Futures Prices are Useful Predictors of the Spot Price of Crude Oil.

• Author: Ellwanger, Reinhard

1. INTRODUCTION

   Given the importance of crude oil as a macroeconomic determinant used in models of central banks, in investment decisions, and in oil-intensive goods purchases, there is wide interest in accurately predicting the price of crude oil. (1) A frequently cited result in this literature is that futures prices are not particularly useful to forecast the spot price of crude oil (Alquist and Kilian, 2010; Reeve and Vigfusson, 2011; Baumeister and Kilian, 2012; Alquist et al., 2013; Baumeister and Kilian, 2014). In this paper, we document that future-based forecasts have always been useful for short-horizon forecasts of the average spot price of crude oil and are now very accurate at longer horizons. This occurs for two reasons.

   First, we show that futures curves constructed using end-of-month prices contain substantive predictive power for future average prices at short horizons. Incorporating end-of-period information improves the mean-squared prediction error (MSPE) and the directional accuracy relative to the no-change forecast for average spot prices by 40 percent at the one-month horizon. The improvements remain statistically significant for forecasts up to 12 months ahead. They are remarkably robust and independent of the sample period.

   Second, the predictive content of crude oil futures prices at longer forecast horizons has improved since the mid-2000s. We show that, whenever the end of the forecast evaluation period is extended beyond 2014, futures-based forecasts are found to be statistically significantly more accurate predictors of the spot price than the no-change forecast at horizons of one year to five years ahead. This result holds for forecasts of both nominal prices (as in Alquist and Kilian, 2010) and real prices (as in Baumeister and Kilian, 2012). It is particularly strong for multi-year-ahead forecasts, which were previously difficult to evaluate due to the lack of a proper evaluation period for longer-dated futures contracts. This corroborates and generalizes some existing evidence on the usefulness of future-based forecasts of real prices at longer horizons. (2)

   A key insight from our exercises is that futures-based forecasts should always be constructed using end-of-period prices rather than the average price that is standard in forecasts of the real price of oil (Baumeister and Kilian, 2012; Alquist et al., 2013). This seemingly innocuous difference yields substantial improvements for short-horizon forecasts. The use of end-of-period prices is preferable because averaging changes the underlying data process (Rossana and Seater, 1995), which leads to a mechanical loss of information that is particularly relevant for forecasting persistent processes (Wei, 1978; Lutkepohl, 1984). Ellwanger and Snudden (2021) propose a parsimonious solution to the information loss via period-end price sampling (PEPS). They show that real end-of-month spot prices can improve the forecast accuracy of no-change forecasts and of model-based forecasts by preserving the informational content of the last available price. In this paper, we show that the same principle can be applied to forecasts constructed from futures prices.

   Futures curves constructed with end-of-month prices have previously been used in Alquist and Kilian (2010) in the context of forecasting of the end-of-month nominal crude oil price. However, the model was never used to forecast average spot prices, which are standard for real prices. While the distinction between end-of-period and average futures prices is crucial, the role of the deflator appears to be negligible for our results: using information from end-of-period futures prices work similarly well for forecasting average nominal and real prices.

   The results contribute to a recurring debate on the role of futures prices in forecasting oil prices. Because of their simplicity and ease of implementation, futures-based forecasts are popular among policy makers, investors and market participants. Early results from the academic literature documented some predictability from oil futures prices, at least at specific horizons (Ma, 1989; Kumar, 1992; Chinn et al., 2005; Coppola, 2008). However, influential reviews that extended the sample period beyond the early 2000s found little evidence that futures-based forecasts are helpful to forecast oil prices and recommended against their use (Alquist and Kilian, 2010; Baumeister and Kilian, 2012). Still, futures prices have remained a steady ingredient in the construction of forecast combinations (Baumeister and Kilian, 2015; Funk, 2018; Garratt et al., 2019), while other approaches focused on improving futures-based forecast by separating their expectations component from the risk premium (Baumeister and Kilian, 2016). Our results show that a decade's worth of additional data, as well as a simple modification to the originally proposed implementation, changes the assessment of futures-based forecasts of the price of oil.

2. FUTURES-BASED FORECASTS

   The goal of this paper is to study the predictive content of oil futures for the spot price of crude oil. The spot price of oil is determined in market transactions for immediate delivery and used as a key macroeconomic indicator by both academics and policy makers (see, e.g. Alquist and Kilian, 2010). By contrast, futures contracts are financial instruments that allow traders to lock in today a price at which to buy or sell a fixed quantity of oil on a predetermined date in the future. The inherent forward-looking nature of these contracts contributes to the wide-spread interest of futures as predictors of spot prices.

   Following existing practice, we construct futures-based forecasts for monthly data using the percentage spread of the futures price with maturity h, [F.sub.t,x.sup.h], over the spot price, [S.sub.t,x]. (3) For nominal prices, the h-step-ahead forecast is

   [Please download the PDF to view the mathematical expression] (1)

   where t denotes the current month, h denotes the forecast horizon, and x is an indicator for the price series that distinguishes between end-of-period observations (x = n) and monthly average observations (x = a). The monthly average price is the average of the n daily closing prices within the month, [Please download the PDF to view the mathematical expression]. In a similar fashion, futures-based forecasts for real prices are constructed via:

   [Please download the PDF to view the mathematical expression] (2)

   where [E.sub.t]([[pi].sub.t.sup.h]) is the expected U.S. inflation rate over the next h periods, and [R.sub.t,x], x [member of] {a, n}, is the monthly measure of the real price of crude oil.

   The distinction between average and end-of-period futures and spot prices clarifies the use of alternative futures-spreads and spot prices in the literature. For example, Alquist and Kilian (2010) forecast the end-of-month nominal spot price, [??] using end-of-month futures prices, [F.sub.t,x.sup.h] = [F.sub.t,n.sup.h]. (4) By contrast, average prices are typically considered to be more economically relevant for the construction of macroeconomic variables and total payoffs to oil intensive physical investments. As such, the standard series for the real price of oil used in structural work and forecasting applications has always been the average monthly price, [R.sub.t,a] (see, e.g., Kilian, 2009; Alquist et al., 2013; Baumeister and Kilian, 2014, 2015).

   In most applications, the futures-based forecast for real prices, [R.sub.t,a], has been constructed with average futures prices, [F.sub.t,a.sup.h]. (5) However, averaging oil prices can lead to a loss of information about price levels relative to end-of-period observations (Benmoussa et al., 2020). A key contribution of this study is to systematically compare the relative forecast performance of end-of-period futures prices, [F.sub.t,n.sup.h], and average futures prices, [F.sub.t,a.sup.h], for the monthly average real price of oil, [R.sub.t,a].

3. APPLICATION TO REAL-TIME FORECASTS

   We construct monthly, recursive, real-time, and out-of-sample forecasts following Baumeister and Kilian (2012). Our baseline estimates are for West Texas Intermediate (WTI) crude oil. Forecasts for spot prices of alternative crude oil benchmarks, Brent and the U.S. refiners acquisition cost of imported crude oil, are considered in the robustness analysis. Monthly and daily spot prices for all crude oil series were obtained from the Energy Information Administration (EIA). Daily futures prices were collected from Haver. Contracts for different delivery months are traded with maturities up to 7 years. Contracts are used as continuous series, [F.sub.t,i.sup.h], with h =1 referring to the front contract, h = 2 referring to the second back contract, etc. Because trading for the front contract stops several days prior to the last business day of the month preceding delivery, the front contract rolls over to the next contract before the end of the month, typically around the 21st of the month. (6) This means that the standard average futures price is based on prices for two adjacent contracts. (7)

   For forecast horizons of up to one year, our sample starts in 1992M1. For longer-term contracts, the sample starts when the contract values begin to be regularly reported: 1995M5 for the 2-year-contract, 2006M3 for the 3-year contract, and 2007M8 for the 5-year contract. (8) For all forecasts, the sample period ends in 2021M1.

   To construct real prices, monthly prices are deflated using real-time vintages of the seasonally adjusted U.S. consumer price index obtained from the FRASER database of the Federal Reserve Bank of St. Louis and the Philadelphia Federal Reserve. Expected inflation is derived from the CPI price index, which is projected using the historical average for CPI inflation from 1986M7 following Baumeister and Kilian (2012).

   Forecast evaluation is conducted using the mean-squared prediction error (MSPE) ratio and the success ratio for...