A General Approach to Recovering Market Expectations from Futures Prices (with an Application to Crude Oil)

Transcription

1 A General Approach to Recovering Market Expectations from Futures Prices (with an Application to Crude Oil) Christiane Baumeister Lutz Kilian University of Notre Dame University of Michigan CEPR

2 Motivation Expectations of prices play a key role in a wide range of forward-looking economic models. Potential sources of price expectations data: Household and firm surveys Expert forecasts Futures prices Example: Expectations of the market price of crude oil

3 Why We Care About Oil Price Expectations 1. They are one of the key economic variables for the assessment of macroeconomic performance and risks at central banks and international organizations. 2. They play an important role in modelling car purchases and for designing environmental and regulatory policies in microeconomics (e.g., Busse, Knittel and Zettelmeyer 2013; Kellogg 2014; Allcott and Wozny 2014). 3. They also have an immediate impact on a wide range of industries such as the automobile, airline and utility companies. 4. They have implications for the economic viability of the production of crude oil from Canadian oil sands and the viability of U.S. shale oil production.

4 The Traditional Consensus The standard practice among policymakers and central bankers, in the business community, in the financial press and in the academic literature, has been to interpret the price of West Texas Intermediate (WTI) crude oil futures as the market expectation of the spot price of WTI crude oil. The use of oil futures prices as out-of-sample oil price forecasts relies on this interpretation. So does the use of oil futures prices as a measure of oil price expectations of firms and consumers in microeconomic models. This practice amounts to treating the risk premium as zero (or at least negligible).

5 The popularity of this practice has several reasons: 1. Futures prices are simple to use and readily available in real time. 2. There is a reluctance to depart from what is viewed as the collective wisdom of the financial market which presumably knows better than any individual oil price forecaster. 3. Relying on what is perceived to be the market expectation also absolves the user from any culpability for prediction errors because no one can reasonably be expected to beat the market. 4. Futures prices have some forecasting power at longer horizons, although their forecast accuracy has varied substantially over time. 5. Until recently there were few alternatives available.

6 The Emerging New Consensus The traditional consensus has been challenged in recent years by a large number of empirical studies documenting the existence of time-varying risk premia in the oil futures market. A new consensus has been emerging in the academic literature that time-varying risk premia are an important feature of the crude oil market. Singleton (MSci 2014): The evidence for time-varying risk premiums in oil markets seems compelling.

7 Standard no arbitrage arguments imply that cov, / F E S S Q E Q h t t t h t h t h t t h where cov S, Q / E Q t h t h t t h refers to the risk premium. In the absence of a risk premium, expectation. F h t is zero in St h This prediction error in percent also is the return on futures because the price of a futures contract held to maturity is S. t h Evidence of a predictable component in futures returns h such that E t Ft St h 0 is consistent with the presence of a time-varying risk premium.

8 5 Reasons Why a More Systematic Study Is Needed 1. Existing studies rely on different design parameters: They differ greatly in the sample period covered. They also sometimes differ in the horizon for which the risk premium is computed. Many studies evaluate the predictor of interest over very short time periods only. This is a particular concern given the welldocumented instability of predictive relationships in oil markets. Example: Hamilton and Wu (IER 2014) document that the empirical results in Singleton (2014) are not robust to extending the sample by only a few years.

9 2. Sometimes little distinction is made between results for crude oil and for other commodities: Examples: Singleton (2014) cites Fama and French (1987) as having provided evidence of a time-varying risk premium in the crude oil market, yet oil was never considered in their paper. Other studies commonly cited in the debate about time-varying risk premia in oil futures prices that, in fact, do not analyze the futures market for crude oil include Bessembinder and Chan (1992), Chong and Miffre (2010), and Cheng, Kirilenko and Xiong (2012).

10 3. Many studies do not explicitly focus on crude oil, but estimate time-varying risk premia for portfolios: Portfolios of several energy commodities including, for example, natural gas along with crude oil. Portfolios including refined products such as gasoline or heating oil along with crude oil. Example: Hong and Yogo (2012) provide results for an energy portfolio consisting of heating oil, gasoline, crude oil, natural gas, and propane gas. Such analyses are not informative about the question of timevarying risk premia in the crude oil market.

11 4. There is no agreement on how to evaluate the risk premium: Some studies report measures of futures returns. 2 R or incremental 2 R for Many studies focus exclusively on the question of whether the t-statistic of the preferred predictor is statistically significant at conventional significance levels (possibly after conditioning on other predictors). Risk premia are reported, if at all, not in dollar terms, as required for computing expectations, but as fractions of the futures price.

12 5. Although there is an emerging consensus that there is a timevarying risk premium, there is no consensus on how to estimate that risk premium. Whereas one study might favor one set of predictors, the next study may focus on an entirely different set of predictors. This fact not only raises questions about the economic plausibility of these models, but it suggests that there may be scope for combining predictors. It also suggests that these results may be subject to data mining biases (e.g., Inoue and Kilian ER 2004).

13 Our Approach 1. We reexamine the most influential and most widely cited studies in this literature. When the original study did not consider crude oil specifically we extend the analysis to the oil futures market. 2. We extend the sample until June 2014, which in many cases amounts to a substantial increase in the sample size. 3. We consider prediction horizons of 3, 6, 9, and 12 months for all models. 4. We evaluate all model specifications based on the same evaluation period to the extent that the data are available. 5. We quantify the estimated risk premia in dollar terms and investigate their sign, their magnitude and their variability across alternative model specifications.

14 Empirical Models of Time-Varying Risk Premia There are three approaches to modelling predictable variation in futures returns: 1. Basis regressions (e.g., Fama and French 1987, 1988): 2. Regressions of futures returns on financial and macroeconomic predictors thought to be correlated with returns (e.g., De Roon et al. 2000; Sadorsky 2002; Pagano and Pisani 2009; Acharya et al. 2013; Etula 2013; Singleton 2014). 3. Term structure models (e.g., Hamilton and Wu 2014)

15 where f h t t Approach 1: Basis regressions h, s s f s u (1) t h t t t t h s is the basis (see Fama and French 1987). A constant average risk premium would be reflected in nonzero intercept. Evidence that 1 implies predictable variation in the realized returns and hence a time-varying risk premium (e.g., Serletis 1991, Chernenko et al. 2004, Alquist and Kilian 2010). The risk adjusted futures forecast is algebraically equivalent to 1 ˆ ˆ h S F S / S. the oil price forecast t t t t

16 Approach 2: Futures Return Regressions F h t St h / St h xt vt h, (2) where the regressor x t denotes a vector containing the set of candidate predictors. These predictors may reflect the state of the economy, of the oil market, or of related commodity markets. The risk premium is the predicted value of equation (2).

17 Monthly Predictor Variables for Oil Futures Returns Article Model Predictors Bessembinder B1 Returns on CRSP value-weighted equity index (1992) B2 Returns on CRSP value-weighted equity index Unexpected CPI inflation Change in expected CPI inflation Change in 3-month T-bill rate Change in the term structure (20YGB 3-month T-bill) Change in default premium (Baa 20YGB) Unexpected change in U.S. industrial production Bessembinder BC Dividend yield on CRSP value-weighted equity index and Chan 3-month T-bill rate (1992) Junk bond premium (Baa Aaa) Sadorsky (2002) S Return on dividend yield on S&P 500 common stock portfolio Return on junk bond premium (Baa Aaa) Return on 3-month T-bill rate Market portfolio excess return

18 De Roon, Nijman, and DNV1 Returns on S&P 500 stock price index Own-market hedging pressure Veld (2000) Cross-market hedging pressure for gold, silver, platinum, heating oil DNV2 Own-market hedging pressure scaled by its standard deviation Own-market price pressure scaled by its standard deviation DNV3 DNV1 + own-market price pressure Gorton, Hayashi, and Rouwenhorst (2013) GHR1 Normalized U.S. crude oil commercial inventories (no SPR) GHR2 Own-market hedging pressure Hong and HY1 1-month T-bill rate Yogo (2012) Yield spread (Aaa 1MTbill) Basis by horizon HY2 HY1 + growth rate of oil market dollar open interest

19 Pagano and Pisani (2009) PP1 PP2 PP3 Degree of capacity utilization in U.S. manufacturing Term spreads (2YGB 1YGB, 5YGB 2YGB, 10YGB 5YGB) Composite leading indicator for OECD + 6 NMEs Bessembinder and Seguin (1993) BS Ratio of trading volume of oil futures contracts to open interest by horizon NOTES: The sample period is except for the series from the CRSP database which are only available until and the series in BS which start only in for horizons 3, 6, and 9, and in for horizon 12.

20 Empirical Results for the Return Regressions The return regressions are fitted on the full sample and predicted values for each point in time are constructed from the full-sample regression estimates. h For each model, the risk-adjusted forecast is F t RPt, where RP h t represents the predicted value from the estimated return regression expressed in U.S. dollars. h

21 Approach 3: Term-Structure Models A very different approach to estimating the time-varying risk premium in the oil futures market was proposed by Hamilton and Wu (JIMF 2014). Rather than specifying predictors of the return, they infer the risk premium indirectly from the observed time series properties of weekly oil futures prices. Their premise is that some participants in this market use oil futures contracts to hedge oil price risk. The arbitrageurs who take the other side of these contracts receive compensation for their assumption of nondiversifiable risk in the form of positive expected returns from their positions.

22 Building on Ang and Piazzesi (2003), Hamilton and Wu propose a model of the determination of futures prices that relies on an affine factor structure for oil futures prices. Time-varying risk premia are identified from differences between observed oil futures prices and the rational expectation of oil futures prices implied by the term structure model. Risk-adjusted forecasts are constructed by removing this risk premium expressed in dollars from the futures price. In implementing this approach we rely on the same code as Hamilton and Wu (2014), but we extend the sample to June 2014.

23 Alternative Monthly Estimates of the Time-Varying Risk Premium in the Oil Futures Market at the 12-Month Horizon Dollars

24 Evidence on the Time-Varying Risk Premium The standard deviation of the risk premium across alternative specifications ranges from $0.52 in a given month to $ Alternative estimates of the risk premium may differ by as much as $56 for the same month. This raises the question of which estimates we can rely on and which ought to be discarded. Answering this question is essential for constructing a reliable measure of oil price expectations.

25 A Selection Criterion for Risk Premium Estimates Many economic models require measures of how the market expectation of the price of oil, denoted by Et( St h), has evolved over time in the past. Leading example: Models of automobile purchases (e.g., Kahn, QJE 1986; Busse et al., AER 2013; Allcott and Wozny, REStat, forthcoming) Our objective is to recover the time series that best characterizes what the financial market perceived to be the expectation of the spot price of oil at each point in time over our sample.

26 1. The conventional metric in assessing the accuracy of oil price expectations measures is their MSPE, defined as 2 ES [ E( S )]. t h t t h 2. Standard arbitrage arguments imply that the conditional h h expectation of the price of oil, Et[ St h] Ft RPt. 3. The conditional expectation minimizes the MSPE under any prediction error loss function that is symmetric about zero (see Granger 1969; Granger and Newbold 1986). Hence, F h t RP minimizes the MSPE. h t h h If F t RPt, h does not have lower MSPE than F t, the estimate of the time-varying risk premium is not credible. The most plausible risk premium model delivers the largest MSPE reduction.

27 Inference On Expectation Based on Two Metrics 1. All MSPE ratios have been normalized relative to the monthly no-change forecast of the WTI spot price of oil. A ratio below 1 denotes improved accuracy. MSPE reductions are evaluated based on the tests of Diebold and Mariano (1995) and Clark-West (2007), as appropriate. 2. Success ratios above 0.5 indicate improvements in directional accuracy on the no-change forecast and are evaluated based on the test of Pesaran-Timmermann (2009). Boldface indicates an improvement on the monthly nochange forecast. Statistically significant improvements test are marked using * (5% level) and ** (10% level).

28 Predictive Accuracy of Risk-Adjusted Futures Prices Based on Full-Sample Estimates during Horizon No Risk Premium F h t Time-Varying Risk Premium S 1 ˆ ˆ h F S / S t t t t Constant Risk Premium h S 1 ˆ F S / S t t t t (a) MSPE Ratio * (b) Success Ratio ** * *

29 Predictive Accuracy of Risk-Adjusted Futures Prices Based on Full-Sample Estimates evaluated on h Horizon F t B1 B2 BC S DNV1 DNV2 DNV3 (a) MSPE Ratio * ** ** ** * ** * ** ** ** * * * * * ** * * * * * * * * * (b) Success Ratio ** ** * * * * * Horizon GHR1 GHR2 HY1 HY2 PP1 PP2 PP3 BS HW (a) MSPE Ratio ** * * ** * * * * * * * * ** * * ** ** ** * * * * * * * * * * (b) Success Ratio * * * * * * * ** *

30 Summary of Results There are important differences across return specifications that were considered about equally successful based on other metrics. Some return models improve on the accuracy of the unadjusted futures price, even when the basis model does not. The Hamilton-Wu term structure model provides the most accurate measures of the market expectation of the price of oil. It is most accurate not only by the MSPE metric, but also based on directional accuracy.

31 Generalized Return Regressions A potential concern is that there is little agreement on the appropriate set of predictors. This suggests forming a return regression (labelled All Predictors ) that includes all 30 return predictors considered in the literature (except for BS because of data limitations). Based on the unrestricted return regression, the statistical significance of each predictor is assessed based on a two-sided t -test of the null of no predictability at the 10% level. Only the statistically significant predictors are retained in the return regression labeled After Pre-testing. These predictors are shown in bold in the next table.

32 p-values for t-tests on Predictors in all-predictor model Horizon (Months) B2 Returns on CRSP value-weighted equity index Change in 3-month T-bill rate Change in the term structure Change in default premium Unexpected change in U.S. industrial production Change in expected CPI inflation Unexpected CPI inflation DNV1 Returns on S&P 500 stock price index Gold hedging pressure Silver hedging pressure Platinum hedging pressure Heating oil hedging pressure Own-market hedging pressure GHR1 Normalized U.S. crude oil commercial inventories (no SPR)

33 HY1 1-month T-bill rate Yield spread Growth rate of oil market dollar open interest Basis BC Dividend yield on CRSP valueweighted equity index month T-bill rate Junk bond premium S Return on dividend yield on S&P 500 common stock portfolio Return on junk bond premium Market portfolio excess return PP1 Degree of capacity utilization in U.S. manufacturing PP2 Term spreads Term spreads Term spreads PP3 Composite leading indicator for OECD + 6 NMEs DNV3 Own-market price pressure

34 Predictive Accuracy of Risk-Adjusted Futures Prices Based on Full-Sample Estimates Evaluated on Horizon h F t All predictors After pretesting HW (a) MSPE Ratio ** ** * ** * * * * * * * * * (b) Success Ratio * * * * * * * * * * * *

35 Oil Price Expectations Based on All-Predictor Regression Dollars month Oil Futures Price without risk adjustment risk-adjusted Dollars month Oil Futures Price month Oil Futures Price month Oil Futures Price Dollars Dollars

36 Oil Price Expectations based on the Hamilton-Wu Model Dollars month Oil Futures Price without risk adjustment risk-adjusted Dollars month Oil Futures Price month Oil Futures Price month Oil Futures Price Dollars Dollars

37 What Does the Market Think? 12-Month Financial Market Oil Price Expectation Dollars NOTES: Risk-adjusted futures price based on Hamilton-Wu model.

38 Selected trajectories of h h F t, the Realized Spot Price S t, and F t RPt, from the HW Model h 40 April July 2004 Dollars Dollars t - 3 t t+3 t+6 t+9 t October 2005 spot price futures price risk-adjusted futures price 50 t - 3 t t+3 t+6 t+9 t +12 Dollars Dollars t - 3 t t+3 t+6 t+9 t January t - 3 t t+3 t+6 t+9 t +12

39 How Our Approach Differs from Earlier Studies 1. Many studies of the time-varying risk premium focus on insample evidence. Some studies also report simulated out-of-sample results based on rolling or recursive regressions for the excess returns. Unlike these earlier studies, we are not concerned with the predictive power of the excess return regression, but with the ability of the risk-adjusted futures price to predict the spot price. The latter question is only rarely addressed in the existing literature. One example is Pagano and Pisani (BE 2009).

40 2. Unlike in Pagano and Pisani, our objective is not to form expectations about the of price oil beyond the end of the available estimation sample. Rather our objective is to recover the market expectations that prevailed in the past. If the econometrician s objective is to recover an estimate of the market expectation that prevailed historically, clearly the most efficient approach is to use regression estimates based complete and fully revised data for the full sample (as opposed to realtime data). Predictive success as defined and measured here does not necessarily imply predictive success under conditions faced by applied forecasters, given the differences in the information set.

41 3. Our approach to selecting the most accurate expectations measure helps control for data mining in fitting excess returns. Searching for the most accurate return predictors inevitably invites overfitting, as researchers individually or collectively mine the data for the most successful predictive model of excess returns (see Inoue and Kilian ER 2004). Because our construction of the oil price expectations measure relies on a different loss function than the loss function used in fitting the excess return, we automatically penalize models of the time-varying risk premium that suffer from overfitting.

42 The model, i N 1,...,, that minimizes the MSPE of the return regression, defined as the average of h h h 2 t t h t h it, [( F S ) / S rp ], where rp it, is the fitted value from return regression i (and is expressed as a percent change or, equivalently, as a fraction), clearly is not in general the same as the model that minimizes the MSPE of the forecast of the spot price of crude oil in dollars based on the risk-adjusted futures price, given by the average of h h 2 t h t it, [ S F /(1 rp )]. This point is related to, but distinct from the result in Clements and Hendry (1998) that the ranking of two predictive models may change depending on whether we evaluate the MSPE of the growth rate or the log level of the dependent variable.

43 Evidence that our approach guards against overfitting the futures returns 12-month Oil Futures Returns: All predictors Percent observed expected month Oil Futures Returns: Hamilton-Wu Percent observed expected

44 Implications for Real-Time Oil Price Forecasts So far we have focused on measuring expectations that prevailed historically, as required for modelling purchases of automobiles or heating systems, for example. What about adapting these tools to help central banks and international organizations to form real-time forecasts of the price of oil? This requires the use of the data available at the time rather than complete and fully revised data. Below we abstract from the fact that some predictors are not readily available in real time. Hence, our results provide an upper bound on the real-time forecasting ability of these models. The initial estimation window ends in

45 Inference on the Recursive MSPE Reductions We follow the literature in assessing the statistical significance of the MSPE reductions based on the test of Clark and West (2007). This test (like similar tests in the literature) is biased toward rejecting the null of equal MSPEs. Thus, these test results have to be interpreted with caution. The reason is that it tests the null of no predictability in population rather than the null of equal out-of-sample MSPEs (see Inoue and Kilian ER 2004; Kilian JBES 2015). The alternative test of Giacomini and White (2006) does not apply either in our context because it does not allow for recursive estimation.

46 Risk-Adjusted Out-of-Sample Forecasts of the Spot Price of Oil: HW Model and Best Alternative Model evaluated on Horizon h F t Recursive Window HW PP3 Rolling Recursive Window Window (60 months) (a) MSPE Ratio ** * (b) Success Ratio * ** * * 0.541

47 Sensitivity Analysis: Quarterly Return Models Most empirical studies of the time-varying risk premium in the oil futures market rely on monthly return predictors. Only Acharya et al. (JFE 2013) and Etula (JFEconometrics 2013) are based on quarterly data. Their analysis includes some alternative predictors that are only available at quarterly frequency. Our substantive results are robust to changing the data frequency and adding these predictors.

48 Quarterly Predictors for Oil Futures Returns Article Model Predictors Etula (2013) E1 Effective risk aversion (broker-dealer variable) S&P500 excess return (proxy for market risk) E2 Effective risk aversion (broker-dealer variable) Lagged oil futures returns E3 Effective risk aversion (broker-dealer variable) Lagged oil futures returns VIX implied volatility for S&P500 3-month T-bill rate Yield spread (Aaa 3-month T-Bill) Dividend yield on S&P 500 common stock portfolio U.S. CPI inflation E4 E2 + basis + own-market hedging pressure

49 Quarterly Predictors for Oil Futures Returns Article Model Predictors Acharya, ALR1 Expected default frequency (EDF) in oil & gas sector Lochstoer & Basis Ramadorai Default spread (Baa Aaa) (2013) Median SPF forecast of quarterly GDP growth 3-month T-bill rate ALR2 Zmijewski-score (Zm) of default risk in oil & gas sector Basis Default spread (Baa Aaa) Median SPF forecast of quarterly GDP growth 3-month T-bill rate ALR3 ALR1 + Realized quarterly variance of oil futures returns (RV) + Interaction between EDF and RV ALR4 ALR2 + Realized quarterly variance of oil futures returns (RV) + Interaction between Zm and RV ALR5 ALR1 + Effective risk aversion (broker-dealer variable) + Interaction between EDF and effective risk aversion ALR6 ALR2 + Effective risk aversion (broker-dealer variable) + Interaction between Zm and effective risk aversion

50 Alternative Quarterly Estimates of the Time-Varying Risk Premium in the Oil Futures Market at the 4-Quarter Horizon Dollars NOTES: 11 alternative estimates of the quarterly time-varying risk premium proposed in the literature. Qualitatively similar results are obtained for other horizons.

51 Quarterly Oil Price Expectations based on the HW Term Structure Model Dollars quarter Oil Futures Price without risk adjustment risk-adjusted Dollars quarter Oil Futures Price quarter Oil Futures Price quarter Oil Futures Price Dollars Dollars

52 Risk-Adjusted Out-of-Sample Forecasts of the Nominal WTI Spot Price Based on Quarterly Recursive Estimates: Evaluated on 1992.I-2014.II h Horizon F t HW E1 E2 E3 E4 (a) MSPE Ratio ** ** * * (b) Success Ratio ** ** Horizon ALR1 ALR2 ALR3 ALR4 ALR5 ALR6 (a) MSPE Ratio * * * (b) Success Ratio

53 Conclusion Our approach to recovering the market expectation of the spot price can be applied, whenever there is disagreement between alternative models of the time-varying risk premium. Examples: Futures markets for foreign exchange, interest rates and other commodities. Our results also provide the basis for measuring shocks to expectations and studying their impact on the economy (see Baumeister and Kilian 2015a,b).