## _wp13190

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---

### I. Introduction and research questions
- Context:
  - Unconventional monetary policies (UMP) became important after the 2008–09 global financial crisis and their effects on asset prices remain uncertain.
- Concerns:
  - Potential for UMPs to cause spillovers by distorting exchange rates and other asset prices.
  - Media claims linking UMPs to higher food commodity prices (example cited: Guardian, November 5, 2010).
- Key concepts:
  - “Excessive speculation” definitions: amount beyond hedging needs (Working’s T, Irwin and Sanders, 2010) or “sudden or unreasonable fluctuations or unwarranted changes in the price of [a] commodity” (CFTC).
  - Speculative bubbles as asset prices rising above fundamentals under rational expectations.
- Research questions:
  - Do UMPs raise or reduce uncertainty about the outlook for risk asset prices?
  - Are effects symmetric (affecting upside and downside risks)?
  - Does “excessive speculation” increase following a UMP event?
- Motive:
  - Greater probability of policy interest rates hitting the zero lower bound after the crisis increases the importance of understanding UMP effects and potential harmful side-effects.

### II. Empirical approach and hypothesis testing
- Null hypothesis:
  - UMPs have no effect on the distribution of asset price risk.
- Methodology:
  - Event study methodology applied to U.S. UMPs (speeches and public statements after FOMC meetings).
  - Estimate risk-neutral density functions (RNDs) from options prices by fitting a weighted average log-normal distribution subject to arbitrage constraints.
  - Fit performed for the 20 days immediately preceding a UMP event and for one test date after the event (t+1; estimation window t-1 to t-20).
- Assets analyzed:
  - Euro–U.S. dollar exchange rate; S&P500 equity index; five commodities: gold, crude oil, natural gas, corn, soybeans.
- Measures and tests:
  - Tail risk measures (5th and 95th percentile) and implied volatilities of liquid at-the-money options.
  - Hypothesis tests assess changes in asset price risk around UMP events.
- Detecting “excessive speculation”:
  - Formal testing difficult; evidence would be reflected in prices or RNDs.
  - Investor positioning for very large price gains (e.g., purchasing deep out-of-the-money call options) would create strong positive skew in the RND — a likely necessary, but perhaps not sufficient, condition for excessive speculation.

### III. Prior findings and contribution
- Prior consensus:
  - Little evidence that UMPs cause significant short-term changes in “risk asset” prices.
- Contribution of this paper:
  - Assesses effect of UMPs on the distribution of asset price risk (tails, skewness, implied volatilities) rather than only mean price levels.
  - Uses RND-based measures and event study framework to examine tail risk.

### IV. Definition of UMP and transmission channels
- UMP measures considered:
  - Lending to financial institutions; providing liquidity to important credit markets; large-scale asset purchase programs (LSAPs).
- Objectives:
  - Lending/liquidity: prevent fire sales from vanishing liquidity.
  - LSAPs: reduce interest rates along the term structure to stimulate activity.
- Four primary channels:
  - Portfolio balance channel: purchases alter relative valuations of imperfect substitutes (including commodities), increasing demand.
  - Signaling channel: unconventional measures signal lower policy rates in the future.
  - Confidence channel: announcements may signal worse prospects or boost confidence.
  - Liquidity/risk-premia channel: UMP may enhance market liquidity and reduce risk premia.
- Additional commodity channels:
  - Via interest rates and exchange rates; lower real interest rates and a depreciating U.S. dollar should lead to higher commodity prices.

### V. Methodology — recovering risk-neutral distributions (RNDs) from options
- Objective:
  - Map option price changes to changes in underlying probabilities under risk neutrality.
- Approach:
  - Fit a weighted mixture of lognormal distributions to options with identical expiries but different strikes to recover estimated density (captures fat tails and skew).
  - Compute cumulative-percentile statistics (e.g., 5th and 95th percentiles).
- Parametric specification and estimation:
  - fN(Sτ) = weighted average of N-component lognormal densities with weights ωi, parameters μi, σi, and βi = σi sqrt(τ).
  - Fit by minimizing squared distance between fitted and actual call and put prices subject to no-arbitrage discounting and weight constraints.
  - Use four lognormal mixtures (initially ω1 = ... = ω4), starting values μ ≈ 0 and σ = σIV (implied volatility of ATM option).
- Tail-risk metrics:
  - Tail risk measured as log distance between the 5th percentile price and mean (left/downside) and between the 95th percentile price and mean (right/upside), under risk neutrality.

### VI. Event-study design and statistical tests
- Event dating:
  - Tests on day following event (t+1) to account for market-close timing; estimation window = preceding 20 days (t-1 to t-20).
- Tests applied:
  - Patell’s (1976) aggregated t-test comparing ATM implied volatility and left/right tails at t+1 to sample mean over preceding 20 days.
  - Corrado (2010) small-sample ranking test (nonparametric).
  - Fixed-effects panel regression: xij = αi + γ d + εij, with d = 0 for t-20..t-1 and d = 1 at t+1; t-statistic on γ tests UMP event significance.
  - Conditional specification: interact event dummy with VIX gap (VIX at t-1 minus its mean at t-1 across all 14 events) to estimate γ2 and capture amplification under high uncertainty.

### VII. Data
- Assets: EUR/USD exchange rate, S&P500 equity index, gold, crude oil, natural gas, corn, soybeans.
- Options data: daily frequency from Thomson Reuters Datastream and exchanges; horizon = three months (closest expiration to three months ahead of each event).
- For each event:
  - About seven call and put options centered around ATM strike.
  - Spot price = current cash price.
  - Risk-free rate = 3-month yield from the zero coupon U.S. Treasury curve.
- Monetary policy events:
  - Standard dating for QE1, QE2, QE3; events are verbal or written communications (not actual operations).

### VIII. Key results (Section V)
- Sample:
  - 14 UMP events between 2008 and 2012.
- Main findings:
  - Reject null of no change in log distance between futures price and both left- and right-hand tails for full sample: tails shrink and move closer to futures prices following UMP easing events, implying reductions in both upside and downside tail risks.
  - No significant impact on at-the-money implied volatility.
  - Effects stronger on tails (deep OTM options) than on smaller price changes; absolute impact on tail risks larger for commodities than for equities and exchange rates.
  - Example magnitude:
    - Average shift in the left tail for the S&P500 is about 4 percentage points, reducing log distance to the mean from approximately 25 percent to 21 percent.
  - Asymmetry:
    - Left tail shifts towards the mean more than the right tail (downside risk decline larger than upside). Exception: EUR/USD where narrowing was symmetric.
  - No statistically significant impact on price levels (mean-preserving shift).
  - Asset-level tests:
    - Decline in left and right tail risk statistically significant for almost all assets per Patell’s t-test and rank test; wheat excluded from aggregate tests due to illiquid OTM options.
  - Implied volatility:
    - Typically declines but statistically significant only for gold and only for one test.
- QE phase heterogeneity:
  - QE1 and QE3 produced statistically significant and larger inward shifts of tails; QE2 produced smaller and not significant inward shifts.
- Role of initial conditions (VIX interaction):
  - Event dummy γ1 similar to baseline γ; γ2 (interaction with VIX gap) statistically significant only for right tail and amplifies UMP effect.
  - Example: VIX gap during event 1 = 31.6; with estimated γ2 = -0.07, initial condition contributed about 2 percentage points of inward shift of the right tail.

### IX. Interpretation and discussion (Section V.B)
- Overarching interpretation:
  - UMP easing events reduce “tail risk” (price change expected with a 5 percent probability), especially downside left tail risk, supporting the view that UMP reduced market uncertainty and eased financial conditions.
- Mechanisms and implications:
  - UMP effects largest on tails rather than the mean: deep in-/out-of-the-money option premiums change more than ATM implied volatility.
  - Cannot disentangle changes in objective beliefs vs changes in investor risk aversion with current technology; likely both decline as investor confidence improves.
  - Both downside and upside risks decline — possible reason: market participants may adopt symmetric exposure strategies (e.g., long strangle buying of deep OTM calls and puts).
  - No evidence of short-run “excess speculation” (no large rightward mean shift or rise in right tail risk); distribution shift is mean-preserving.

### X. Case study — TALF announcement (November 25, 2008 at 8:15 am EST)
- Immediate outcomes (t-1 to t+1):
  - Futures prices mixed; ATM implied volatility broadly declined; 5th and 95th percentile tails shifted inward toward the futures price (lower tail risks priced in).
  - Natural gas exception: right tail shifted in on t but widened on t+1 (influenced by EIA Natural Gas Monthly release on November 26).
- 10-day horizon:
  - Commodity prices eased while equities and exchange rates picked up.
  - Energy outcomes strongly affected by EIA Short-Term Energy Outlook on December 9, 2008.
  - Probability density functions: distributions narrowed on event day for oil, corn, soybeans; narrowing amplified over 10 days with right tail becoming significantly thinner.
- Conclusion:
  - TALF announcement contributed to broad and substantial reduction in tail risks, especially left tail.

### XI. Quantitative changes 10 days after the event (Table 4 — Change 10 Days After the Event Date compared to day preceding the event)
- Change 10 Days After the Event Date — Futures price (percent):
  - Oil: -15.8
  - Natural Gas: -16.8
  - Gold: -5.6
  - S&P500: 5.0
  - EURUSD: 0.3
  - Corn: -11.7
  - Soybeans: -8.2
- Change 10 Days After the Event Date — Implied volatility (percentage points):
  - Oil: 29.6
  - Natural Gas: 12.5
  - Gold: -4.8
  - S&P500: 0.7
  - EURUSD: -1.6
  - Corn: -9.3
  - Soybeans: -3.2
- Change 10 Days After the Event Date — VaR, 5% (percent):
  - Oil: -40.1
  - Natural Gas: -25.1
  - Gold: 5.4
  - S&P500: 41.9
  - EURUSD: 3.2
  - Corn: 7.3
  - Soybeans: -2.9
- Change 10 Days After the Event Date — VaR, 95% (percent):
  - Oil: -5.2
  - Natural Gas: -11.6
  - Gold: -13.6
  - S&P500: -13.9
  - EURUSD: -2.0
  - Corn: -22.4
  - Soybeans: -12.1

### XII. Immediate event-window changes (day preceding to day following the event — Table 4 alternate)
- Futures price (percent):
  - Oil: 0.6
  - Natural Gas: 0.5
  - Gold: -1.1
  - S&P500: 4.5
  - EURUSD: 0.2
  - Corn: 0.0
  - Soybeans: 0.3
- Implied volatility (percentage points):
  - Oil: -0.6
  - Natural Gas: 1.8
  - Gold: -1.4
  - S&P500: -4.5
  - EURUSD: -0.3
  - Corn: 0.0
  - Soybeans: -0.7
- VaR, 5% (percent):
  - Oil: 3.0
  - Natural Gas: -1.2
  - Gold: 5.9
  - S&P500: 44.6
  - EURUSD: 0.8
  - Corn: 0.8
  - Soybeans: 1.0
- VaR, 95% (percent):
  - Oil: -0.5
  - Natural Gas: 1.5
  - Gold: -6.3
  - S&P500: -15.6
  - EURUSD: -0.1
  - Corn: -0.5
  - Soybeans: -0.1

### XIII. Appendix — event dating and selected panels/figures (high-level)
- Monetary policy event dates (Table 2): 14 events (QE1, QE2, QE3) dated 11/25/2008 through 9/13/2012 (detailed event list included in source).
- Displayed estimated impact coefficients and confidence intervals (Panel 1 and Panel 2) — selected coefficient labels and values shown in figures:
  - Example labels (All Assets and All Events): Implied volatility; Left tail; Right tail — coefficients displayed: -0.2, 5.5, -3.1.
  - Phase heterogeneity figures show coefficient patterns for QE1, QE2, QE3 (examples: QE3 coefficients: -2.4, 7.8, -5.1).
- Patell and rank test statistics displayed in figure sequences (values shown in plot; assets listed: Corn, Soybeans, Wheat, Oil, Natural gas, Gold, S&P500, USD/EUR).
- Probability density functions for selected assets for Event 1 plotted (S&P 500; EURUSD; Oil; Gold; Corn; Soybeans) showing Event -10, Event -1, Event +10.

### XIV. Conclusions (Section VI)
- Summary conclusions:
  - UMP events in the United States caused reductions in asset price tail risk as measured by RNDs estimated from options.
  - Downside (left) tail risk falls most notably; QE1 and QE3 had stronger effects than QE2.
  - UMP easing events can bolster market confidence in times of high uncertainty by lowering probabilities of extreme outcomes even when mean price levels do not shift significantly.

*Source: _wp13190 - References (excerpt).*

### References .............................................................................................................

### References

### I. Introduction and Research Questions
- Context: Unconventional monetary policies (UMP) became important after the 2008–09 global financial crisis and their effects on asset prices remain uncertain.
- Concerns highlighted:
  - Potential for UMPs to cause spillovers damaging other countries by distorting exchange rates and other asset prices.
  - Media claims linking UMPs to higher food commodity prices with adverse effects on food importing countries and the poor (example cited: Guardian, November 5, 2010).
- Key conceptual issues:
  - “Excessive speculation” is defined variously: as an amount of speculation beyond that necessary relative to hedging needs (Working’s T, Irwin and Sanders, 2010) or as “sudden or unreasonable fluctuations or unwarranted changes in the price of [a] commodity” (CFTC).
  - Speculative bubbles described as asset prices rising above fundamentals under rational expectations.
- Research questions posed:
  - Do UMPs raise or reduce uncertainty about the outlook for risk asset prices?
  - Are effects symmetric (affecting upside and downside risks)?
  - Does “excessive speculation” increase following a UMP event?
- Motive: The recent crisis increased the probability of policy interest rates hitting the zero lower bound, reinforcing the importance of understanding UMP effects and potential harmful side-effects.

### II. Empirical Approach and Hypothesis Testing
- Null hypothesis: UMPs have no effect on the distribution of asset price risk.
- Methodology overview:
  - Event study methodology applied to U.S. UMPs (including important speeches by Federal Reserve officials and public statements released after Federal Open Market Committee meetings).
  - Estimate risk-neutral density functions (RNDs) from options prices.
  - Fit a weighted average log-normal distribution to the options data, subject to arbitrage constraints.
  - Fit performed for the 20 days immediately preceding a UMP event and for one test date after the event.
- Assets analyzed:
  - Euro–U.S. dollar exchange rate
  - S&P500 equity index
  - Five commodities: gold, crude oil, natural gas, corn, and soybeans
- Measures and tests:
  - Focus on measures of tail risk and implied volatilities of liquid at-the-money options contracts.
  - Conduct hypothesis tests to assess whether and how asset price risk changed around UMP events.
- Detecting “excessive speculation”:
  - Formal testing is difficult due to imprecision in pinning down fundamental values.
  - Presence would be reflected in prices or RNDs (or both).
  - Evidence of investor positioning for very large price gains (e.g., purchasing deep out-of-the-money call options) would create strong positive skew in the RND; this would likely be a necessary, but perhaps not sufficient, condition for excessive speculation.

### III. Prior Findings and Paper Contribution
- Existing consensus noted: little evidence that such policies cause significant short-term changes in “risk asset” prices (see section II.B).
- Contribution of this paper:
  - Extends prior analysis by assessing the effect of UMPs on the distribution of asset price risk rather than only mean price levels.
  - Uses RND-based measures and event study framework to examine tail risk, skewness, and implied volatilities.

### IV. Structure of the Paper and Supporting Material
- Plan of the paper:
  - Section II: theory linking commodity pricing and monetary policy.
  - Section III: theoretical and empirical methodology.
  - Section IV: data overview.
- Appendices and supporting tables/figures listed in the source:
  - Appendix Tables:
    - Table 1. Spot Delivery and Derivative Contract Specifications
    - Table 2. Monetary Policy Event Dates, November 2008–September 2012
    - Table 3. Change Over the Event Date
    - Table 4. Change 10 Days after the Event Date
  - Appendix Figures:
    - Panel 1. Estimated UMP Impact Coefficients and 95 Percent Confidence Intervals 2008–12
    - Panel 2. Estimated UMP Impact Coefficients and 95 Percent Confidence Intervals by UMP Phase: QE1, QE2, and QE3
    - Panel 3. Estimated UMP Impact Coefficients Including Initial Conditions and 95 Percent Confidence Intervals
    - Panel 4. Probability Density Functions for Selected Assets: Event 1

*Source: _wp13190 - References (excerpt).*

### Section V presents the key results, while in Section VI we offer our interpretation. Section

### _wp13190 - Section V presents the key results, while in Section VI we offer our interpretation. Section

### Definition and channels of Unconventional Monetary Policy (UMP)
- UMP measures considered: lending to financial institutions; providing liquidity to important credit markets; large-scale asset purchase programs (LSAPs).
- Objectives:
  - Lending and liquidity measures: prevent fire sales triggered by vanishing liquidity.
  - LSAPs: target reduction of interest rates along the term structure to stimulate economic activity.
- Four primary channels through which UMP can affect asset prices:
  - Portfolio balance channel: central bank purchases alter relative valuation of imperfect substitutes (including commodities), increasing demand for them.
  - Signaling channel: unconventional measures signal lower policy rates in the future.
  - Confidence channel: announcements may signal worse economic prospects (offsetting signaling) or may boost confidence (see Joyce and others, 2010; Wright, 2011).
  - Liquidity/risk-premia channel: UMP may enhance market liquidity and reduce risk premia (e.g., Gagnon et al, 2010).
- Additional channels for commodity prices: through interest rates and exchange rates; lower real interest rates and a depreciating U.S. dollar should lead to higher commodity prices (Frankel, 2008).

### Empirical background and prior findings
- General empirical findings:
  - UMP easing (announcements and operations) reduces interest rates and depreciates the domestic currency, especially over short horizons (one day).
  - U.S. asset purchase announcements: lowered Treasury yields and depreciated U.S. dollar (Gagnon et al, 2010; Neeley, 2010; Glick and Leduc, 2011, 2013; Szczerbowics, 2011; Rosa, 2013).
  - U.K. gilt yields and sterling showed similar responses (Joyce and others, 2010; Glick and Leduc, 2011).
- Portfolio and cross-border effects:
  - Fratzscher, Lo Duca, and Straub (2012): UMPs affect portfolio decisions and capital flows; actual purchases led to higher capital inflows to emerging market investment funds—typically associated with rising commodity prices.
- Mixed evidence on commodities and equities:
  - Kozicki, Santor and Suchanek (2011): no consistent evidence that U.S. LSAP announcements increased commodity prices (17 commodity futures, 2–3 day window).
  - Glick and Leduc (2011): LSAP announcements generally led to declines in commodity prices, especially in 2008–09; stronger effects on energy prices in U.S. vs U.K.
  - Bayoumi and Bui (2011): QE1 had stronger initial impact (including on commodity prices) than QE2; QE2 effects on commodity prices and equities generally not statistically significant.
  - Rosa (2013): FOMC asset purchase announcements had significant effects on levels and volatility of energy futures, mainly through exchange-rate channel; finds a negative relationship between unanticipated LSAP announcements and oil price futures.
- Higher-moment effects:
  - Bekaert, Hoerova, and Lo Duca (2010): accommodative monetary policy decreases risk aversion (increases risk appetite) in the stock market after about nine months; effects on market uncertainty similar but weaker.

### Methodology: recovering risk-neutral distributions (RNDs) from options
- Objective: map observable changes in option prices to changes in underlying probabilities, assuming risk neutrality.
- Approach:
  - Fit a weighted mixture of lognormal distributions to sets of options with identical expiries but different strikes to recover an estimated density (captures fat tails and skew).
  - Use fitted RND to compute cumulative-percentile statistics (e.g., 5th and 95th percentiles) rather than relying on mean/variance due to non-normality.
- Key theoretical identities:
  - Futures/option pricing relationships expressed in integrals over the risk-neutral density (equations (1)–(5) in source).
  - Cox and Ross (1976) formulation used to derive fN(Sτ) from option prices, with second derivative of call price with respect to strike giving RND (equation (5)).
- Parametric estimation:
  - Assume fN(Sτ) is a weighted average of N-component lognormal densities with weights ωi (equation (6)).
  - Parameters: μi (drift), σi (volatility), ωi (weights); βi = σi sqrt(τ) (equation (8)).
  - Fit via minimizing squared distance between fitted and actual call and put prices subject to no-arbitrage discounting condition and weight constraints (equations (9)–(13)).
  - Use four lognormal mixtures (initially ω1 = ... = ω4), starting values μ ≈ 0 and σ = σIV (implied volatility of the at-the-money option).
- Tail-risk metrics:
  - Tail risk measured as log distance between the 5th percentile price and mean (left/downside) and between the 95th percentile price and mean (right/upside), assuming risk neutrality.

### Event-study design and statistical tests
- Event dating: tests conducted on day following event (t+1) to account for market-close timing; estimation window = preceding 20 days (t-1 to t-20).
- Tests used:
  - Patell’s (1976) aggregated t-test comparing ATM implied volatility and left/right tails at t+1 to sample mean over preceding 20 days.
  - Corrado (2010) small-sample ranking test (nonparametric) to avoid normality assumption.
  - Fixed-effects panel regression to control for clustering/overlaps: xij = αi + γ d + εij, with d = 0 for t-20..t-1 and d = 1 at t+1; t-statistic on γ tests UMP event significance (equation (16)).
  - Extension allowing conditioning on initial conditions: interact event dummy with VIX gap (difference between VIX at t-1 and its mean at t-1 across all 14 events) to estimate γ2 (equation (17)). This captures amplification of event effects under high uncertainty.

### Data
- Assets included: EUR/USD exchange rate, S&P500 equity index, gold, crude oil, natural gas, corn, soybeans.
- Options data: daily frequency from Thomson Reuters Datastream and exchanges; horizon = three months (closest expiration to three months ahead of each event).
- For each event: about seven call and put options centered around ATM strike; spot price = current cash price; risk-free rate = 3-month yield from the zero coupon U.S. Treasury curve.
- Monetary policy events: standard dating for QE1, QE2, QE3; events are verbal or written communications (not actual operations).

### Key results (Section V)
- Sample: 14 UMP events between 2008 and 2012.
- Main findings:
  - Reject null of no change in log distance between futures price and both left- and right-hand tails for full sample: tails shrink and move closer to futures prices following UMP easing events, implying reductions in both upside and downside tail risks.
  - No significant impact on at-the-money implied volatility.
  - Effects stronger on tails (deep OTM options) than on smaller price changes; absolute impact on tail risks larger for commodities than for equities and exchange rates.
  - Example magnitude: average shift in the left tail for the S&P500 is about 4 percentage points, reducing log distance to the mean from (approximately) 25 percent to 21 percent.
  - Asymmetry: left tail shifts towards the mean more than the right tail (downside risk decline larger than upside). Exception: EUR/USD where narrowing was symmetric.
  - No statistically significant impact on price levels (mean-preserving shift).
  - Asset-level tests: decline in left and right tail risk statistically significant for almost all assets per Patell’s t-test and rank test; wheat excluded from aggregate tests due to illiquid OTM options.
  - Implied volatility typically declines but statistically significant only for gold and only for one test.
- QE phase heterogeneity:
  - QE1 and QE3 produced statistically significant and larger inward shifts of tails; QE2 produced smaller and not significant inward shifts.
- Role of initial conditions (VIX interaction):
  - Event dummy γ1 similar to γ from baseline; γ2 (interaction with VIX gap) statistically significant only for right tail and amplifies UMP effect.
  - Example: VIX gap during event 1 = 31.6; with estimated γ2 = -0.07, initial condition contributed about 2 percentage points of inward shift of the right tail.

### Interpretation and discussion (Section V.B)
- Overarching interpretation:
  - UMP easing events reduce “tail risk” (price change expected with a 5 percent probability), especially downside left tail risk, supporting the view that UMP reduced market uncertainty and eased financial conditions.
- Mechanisms and implications:
  - UMP effects largest on tails rather than the mean: deep in-/out-of-the-money option premiums change more than at-the-money implied volatility.
  - Cannot disentangle changes in objective beliefs vs changes in investor risk aversion with current technology; likely both decline as investor confidence improves.
  - Both downside and upside risks decline—possible reason: market participants may adopt symmetric exposure strategies (e.g., long strangle buying of deep OTM calls and puts).
  - No evidence of short-run “excess speculation” (no large rightward mean shift or rise in right tail risk); distribution shift is mean-preserving.
- Case study: TALF announcement (November 25, 2008 at 8:15 am EST)
  - t-1 to t+1: futures prices mixed; ATM implied volatility broadly declined; 5th and 95th percentile tails shifted inward toward the futures price (lower tail risks priced in).
  - Natural gas exception: right tail shifted in on t but widened on t+1 (influenced by EIA Natural Gas Monthly release on November 26).
  - Over 10-day horizon: commodity prices eased while equities and exchange rates picked up; energy outcomes strongly affected by EIA Short-Term Energy Outlook on December 9, 2008.
  - Probability density functions: distributions narrowed on event day for oil, corn, soybeans; narrowing amplified over 10 days with right tail becoming significantly thinner.
  - Conclusion: TALF announcement contributed to broad and substantial reduction in tail risks, especially left tail.

### Conclusion (Section VI)
- Summary conclusions:
  - UMP events in the United States caused reductions in asset price tail risk as measured by RNDs estimated from options.
  - Downside (left) tail risk falls most notably; QE1 and QE3 had stronger effects than QE2.
  - UMP easing events can bolster market confidence in times of high uncertainty by lowering probabilities of extreme outcomes even when mean price levels do not shift significantly.

*Source: IMF working paper content (excerpt provided).*

### REFERENCES

### _wp13190 - REFERENCES

### References
- Bahra, B., 1997, “Implied Risk-Neutral Probability Density Functions from Options Prices: Theory and Application,” Bank of England Working Paper No. 66.
- Bayoumi, Tamim, and Trung Bui, 2011, “Unforeseen Events Wait Lurking: Estimating Policy Spillovers from U.S. to Foreign Asset Prices,” IMF Working Paper, 11/183 (Washington: International Monetary Fund).
- Bekaert, Geert, Marie Hoerova, and Marco Lo Duca, 2010, “Risk, Uncertainty and Monetary Policy,” National Bureau of Economic Research Working Paper No. 16397.
- Cheng, Kevin, 2010, “A New Framework to Estimate the Risk-Neutral Probability Density Functions Embedded in Options Prices,” IMF Working Paper 10/1881 (Washington: International Monetary Fund).
- Corrado, Charles, 2010, “Event Studies: A Methodology Review,” Accounting and Finance Association of Australia and New Zealand Accounting and Finance Journal, Vol. 51, pp. 207–234.
- Cox, John C., and Stephen A. Ross, 1976, “The Valuation of Options for Alternative Stochastic Processes,” Journal of Financial Economics, pp. 145-166.
- Frankel, Jeffrey, 2008, “The Effect of Monetary Policy on Real Commodity Prices,” in Asset Prices and Monetary Policy, John Campbell ed., pp. 291–327 (Chicago: University of Chicago Press).
- Fratzscher, Marcel, Marco Lo Duca, and Roland Straub, 2012, “Quantitative Easing, Portfolio Choice, and International Capital Flows,” ECB Working Paper.
- Gagnon, Joseph, Matthew Raskin, Julie Remache, and Brian Sack, 2010, “Large-Scale Asset Purchases by the Federal Reserve: Did they Work?” Federal Reserve Bank of New York Staff Report No. 441.
- Glick, Reuven, and Sylvain Leduc, 2011, “Central Bank Announcements of Asset Purchases and the Impact on Global Financial and Commodity Markets,” Federal Reserve Bank of San Francisco Working Paper, 2011–30.
- Glick, Reuven, and Sylvain Leduc, 2013, “The Effects of Unconventional and Conventional U.S. Monetary Policy on the Dollar,” Federal Reserve Bank of San Francisco Working Paper.
- Irwin, Scott, and Dwight Sanders, 2010, “Speculation and Financial Fund Activity,” OECD Working Party on Agricultural Policies and Markets Draft Report: Annex 1.
- Joyce, Michael, Ana Lasaosa, Ibrahim Stevens, and Matthew Tong, 2010, “The Financial Market Impact of Quantitative Easing,” Bank of England Working Paper No. 393.
- Kozicki, Sharon, Santor, Eric, and Suchanek, Lena, 2011, “Unconventional Monetary Policy: The International Experience with Central Bank Asset Purchases,” Bank of Canada Review.
- Kozicki, Sharon, Santor, Eric, and Suchanek, Lena, 2011, “The Impact of Large Scale Asset Purchases on Commodity Prices,” Bank of Canada Working Paper.
- Melick, William, and Charles Thomas, 1997, “Recovering an Asset’s Implied PDF from Options Prices: An Application to Crude Oil during the Gulf Crisis,” Journal of Financial and Quantitative Analysis, Vol. 32, pp. 91–115.
- Neeley, Christopher, 2010, “The Large-Scale Asset Purchases Had Large International Effects,” Federal Reserve Bank of St. Louis Working Paper 2010–018D.
- Patell, James, 1976, “Corporate Forecasts of Earnings per Share and Stock Price Behavior: Empirical Tests,” Journal of Accounting Research, pp. 246–276.
- Rosa, Carlo, 2013, “The High-Frequency Response of Energy Prices to Monetary Policy: Understanding the Empirical Evidence,” Federal Reserve Bank of New York Staff Report No. 598.
- Szczerbowicz, Urszula, 2011, “Are Unconventional Monetary Policies Effective?” Working Papers CELEG 1107, Dipartimento di Economia e Finanza, LUISS Guido.
- Wright, Jonathan, 2011, “What Does Monetary Policy do to Long-Term Interest Rates at the Zero Lower Bound?” Department of Economics, Johns Hopkins University, Working Paper.

### Appendix — Tables

- Table 1. Spot Delivery and Derivative Contract Specifications (selected entries):
  - S&P 500 Index (Chicago Mercantile Exchange)
    - Futures: Months Traded: Mar, Jun, Sep, Dec
    - Contract Size: $250 x S&P 500 futures price
    - Pricing Unit: U.S. dollars per contract
    - Options: Mar, Jun, Sep, Dec; One S&P 500 futures contract
    - Spot: Capitalization-weighted index of 500 stocks; U.S. dollars per contract
  - EUR/USD (LIFFE Amex exchange (Amsterdam))
    - Futures: Months Traded: Mar, Jun, Sep, Dec
    - Contract Size: 20,000 EUR
    - Pricing Unit: U.S. dollars per 100 euro
    - Options: Mar, Jun, Sep, Dec; One EUR/USD futures contract
    - Spot: Euro/U.S. dollar rate set by EuroFX at 1 pm Amsterdam time; U.S. dollars per 100 euro
  - Gold (New York Mercantile Exchange / COMEX)
    - Contract Size: 100 troy ounces
    - Pricing Unit: U.S. dollars per troy ounce
    - Options: One COMEX Gold futures contract
    - Spot: Gold (a minimum of 995 fineness); U.S. dollars per troy ounce
  - Oil (New York Mercantile Exchange)
    - Futures: Contract Size: 1,000 barrels
    - Pricing Unit: U.S. dollars per barrel
    - Options: One crude oil futures contract of 1,000 barrels
    - Spot: Light sweet crude oil; U.S. dollars per barrel
  - Natural Gas (New York Mercantile Exchange)
    - Contract Size: 10,000 MMBtu
    - Pricing Unit: U.S. dollars per MMBtu
    - Months Traded: Consecutive months for the current year plus the next twelve full calendar years
    - Options: Consecutive months for the current year plus the next three full calendar years; One crude oil futures contract of 1,000 barrels
    - Spot: Natural gas delivered at Henry Hub, LA; U.S. dollars per MMBtu
  - Yellow corn grade #2 (Chicago Mercantile Exchange)
    - Futures Months Traded: Mar, May, Jul, Sep, Dec
    - Contract Size: 5,000 bushels (127 MT)
    - Pricing Unit: U.S. cents per bushel
    - Options: Mar, May, Jul, Sep, Dec. The monthly option contract exercises into the nearby futures contract.
    - Spot: Yellow corn grade #2; U.S. cents per bushel
  - Yellow soybean grade #2 (Chicago Mercantile Exchange)
    - Futures Months Traded: Jan, Mar, May, Jul, Aug, Sep, Nov.
    - Contract Size: 5,000 bushels (136 MT)
    - Pricing Unit: U.S. cents per bushel
    - Options: Jan, Mar, May, Jul, Aug, Sep, Nov. The monthly option contract exercises into the nearby futures contract.
    - Spot: Yellow soybean grade #2; U.S. cents per bushel
  - Additional contract month conventions:
    - LIFFE Amex exchange (Amsterdam): Current calendar month; the next two calendar months; any Feb, Apr, Aug, and Oct falling within a 23-month period; and any Jun and Dec falling within a 72-month period beginning with the current month.
    - NYMEX: Consecutive months are listed for the current year and the next five years; in addition, the Jun and Dec contract months are listed beyond the sixth year.

- Table 2. Monetary Policy Event Dates, November 2008 to September 2012 (No., Phase, Date, Description / Announcement)
  - 1. QE 1 — 11/25/2008 — Initial LSAP announcement — Fed announces purchases of $100 billion in GSE debt and up to $500 billion in MBS.
  - 2. QE 1 — 12/1/2008 — Bernanke Speech — Chairman Bernanke mentions that the Fed could purchase long-term Treasuries.
  - 3. QE 1 — 12/16/2008 — FOMC Statement — FOMC statement first mentions possible purchase of long-term Treasuries.
  - 4. QE 1 — 1/28/2009 — FOMC Statement — FOMC statement says that it is ready to expand agency debt and MBS purchases, as well as to purchase long-term Treasuries.
  - 5. QE 1 — 3/18/2009 — FOMC Statement — FOMC will purchase an additional $750 billion in agency MBS, to increase its purchases of agency debt by $100 billion, and $300 billion in long-term Treasuries.
  - 6. QE 1 — 8/12/2009 — FOMC Statement — Fed will purchase a total of up to $1.25 trillion of agency MBS and up to $200 billion of agency debt by end-2009. Also, the Fed is in the process of buying $300 billion of Treasury securities.
  - 7. QE 1 — 9/23/2009 — FOMC Statement — Fed's purchases of $300 billion of Treasury securities will be completed by the end of October 2009.
  - 8. QE 1 — 11/4/2009 — FOMC Statement — The amount of agency debt to be purchased by the Fed reduced to $175 billion. MBS and agency debt purchases are to be completed by end-2010Q1.
  - 9. QE 2 — 8/10/2010 — FOMC Statement — Fed will keep constant its holdings of securities at their current level by reinvesting principal payments from agency debt and agency MBS in longer-term Treasury securities. FOMC will continue to roll over the Fed's holdings of Treasury securities as they mature.
  - 10. QE 2 — 8/27/2010 — Bernanke Speech, Jackson Hole — Chairman Bernanke names "conducting additional purchases of longer-term securities" as a tool, "is prepared to provide additional monetary accommodation through unconventional measures ..."
  - 11. QE 2 — 10/15/2010 — Bernanke Speech, Boston — Chairman Bernanke states the Fed will continue keeping interest rates low and mentions further quantitative easing.
  - 12. QE 2 — 11/3/2010 — FOMC Statement — Fed intends to purchase a further $600 billion of longer-term Treasury securities by the end of 2011Q2, a pace of about $75 billion per month.
  - 13. QE 3 — 8/31/2012 — Bernanke Speech, Jackson Hole — Chairman Bernanke hints at QE3: "The Federal Reserve will provide additional policy accommodation as needed to promote a stronger economic recovery and sustained improvement in labor market conditions in a context of price stability."
  - 14. QE 3 — 9/13/2012 — FOMC Statement — The Fed will purchase additional agency MBS at a pace of $40 billion per month.

- Table 3. Change Over the Event Date (From the day preceding the event to the day following the event) — Sources: Datastream; and authors’ calculations.
  - (No numeric table contents printed in source for Table 3 beyond caption; refer to Table 4 for numeric changes 10 days after the event.)

- Table 4. Change 10 Days After the Event Date (Compared to the day preceding the event) — Sources: Datastream; and authors’ calculations.
  - Change 10 Days After the Event Date — Futures price (percent):
    - Oil: -15.8
    - Natural Gas: -16.8
    - Gold: -5.6
    - S&P500: 5.0
    - EURUSD: 0.3
    - Corn: -11.7
    - Soybeans: -8.2
  - Change 10 Days After the Event Date — Implied volatility (percentage points):
    - Oil: 29.6
    - Natural Gas: 12.5
    - Gold: -4.8
    - S&P500: 0.7
    - EURUSD: -1.6
    - Corn: -9.3
    - Soybeans: -3.2
  - Change 10 Days After the Event Date — VaR, 5% (percent):
    - Oil: -40.1
    - Natural Gas: -25.1
    - Gold: 5.4
    - S&P500: 41.9
    - EURUSD: 3.2
    - Corn: 7.3
    - Soybeans: -2.9
  - Change 10 Days After the Event Date — VaR, 95% (percent):
    - Oil: -5.2
    - Natural Gas: -11.6
    - Gold: -13.6
    - S&P500: -13.9
    - EURUSD: -2.0
    - Corn: -22.4
    - Soybeans: -12.1

- Table 4 (Alternate shorter horizon figures listed in source — From day preceding to day following the event) — Change in immediate event window:
  - Futures price (percent):
    - Oil: 0.6
    - Natural Gas: 0.5
    - Gold: -1.1
    - S&P500: 4.5
    - EURUSD: 0.2
    - Corn: 0.0
    - Soybeans: 0.3
  - Implied volatility (percentage points):
    - Oil: -0.6
    - Natural Gas: 1.8
    - Gold: -1.4
    - S&P500: -4.5
    - EURUSD: -0.3
    - Corn: 0.0
    - Soybeans: -0.7
  - VaR, 5% (percent):
    - Oil: 3.0
    - Natural Gas: -1.2
    - Gold: 5.9
    - S&P500: 44.6
    - EURUSD: 0.8
    - Corn: 0.8
    - Soybeans: 1.0
  - VaR, 95% (percent):
    - Oil: -0.5
    - Natural Gas: 1.5
    - Gold: -6.3
    - S&P500: -15.6
    - EURUSD: -0.1
    - Corn: -0.5
    - Soybeans: -0.1

### Appendix — Figures and Key Displayed Coefficients / Statistics

- Panel 1. Estimated UMP Impact Coefficients and 95 Percent Confidence Intervals, 2008–12:
  - Figure 1. All Assets and All Events — displayed coefficients: -0.2, 5.5, -3.1 (labels: Implied volatility; Left tail; Right tail)
  - Figure 2. Food and Energy and All Events — displayed coefficients: -0.2, 7.4, -3.7
  - Figure 3. Commodities and All Events — displayed coefficients: -0.3, 6.8, -3.7
  - Figure 4. Non-Commodities and All Events — displayed coefficients: 0.0, 2.4, -1.8

- Figure 5. Patell Test and Rank Test t-statistics, All Asset over Events:
  - Displayed t-statistics and rank test scores (sequence of values shown in plot):
    - -4.42, -2.04, -2.53, -3.86, -4.67, -4.87, -2.11, -3.80, 4.31, 2.08, 1.65, 3.57, 2.29, 4.74, 2.08, 3.79, -1.80, -1.17, -0.34, -0.09, 1.03, -2.47, -1.34, -0.69, -3.48, -1.90, -2.21, -3.64, -2.64, -1.90, -2.21, -3.64, 3.49, 1.87, 1.70, 3.46, 2.11, 1.87, 1.70, 3.46, 0.45, 0.57, 0.11, 0.16, -0.71, 0.57, 0.11, 0.16
  - Figure legend: White bars - rank test score; Solid bars - Patell t-statistic
  - Assets listed on axis: Corn, Soybeans, Wheat, Oil, Natural gas, Gold, S&P500, USD/EUR; metrics: implied volatility, 95th percentile (right tail), 5th percentile (left tail), at-the-money

- Panel 2. Estimated UMP Impact Coefficients and 95 Percent Confidence Intervals by UMP Phase: QE1, QE2, and QE3:
  - Figure 6. All Assets and All Events — coefficients: -0.2, 5.5, -3.1
  - Figure 7. All Assets and QE1 Events — coefficients: 0.2, 6.1, -3.7
  - Figure 8. All Assets and QE2 Events — coefficients: -0.2, 5.4, -1.6
  - Figure 9. All Assets and QE3 Events — coefficients: -2.4, 7.8, -5.1

- Panel 3. Estimated UMP Impact Coefficients Including Initial Conditions and 95 Percent Confidence Intervals:
  - Figure 10. Impact Coefficient on Event Dummy — coefficients: -0.2, 5.5, -3.1
  - Figure 11. Impact Coefficient on Initial Condition — coefficients: 0.04, 0.04, -0.07, -0.15, -0.10, -0.05, 0.00, 0.05, 0.10, 0.15, 0.20 (plotted across Implied volatility; Left tail; Right tail)

- Panel 4. Probability Density Functions for Selected Assets: Event 1 (Price on the x-axis; probability on the y-axis):
  - S&P 500 (250 U.S. dollars per index point) — plotted probability density with price axis 0 to 3,000 (visual)
  - EURUSD (U.S. dollars per 100 euro) — plotted probability density with price axis 0 to 200 (visual)
  - Oil (U.S. dollars per barrel) — plotted probability density with price axis 0 to 300 (visual)
  - Gold (U.S. dollars per troy ounce) — plotted probability density with price axis 250 to 1,500 (visual)
  - Corn (U.S. cents per bushel) — plotted probability density with price axis 0 to 1,000 (visual)
  - Soybeans (U.S. cents per bushel) — plotted probability density with price axis 0 to 2,000 (visual)
  - Event series shown: Event -10; Event -1; Event +10

*Source: _wp13190 - REFERENCES (PDF chapter/section).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13190.pdf_