Matthias Fleckenstein, Francis A. Longstaff, Hanno Lustig

Q Group Conference

October 2015

- Deflation has played a central role during the worst economic meltdowns in U.S. history.
- Panic of 1837
- Long Depression of 1874-1896
- Great Depression of the 1930s

- Growing fears of deflation in the financial press.
- “Nightmare scenario”
- “Looming disaster”
- “Growing threat”

Mitigating risk of deflation is an explicit motivation behind many recent measures by the Federal Reserve such as the Quantitative Easing Programs

Relatively little is known about the probability of deflation.

Reason may be that the distribution of inflation is difficult to measure.

Ang, Bekaert, and Wei (2007) show that econometric models perform poorly in estimating first moment of inflation.

Survey data does better, but only looks at first moments, not tail probabilities.

We use a new market based approach to measure deflation risk.

-First we solve for the risk-neutral density of inflation from the market prices of inflation calls and puts.

-Then we solve for the inflation risk premium via MLE estimation of an affine term structure model using the term structure of inflation swap rates.

-Finally, we solve for the objective density of inflation by adjusting the pricing measure for the market price of risk.

-Long run expected inflation is about 3.00 percent.

-Average inflation risk premium is close to zero for horizons out to about 20 years.

-Inflation volatility is roughly 1.50 percent.

Probability of deflation sizable.

-Bernanke, Aug 27, 2010, “Falling into deflation is not a significant risk.”

-On same date, market-implied probability of deflation was 27.35 percent for two-year horizon, 16.15 percent for five-year horizon, and 6.39 percent for a ten-year horizon.

-Tail risk of deflation priced similarly to other types of tail risk such as catastrophe insurance and corporate bond defaults.

-Deflation correlated with other types of financial and economic tail risk such as systemic credit risk, liquidity risk, and unemployment.

-Inflation risk is priced less severely by the market.

-Inflation swaps

– Maturities from one to 55 years for the period from July 23, 2004 to July 29, 2014.

-Inflation caps and floors

-Strikes from âˆ’ 2% to 6 % in increments of 50bps, and maturities from 1 to 30 years for the period from October 5, 2009 to July 29, 2014.

-Inflation surveys

-University of Michigan Survey of Consumers, the Philadelphia Federal Reserve Bank Survey of Professional Forecasters, and the Livingston Survey for the period from July 2004 to July 2014.

-Measures of financial tail risk

-One-year Refcorp-Treasury yield spread, 10–15 % CDX IG index tranche prices, one-year Libor-Treasury spread, five-year swap spread, VIX index, Merrill Lynch MOVE index, Baa spread over the five-year Treasury rate, spread for a five-year CDS contract on the U.S. Treasury.

-Macroeconomic variables

-U.S. industrial production, U.S. unemployment rate, University of Michigan consumer confidence index.

**Summary Statistics for Inflation Caps and Floors.** This table reports the average values for inflation caps and floors for the indicated maturities and strikes. The average values are expressed in terms of basis points per $100 notional. Option Maturity is expressed in years. Ave. denotes the average number of caps and floors available each day from which the risk-neutral density of inflation is estimated. N denotes the number of days for which the risk-neutral density of inflation is estimated. The sample consists of daily observations for the period from

October 5, 2009 to July 29, 2014.

**Maximum Likelihood Estimation of the Inflation Swap Model.** This table reports the maximum likelihood estimates of the parameters of the inflation swap model along with their asymptotic standard errors. The model is estimated using daily inflation swap prices for the period from July 23, 2004 to July 29, 2014.

**Summary Statistics for Inflation Risk Premia.**This table reports summary statistics for the estimated inflation risk premia for the indicated horizons. Horizon is expressed in years. The inflation risk premia are measured in basis points. The inflation risk premia are estimated using the period from July 23, 2004 to July 29, 2014.

**Summary Statistics for Expected Inflation.**This table reports summary statistics for the expected inflation rate for the indicated horizons. Horizon is expressed in years. Expected inflation rates are expressed as percentages. The sample consists of daily observations for the periodfrom July 23, 2004 to July 29, 2014.

**Comparison of Survey Forecasts with Market-Implied Forecasts.**This table reports the average values of the survey forecasts for the indicated forecast horizon along with the correspond-ing average of the market-implied expected inflation for the same horizon. Inflation forecasts are expressed as percentages. The sample period is July 2004 to July 2014.

**Summary Statistics for Inflation Volatility.**This table reports summary statistics for the volatility of the annualized inflation rate for the indicated horizons. Horizon is expressed in years. Inflation rates are expressed as percentages. The sample consists of daily observations for the period from July 23, 2004 to July 29, 2014.

**Summary Statistics for Deflation Probabilities.**This table reports summary statistics for the probability of the average inflation rate being below zero for the indicated horizons. Horizon is expressed in years. Probabilities are expressed as percentages. The sample consists of daily observations for the period from October 5, 2009 to July 29, 2014.

**Summary Statistics for the Pricing of Deflation Tail Risk.**This table reports the means of the ratio of the probability of inflation being below the indicated threshhold under the pricing measure divided by the probab

ility of the same event under the actual measure. The mean is taken over only the observations where the probability of the event is greater than 0.01 percent under the actual measure. Horizon is expressed in years. The sample consists of daily observations for the period from October 5, 2009 to July 29, 2014.

**Results from the Regression of Monthly Changes in Deflation Probabilities on Financial and Macroeconomic Variables.**This table reports the t-statistics and adjusted R^{2}s from from the regression of monthly changes in the deflation probabilities for the indicated horizon on the monthly changes in the following variables: the spread between three-month Libor and the overnight index swap (OIS) rate, the five-year swap spread, the VIX volatility index, the CDX North American Investment Grade CDS Index, the return on the CRSP value-weighted

stock index, the five-year U.S. Treasury CDS spread, the five-year German CDS spread, industrial production (IP, percentage change), the unemployment rate (Unemp), and the Conference Board’s Consumer Confidence Index (Conf). Horizon in measured in years. The t-statistics are based on the Newey-West estimator of the covariance matrix (three lags). The superscript âˆ–âˆ– denotes significance at the five-percent level; the superscript âˆ– denotes significance at the ten-percent level. The sample consists of monthly observations for the period from October 2009 to July 2014.

**Summary Statistics for the Probabilities of Inflationary Scenarios.**This table reports summary statistics for the probability of the average inflation rate being above the indicated thresholds for the respective horizons. Horizon is expressed in years. Probabilities are expressed as percentages. The sample consists of daily observations for the period from October 5, 2009 to July 29, 2014.

**Summary Statistics for the Pricing of Inflation Tail Risk.** This table reports the means of the ratio of the probability of inflation being above the indicated thresh hold under the pricing measure divided by the probability of the same event under the actual measure. The mean is taken over only the observations where the probability of the event is greater than 0.01 percent under the actual measure. Horizon is expressed in years. The sample consists of daily observations for the period from October 5, 2009 to July 29, 2014.

-We solve for the objective distribution of inflation using the market prices of inflation swap and option contracts and study the nature of deflation risk.

-Market-implied probabilities of deflation are substantial, even though the expected inflation rate is roughly 2.50 to 3.00 percent for horizons of up to 30 years.

-Deflation risk is priced by the market in a manner similar to that of other major types of tail risk such as catastrophic insurance losses or corporate bond defaults.

-Deflation risk is significantly related to measures capturing stress in the financial system and credit risk in the economy.

-Our results support the view that the risk of economic shocks severe enough to result in deflation is fundamentally related to the risk of major systemic shocks in the financial market.