short-rate differential, risk premium, long-rate differential, exchange rate.
  - Timing: constructed risk premiums and forecast differentials observable on a specific survey day; other variables averaged over the previous week consistent with survey timing.
- Identification strategy:
  - First structural shock (VIX equation) = global risk sentiment shock (affects all variables contemporaneously).
  - Oil price innovations = risk-preserving oil shocks (move expected GDP and interest differentials but not VIX).
  - FX-specific risk premium shock = does not move contemporaneous VIX (interpreted as FX-specific risk shock).
  - Policy divergence shock = innovations in long-term interest rate differentials that do not contemporaneously affect VIX, expected inflation differentials, and the FX risk premium (long-term rates purged of term premium to reflect expected short rates).
- Impulse-response and variance decomposition findings (Figures 9A–9D):
  - Global risk sentiment shock:
    - Persistent U.S. dollar appreciation against CAD, EUR, GBP; U.S. dollar depreciation against JPY (flight-to-safety), and increases FX risk premium (preference for U.S. assets), except JPY which shows safe-haven behavior.
  - Oil price shock:
    - Depreciation of the U.S. dollar against all currencies; an 8 percent increase in oil price leads to U.S. dollar depreciation between 0.25 percent and 0.8 percent on impact.
    - Persistence differs across countries; CAD and JPY responses are more persistent than EUR and GBP.
    - For the Loonie, WTI shocks explain a significant share of FX risk premium dynamics.
  - Cyclical shocks (inflation/output) and short-term rate differential shocks:
    - Transitory or minor effects on exchange rate and FX risk premium.
  - Policy divergence (neutral rate) shocks:
    - Play a larger role for Loonie and Euro exchange rate movements; less so for Pound and Yen where risk premium shocks are relatively more important.
  - FX-specific risk premium shocks:
    - Explain almost half of exchange rate variations at short horizons and a significant part at longer horizons.
  - Global risk shocks:
    - Relevant both directly and indirectly (via FX risk premium) in explaining exchange rate movements.
- Role of monetary policy shocks on FX risk premiums:
  - Identified SVAR shocks explain about 50 percent of forecast error variance of the FX risk premium for most dollar bilaterals.
  - The empirical failure of UIP induces a positive covariance between the UIP-based risk premium and interest rate differentials — e.g., monetary easing (lower domestic rates) can be associated with higher FX risk premiums (mechanism discussed in source).

*Source: IMF staff analysis in _wp16125 - 1.5 and 0.5*

### Appendix A3 has the exchange rate impulse responses using the excess bond premium rather than VIX as the

### _wp16125 - Appendix A3 has the exchange rate impulse responses using the excess bond premium rather than VIX as the

### Appendix A3 and sample comparisons
- Appendix A3 presents exchange rate impulse responses using the excess bond premium as the global risk sentiment factor instead of VIX and compares pre-Great Recession and full-sample results.
- The differences in exchange rate responses to WTI shocks across samples suggest that the impact has declined more recently.
- Possible drivers cited:
  - importance of shale oil production in the US since 2010
  - secular downtrend in North Sea oil production in the UK

### FX risk premium measurement and UIP interpretation
- The FX risk premium used in the paper is calculated using expectation surveys.
- It is possible to interpret the residual of a UIP regression as a risk premium whenever the UIP regression takes the form shown in the source text (notation preserved).
- Empirical regularity: in UIP regressions the coefficient on the interest rate differential is often negative (rather than 1). This bias implies the residual (interpreted as the risk premium) co-varies positively with the interest differential.

### CTW risk adjustment specification and testing
- The CTW (Christiano, Trabandt and Walentin (2011)) specification assumes a functional form that yields a fall in the assessment of domestic risk when the domestic interest rate is reduced.
- Their risk adjustment term is given in the functional form presented in the source text (notation preserved).
- The paper’s measure of the risk adjustment term (the risk premium) allows direct testing of the CTW specification and investigation of how risk is affected by monetary policy shocks.

### Monetary policy surprises and proxy VAR strategy
- The paper blends a traditional recursive identification strategy with monetary policy surprise data using a proxy VAR (Gertler and Karadi 2015).
- Monetary policy shock measures (U.S. and UK) are added to the benchmark VAR; the monetary policy surprise measures are ordered first in the VAR, with the remainder of the ordering unchanged from the benchmark.

Findings on monetary policy shocks:
- U.S. monetary policy shocks (Gertler and Karadi (2015) estimated shocks):
  - have a short-lived negative impact on Euro area and Japan risk premium
  - have a positive effect on the Canadian risk premium (see Figure 10A and 10B in source)
  - UK risk premium is less significantly affected but moves in same direction as Euro and Japan
- UK monetary policy shocks:
  - have some impact on risk premiums and the Euro exchange rate, but effects are generally small and insignificant
- Interpretation:
  - Results generally confirm CTW specification: a positive monetary policy shock appears to increase perceived domestic risk (except Canada, where a positive U.S. monetary shock causes FX risk premium to rise—preference for U.S. assets—and the Loonie to depreciate)
  - Canada’s differing response may reflect close trade links to the United States
  - Monetary policy shocks explain little of the variance of exchange rate dynamics (consistent with theoretical results of section II)

### Event studies: taper tantrum and non-U.S. central bank announcements
- Event studies complement VAR analysis by focusing on major announcements and helping to overcome invertibility problems.

A. Taper Tantrum (May 2013 Bernanke speech)
- Bernanke’s May 2013 speech catalyzed a significant and persistent rally in the U.S. 10-year treasury yield, but did not lead to universal dollar appreciation against all major bilaterals.
- Possible reasons:
  - much of the rally reflected an increase in the U.S. term premium rather than higher expected future policy rates
  - exchange rate moves also reflect interest rate moves in the other currency and changes in FX risk premiums (which tended to decline)
Key bilateral trends:
- Euro:
  - 10-year interest differential decreased by about 100 bps (trend started well before taper tantrum)
  - euro appreciated against the dollar as the decline in the FX risk premium (increasing preference for euro assets) more than offset the falling differential
- Yen:
  - dollar appreciated somewhat against the yen in months following the speech but appreciation was much sharper beforehand
  - pre-speech period: declining 10-year interest differential combined with a rising risk premium (preference for U.S. assets); sharp pre-taper moves reflect start of Abenomics (quantitative and qualitative easing in Japan in April 2013)
  - post-speech: decline in risk premium (preference for Yen assets); dollar continued to appreciate because post-taper decline in 10-year interest differential was more marked for the yen than for the euro (100 bps versus 60 bps)
- Loonie:
  - depreciation against the dollar began well before the taper tantrum, along with a decline in the 10-year interest differential
  - both trends continued after May 2013; risk premium also declined but was volatile, suggesting loonie dynamics driven more by the declining 10-year interest differential
- British Pound:
  - appreciated considerably against the dollar following the Bernanke speech
  - consistent with 10-year interest differential dynamics: though it declined somewhat immediately after the speech, it rose sharply in subsequent months as sterling 10-year UK gilt yield rose more than the 10-year U.S. treasury rate

B. Forward guidance and interest rate announcements/surprises outside the U.S.
- Two focal episodes:
  - Mario Draghi’s Jackson Hole speech in August 2014 and subsequent ECB QE announcement in January 2015
  - Bank of Canada surprise policy rate cut by 25 basis points on January 21, 2015
Key bilateral impacts:
- Euro:
  - prior to Draghi’s Jackson Hole speech, the 10-year interest differential was already declining while the risk premium was rising, supporting a depreciating euro
  - depreciation accelerated after Draghi’s speech and steepened after the QE announcement in January 2015; the decline in the 10-year rate was particularly sharp following that announcement
  - euro stabilized and began to appreciate in April 2015 as the 10-year interest differential rebounded and the risk premium began to decline
- Loonie:
  - after Bank of Canada cut policy rate by 25 basis points on January 21, 2015, the 10-year interest differential declined markedly, briefly rebounded, then declined again
  - depreciating loonie tracked these movements with less monthly volatility
  - initially loonie depreciated less than suggested by the decline in the 10-year interest differential, possibly because the risk premium fell significantly in the quarter following the cut (preference for Canadian assets), consistent with section IV.C results that lower domestic interest rates imply a reduction in the relative risk of holding home-currency assets (Christiano, et al. 2011)

Event study conclusions:
- Policy divergence (proxied by 10-year interest differentials) played an important role in recent dollar appreciation
- FX risk premium movements can offset or reinforce the effect depending on the shock source and dollar bilateral

### Overall conclusions and outlook
- Real and nominal exchange rates among major currencies often move in ways not closely connected to current or past macroeconomic variables.
- The paper focuses on risk premiums and the differential of the expected sum of short-term interest rates (policy divergence) using: simulations of a small macroeconomic model, event studies, and structural VAR analysis.
Key findings:
- Long-term interest rate differentials (policy divergence) are key drivers, especially for the euro and the loonie.
- Risk premiums play a major role in explaining dollar movements.
- Global risk sentiment shocks increase preference for the dollar (and the yen).
- Oil shocks are more relevant for commodity currencies such as the loonie, and to a smaller extent the British pound.
- Cyclical shocks (monetary policy shocks and output growth differential shocks) explain little of exchange rate movements.
- Event studies confirm the role of long-term interest rate differentials in recent dollar appreciation; risk premium movements can offset or reinforce this depending on shock source and bilateral.

Looking ahead (policy-relevant implications):
- If monetary policy divergence persists it will continue to drive dollar movements.
- This effect can be offset or reinforced by FX risk premium movements.
- Depending on the dollar bilateral, oil price dynamics could play an important role.
- An increase in global uncertainty will generally lead to appreciation of the U.S. dollar and Yen.

*Source: excerpt from the provided IMF working paper content unit.*

### 15. MIT press, 2001. 339-412.

### _wp16125 - 15. MIT press, 2001. 339-412.

### Figures: Exchange Rate Impulse Responses and Variance Decompositions
- Figure 9A. Canada
  - Panels:
    - (a). Exchange Rate
    - (b). Risk Premium
    - (c). Exchange Rate – Forecast Error Variance Decomposition
    - (d). Risk Premium – Forecast Error Variance Decomposition
  - Notes:
    - Dynamic responses of the exchange rate to a standard deviation innovation to all shocks in the VAR. x-axis: months, y-axes: percentage points.
    - The shaded bands are 68 percent confidence intervals.
    - An increase in the exchange rate implies a depreciation of the U.S. dollar against the Canadian Loonie.
    - Risk premium responses: x-axis: months, y-axes: 100 x risk premium. An increase in the risk premium can be interpreted as an increase in the preferences for holding U.S. dollar-denominated assets vis a vis the Canadian Loonie.
    - Forecast Error Variance Decomposition: x-axis: months, y-axes: share of variance due to the innovations in the VAR.

- Figure 9B. Euro
  - Panels:
    - (a). Exchange Rate
    - (b). Risk Premium
    - (c). Exchange Rate – Forecast Error Variance Decomposition
    - (d). Risk Premium – Forecast Error Variance Decomposition
  - Notes:
    - An increase in the exchange rate implies a depreciation of the U.S. dollar against the Euro.
    - Risk premium y-axes: percentage points. An increase in the risk premium can be interpreted as an increase in the preferences for holding U.S. dollar-denominated assets vis a vis the Euro.

- Figure 9C. United Kingdom
  - Panels:
    - (a). Exchange Rate
    - (b). Risk Premium
    - (c). Exchange Rate – Forecast Error Variance Decomposition
    - (d). Risk Premium – Forecast Error Variance Decomposition
  - Notes:
    - An increase in the exchange rate implies a depreciation of the U.S. dollar against the Pound.
    - Risk premium interpretation: increase in preferences for holding U.S. dollar-denominated assets vis a vis the Pound.

- Figure 9D. Japan
  - Panels:
    - (a). Exchange Rate
    - (b). Risk premium
    - (c). Exchange Rate – Forecast Error Variance Decomposition
    - (d). Risk Premium – Forecast Error Variance Decomposition
  - Notes:
    - An increase in the exchange rate implies a depreciation of the U.S. dollar against the Yen.
    - Risk premium interpretation: increase in preferences for holding U.S. dollar-denominated assets vis a vis the Yen.

### Monetary Policy Shock Responses (Figures 10A–10B, A5)
- Figure 10A. Impulse Response Functions of the Exchange Rate and the risk Premium to a U.S. Monetary Policy Shock
  - Notes:
    - Dynamic responses to a standard deviation innovation to the monetary policy shock.
    - Red lines: impulse responses to the risk premium; Blue lines: impulse responses to the exchange rates.
    - Shaded bands: 68 percent confidence intervals.
    - x-axis: months, y-axes: percentage points.
    - An increase in the exchange rate implies a depreciation of the U.S. dollar; an increase in the risk premium interpreted as increased preference for U.S. dollar-denominated assets.

- Figure 10B. Impulse Response Functions of the Exchange Rate and the risk Premium to a U.K. Monetary Policy Shock
  - Notes: same conventions as Figure 10A; an increase in the exchange rate implies a depreciation of the U.S. dollar.

- Figure A5. Impulse Response Functions of the Exchange Rate and the Risk Premium to a U.S. Monetary Policy Shock 1993M1-2007M12
  - Panels:
    - (a) Gertler and Karadi Shock
    - (b) Coibion Measures of Monetary Policy Shocks
  - Notes:
    - Dynamic responses to a standard deviation innovation to the monetary policy shock.
    - Red lines: risk premium; Blue lines: exchange rates.
    - Shaded bands: 68 percent confidence intervals.
    - x-axis: months, y-axes: percentage points.
    - An increase in the exchange rate implies a depreciation of the U.S. dollar and an increase in the risk premium interpreted as higher preference for U.S. dollar assets.

### Event Studies (Figures 11–12)
- Figure 11. Event Study: Taper Tantrum
  - Series and annotations shown:
    - Dates and markers include 5/22/13.
    - Panels show time series for $/CAD, $/EUR, $/UKP, $/JPY paired with FX Risk Premium and 10-year interest differentials (foreign minus US).
    - Axis labels and scales appear with numerical ticks such as 0.90, 0.93, 0.96, 0.99, 1.02, 1.05; 1.20, 1.25, 1.30, 1.35, 1.40; 1.50, 1.55, 1.60, 1.65, 1.70; 0.009, 0.010, 0.011, 0.012, 0.013.
    - Risk premium axis interpretation: (>0 = preference for US assets, LHS).
    - 10 year interest differential axis interpretation: (foreign minus US, LHS).

- Figure 12. Event Study: Non-US Monetary Policy Announcements/Surprises
  - Date markers and events include:
    - BOJ QE 10/31/14
    - Canada rate cut, ECB announces QE 1/21/15 - 1/22/15
    - Draghi Jackson Hole speech 8/22/14
  - Panels show $/CAD, $/EUR series with FX Risk Premium and 10-year interest differentials over Jan-14 to Jan-16.
  - Axis ticks include sequences: 0.70, 0.73, 0.76, 0.79, 0.82, 0.85, 0.88, 0.91, 0.94.

### VAR Robustness Checks (Appendix Figures A1–A4)
- Figure A1. Canada Dollar per Euro Bilateral Exchange Rate
  - Panels:
    - (a) Exchange Rate – Impulse Response Functions
    - (b) Exchange Rate – Forecast Error Variance Decomposition
  - Notes:
    - Dynamic responses to standard deviation innovations in the VAR; shaded bands: 68 percent confidence intervals.
    - An increase in the exchange rate implies a depreciation of the Loonie against the Euro.

- Figure A2. Canadian Dollar per UK Pound Bilateral Exchange Rate
  - Panels:
    - (a) Exchange Rate – Impulse Response Functions
    - (b) Exchange Rate – Forecast Error Variance Decomposition
  - Notes:
    - An increase in the exchange rate implies a depreciation of the Loonie against the Pound.

- Figure A3. Impulse Response Functions of the Exchange Rate – Excess Bond Premium instead of VIX. 1993M1 – 2016M03
  - Panels:
    - (a) Canada
    - (b) United Kingdom
    - (c) Euro
    - (d) Japan
  - Notes:
    - Dynamic responses to a standard deviation innovation to all shocks in the VAR; shaded bands: 68 percent confidence intervals.
    - Timestamps: 1993M1 – 2016M03.
    - Exchange rate interpretation: increases imply depreciation of the U.S. Dollar against Loonie, British Pound, Euro, Yen respectively.

- Figure A4. Impulse Response Functions of the Exchange Rate – Excess Bond Premium instead of VIX. 1993M1 – 2007M12
  - Panels:
    - (a) Canada
    - (b) United Kingdom
    - (c) Euro
    - (d) Japan
  - Notes:
    - Dynamic responses to a standard deviation innovation to all shocks in the VAR; shaded bands: 68 percent confidence intervals.
    - Timestamps: 1993M1 – 2007M12.
    - Exchange rate interpretation: increases imply depreciation of the U.S. Dollar against Loonie, UK Pound, Euro, Yen respectively.

### Appendix 1: Analytical Derivation of the FX Risk Premium
- No-arbitrage relation (absence of default risk, capital controls, and transaction costs) between spot (S_t) and forward (F_t*) exchange rates:
  - Equation label: (1.5)
  - Relation presented as: expexp_t t ii t t F S =*
  - Footnote: 1 If equation (1.5) does not hold, say expexp/ _tt ii tt FS <*, it is possible to follow a simple arbitrage strategy by borrowing in domestic currency, converting the funds in foreign currency and buying a foreign bond, and locking the future bond proceeds in domestic currency by entering into the forward contract today.
- Replacement of forward with future spot using stochastic discount factor m_t+j,t to price future (nominal) payoffs:
  - Equation label: (1.6)
  - Shown form: * ,1 exp0 tt tj ii tt tj t S E m S + - + +   - =    
  - Footnote: 2 The existence of a positive stochastic discount factor is equivalent to absence of arbitrage opportunities (see Cochrane 2005 for example).
- Under assumption [ ,1 [m] exp_t i t t t E + = ], rewrite:
  - Equation label: (1.7)
  - Shown form: * , exp t tj i tt tj t S E m S + - +  =  
- Under log-normality:
  - Equation label: (1.8)
  - Shown form: * 0.5[var (m ) var ()] cov(m ,); tt ttjttjt tjtj tj iiEsss + + + + + - +  + +  +
- FX risk premium of horizon j:
  - Equation label: (1.9)
  - Shown form: , 0.5[var (m ) var ()] cov(m ,). tjttjttjtjtj rpss + + + + = - +  - 

### Key methodological notes and conventions
- Throughout figures and appendices:
  - Dynamic responses are to a standard deviation innovation to all shocks in the VAR or to the monetary policy shock, as specified.
  - Shaded bands represent 68 percent confidence intervals.
  - Exchange rate increases are consistently interpreted as depreciations of the U.S. dollar (or of domestic currency vs. foreign currency, as specified).
  - Risk premium interpretation: an increase is interpreted as an increase in preferences for holding U.S. dollar-denominated assets.
  - Time spans explicitly referenced include 1993M1 – 2016M03 and 1993M1 – 2007M12.
  - Event-study dates explicitly referenced include 5/22/13, 10/31/14, 1/21/15 - 1/22/15, 8/22/14, and Jan-14 through Jan-16 sequences shown.

*Source: Authors’ calculations; content as presented in the supplied PDF chapter.*

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