Zinc Futures Return Predictability and Selective Hedging Strategy

Transcription

1 Zinc Futures Return Predictability and Selective Hedging Strategy Jian Jia 1 and Sang Baum Kang 2 This Version: Jan 16, 2017 Abstract: We identify predictors for three-month Zinc futures returns among various macroeconomic and financial variables as well as technical indicators. We use London Metal Exchange (LME) Zinc futures daily data from Jan 1, 1995 to May 31, 2016 to test how the macroeconomic/financial variables combined with the technical indicators predict three-month Zinc futures returns. Additionally, we use the kitchen-sink dynamic predictive regression to implement the selective hedging strategy using three-month Zinc futures contracts. On the other hand, we use a technical indicator, the moving average, as a proxy for identifying up (bull) and down (bear) market conditions. We find that the TED spread, VIX, basis, BDI, and term spread show up as statistically and economically significant in our kitchen-sink specification dynamic predictive regression. The selective hedging strategy not only yields higher profits during our test period than those of no hedge and full hedge strategies but also shows a higher Sharpe Ratio than those of the other two. Overall, these macroeconomic/financial variables reveal substantial economic information content in Zinc futures risk premium forecast. JEL Classification: G13, G31, D81 Keywords: zinc; futures return predictability; selective hedging; trading strategy 1 CORRESPONDING AUTHOR. Illinois Institute of Technology; 10 W 35 th St, 18 th floor, Chicago, IL 60611, U.S.A.; jjia5@hawk.iit.edu; Illinois Institute of Technology; 10 W 35 th St, #18C4-1, Chicago, IL 60616, U.S.A.; skang21@staurt.iit.edu;

2 1 I. Introduction Commodities literature has paid a lot of attention to energies, precious metals, copper, and other base metals. However, academic research in zinc market is very thin. Arguably zinc market is important in global economy as well as financial economics. First, zinc is closely related to steel, because zinc products are used to prevent decay of steel. Zinc has been highly commoditized since at least 19 th century, but steel has not because of its heterogeneity in quality. Second, zinc is the third largest base metal next to copper and aluminum, according to the London Metal Exchange ( LME ). Third, zinc market is relatively more inefficient than other commodity markets (Kristoufek and Vosvrda, 2014). Therefore, Zinc market is an excellent laboratory to an inefficient commodity market. In this paper, we study zinc futures return predictability and its financial risk management implications. To contemplate the implications to financial risk management, we consider a fictitious zinc-processing firm which uses zinc as raw material to manufacture zinc products. The forecasting of zinc price/return adds value to the firms business planning and risk management activities and therefore to shareholders and decision makers. Financial risk management activities may help commodity end-users reduce their exposure to market risk. It is timely and relevant to ask whether zinc futures price returns are predictable, which economic variables predict zinc futures returns, and how the predictability helps to implement selective hedging strategies for zinc price risk management. Over the past few years, academic research in in commodity futures market has increased substantially. The predictability of commodity futures returns and hedge strategies/decisions are an important part of commodity futures literature. The widespread interest in commodity futures is in part associated with the notion that commodity futures may be a good diversification vehicle because of lower or negative correlations with stocks and bonds (Gorton and Rouwenhorst, 2006). Commodity futures is also an effective hedge tool either in production side or in macroeconomic activity side (Bodie, 1983; Hirshleifer 1988; Edwards and Park, 1996). Moreover, recent evidence suggests that momentum strategies in commodities can generate significant profits (Miffre and Rallis, 2007). The unique characteristics, such as the weather conditions, seasonal supply and demand, and storage and transportation cost, make the behavior of commodity price strikingly different from that of other assets such as stocks and bonds. The mainstream theory in commodity pricing, namely the theory of storage (see, Kaldor, 1939; Working, 1948; Brennan, 1958; Telser, 1958), explains the difference between spot and futures prices in term of economic fundamentals. Moreover, it has major implications for the volatility of commodity prices. On the other hand, the hedge pressure hypothesis (see, Keynes, 1927; Hicks, 1939; Cootner, 1960; Hirshleifer, 1988, 1990) focuses on the futures trading decisions of processors or storage firms on futures hedging and price determination. In production side, these studies review either the cost of purchasing the raw commodity or the value of the output produced as the source of risk. Some others show that the commodity price

3 2 shocks link to macroeconomic fluctuations the evidence is not only in oil prices shocks (Bernanke et al., 1997; Hamilton, 2009), but also the boom-bust patterns in metal commodity futures market (e.g. Chile and copper). Chen, Rogoff, and Rossi (2010) use standard regression model and several commodity currencies the exchange rates from a number of commodity exporting countries to show robust forecasting power over global commodity prices. These encouraging results have led to a resurge of interest in forecasting commodity prices/returns, in particular with the use of richer predictor set or more advance models. Numerous economic variables have been explored in previous literature of commodity futures return predictability. One stream of academic studies relies widely on macroeconomic variables (Gargano and Timmermann, 2014). Specifically, these studies investigate the price linkage, the dependence structure, or the information spillover effect between macroeconomic variables and asset markets, including the dollar exchange (Chen and Chen, 2007; Wu et al., 2012), stock prices (Chen, 2014), U.S. and global macroeconomic aggregates, interest rates, various kinds of global economic shocks, commodities, and so on. There remains ongoing, however, debate concerning the predictive power of macroeconomic variables, suggesting that the predictive ability of macroeconomic variables behaves inconsistently, the reason being that different macroeconomic variables might perform different predictability in different commodities. As there are few studies that test the predictability of Zinc futures returns, our study contributes to the finance literature by documenting predictors of Zinc futures return. Meanwhile, technical indicators such as moving average and momentum strategy, which are not necessarily based on economic theory, are widely used in practices. Such technical indicators may work well because metal markets are less efficient than other markets such as crude oil and natural gas. However, the empirical evidence of the performance analysis technique in a commodity market seems to be mixed. The moving average and momentum strategy can yield statistically and economically significant profit with a one- to nine-month holding period for 28 commodities (Shen et. al, 2007, 2010). In the energy sector, the mean-reverting calendar spread and Bollinger Bands could also generate significant profit and higher Sharpe Ratio (Lubnau and Todorova, 2015). However, Marshall, Cahan and Cahan (2008) find evidence that technical strategies are not consistently profitable after investigating the performance of strategies based on 7,000 technique rules in 15 major commodities. However, relatively little empirical work has been undertaken on the predictability of zinc prices by means of technical indicators. This paper contributes to commodity returns predictability literature in several ways. First, this article complements existing papers of commodities price predictability, which has often ignored technical indicators. We document that a combination of technical indicators and macroeconomic/financial predictors forecasts zinc futures realized returns. Previous studies have documented that technical rules are useful for predicting stock and currency returns, while little attention has been paid to emerging commodity market. Moreover, we perform rigorous analysis

4 3 in both static and dynamic predictive regression model to support the predictability of a combination of these two predictor sets. To our knowledge, it is the first paper to combine macroeconomic/financial variables and technical indicators in a unified framework where a technical rule is used as an identifier of upward/downward market and the coefficients of macroeconomic/financial predictors in the upward market are different from those in the downward market. Second, to end-users of metal futures, our study will provide some insights into what trading signals a manager should monitor the macro/financial predictors, the technical rules, or both? We also show that the identified trading signals are instrumental to the end-users of metal futures who implement hedging strategies by using such signals as trading signals. The remainder of this article is structured as follows. Section II introduces the description of different hedging strategies and model specifications. Section III reports the numeric results. Section IV discusses our findings. Section V concludes. II. Description of strategies There are three typical hedging strategies for commodity price risk management: the no hedge strategy, the full hedge strategy, and the selective hedging strategy. We use our dynamic kitchensink predictive model, a regression model including all the macro/financial variables and technical indicator, to generate trading signals, then use the trading signals to implement the selective hedging strategy. We do know that in reality the business world is a lot more complicated and there are lots of hedging strategies other than no hedge or full hedge strategies; therefore, we simply use our no hedge and full hedge strategy on an end-user of metal futures as a proxy for business. The specifications of the strategies are as follows: No hedge strategy Three-month zinc futures are relevant to a zinc processor who buys a raw zinc and sell its zinc product in 3 months. For simplicity assume that the manufacturing company buys the spot zinc from London Metal Exchange (LME) to produce the zinc product. Also, assume that the zinc product is indexed at the LME spot zinc price index. The no hedge strategy for the company is quite simple (See Figure I): At the beginning of each month, the company buys the raw zinc material to manufacture its zinc product from LME at spot price S T of time T. Then three months later, they sell the finished zinc products at LME zinc spot price S T+3 at time T+3 months. Thus, the payoff of the no hedge strategy at time T+3 months is P/L = S T+3 S T.

5 4 Buy raw zinc material at price S T to manufacture zinc product Sell zinc product at price S T+3 T T + 3 months Time Figure I. No hedge strategy specification Full hedge strategy Like the no hedge strategy, the full hedge strategy is also a suitable strategy for the company we defined above based on the zinc production time horizon. Basically, the full hedge strategy means that the company always shorts the three-month zinc futures contract each month. Similarly, Figure II depicts the full hedge strategy specification: At the beginning of each month, the company does business as per the usual procedure, meanwhile taking a short position on the three-month zinc futures contract. Then three months later, the company delivers the zinc product as usual but also buys the raw zinc materials from LME at price S T+3 to cover the short position. Therefore, the payoff of the full hedge strategy for each month is P/L = (S T+3 S T ) + (F T,T+3 S T+3 ) = F T,T+3 S T. Buy raw zinc material at price S T to manufacture zinc product, meanwhile, short 3-month zinc futures at price F T,T+3 Sell zinc product at price S T+3, at same time, buy raw zinc materials at price S T+3 to cover short position T T + 3 months Time Figure II. Full hedge strategy specification Selective hedging strategy However, even though the full hedge strategy can reduce the spot price risk, the full hedge strategy must still face the basis risk. It is necessary to develop a premier hedging strategy to minimize the risk tolerance; therefore, we construct the dynamic kitchen-sink specification

6 5 model 1 to predict the three-month realized futures returns. Furthermore, we use the predictability to generate trading signals for each month, thereby easily implementing the dynamic selective hedging strategy based on the trading signals. Specifically, in a down market (the expected return is negative), the company could take the short position to hedge the downside risk and no position otherwise. We use the macro/financial variables as the major predictors. Meanwhile, we introduce the technical indicator as the proxy for market condition which indicates what the predictability is in both bull and bear markets. The macro/financial 2 variables are as follows: TED spread: the difference between the three-month LIBOR rate and the three-month T-Bill rate. VIX: measures the volatility implied by option prices on the S&P 500 over the coming month. A higher value in the VIX is taken as an indication of market participants expecting an overall negative economic or financial outlook and thus an increased (global) risk aversion. Basis: the difference between the three-month futures price and the spot price at time T, which is Basis t = F (τ) t St. S t BDI: used as a proxy for global trade flows as well as supply and demand trends in production of finished goods and raw materials. The BDI is frequently viewed as a leading indicator of future global economic growth. S&P 500 daily return: Rapach et al. (2013) have indicated that returns in the U.S stock market are predictive for returns in various other global stock and commodity markets. Term spread: defined as the difference between the U.S. 10-year T-Bond and the threemonth T-Bill; it is well known to be a real-time predictor of economic activity. Moving average 3 : We use the relationship between the three-month futures price moving average and the nine-month futures moving average as the MA indicator. It s a dummy variable equals to 1 (buy signal) if the MA(3) is higher than the MA(9), and otherwise. On the other hand, this indicator can be used as a proxy for identifying market condition equals to 1 if the market is bull market and otherwise. 1 We also use univariate regression to test the predictability of each predictor, but the results are not consistent and the dynamic selective hedging does not show stable results. These results are shown in the Appendix. 2 We use the macro/financial variables on a daily basis to match the prompt date structure of LME market. 3 We also try another moving average selection period; however, the combination of three and nine months shows stable results.

7 6 Dynamic model specification We use the following Ordinary Least Square predictive model including both macro predictors and technical indicator (moving average): ret t,t+3 = α + α 1 MA t + β 1 X i,t + β 2 X i,t MA t + ρ i ret t 3i,t 3i+3 + ε t. (1) 8 i=1 where the X i,t represents all the macro/financial predictors we mentioned above. The MA t represents the moving average indicator which is the MA(3,9) indicator; and this indicator is a dummy variable which is the bull market if it equals to 1, and 0 otherwise. Additionally, we include eight historical three-month realized futures returns in our regression as the control variables. We also detrend the three-month realized futures returns to make our results meaningful and stable. Furthermore, we are more interested in the coefficient of β 1 and β 1 + β 2 because the coefficient β 1 could provide the predicted direction/slope when the technical indicator variable is off (bear market), while the coefficient β 1 + β 2 provides the above information for a bull market. It is important to know whether the predicted directions of predictors are consistent in both bull and bear markets. The model (1) is able to predict the expected three-month futures realized returns based on the informative macro/financial variables. Afterward it is executable to implement the selective hedging strategy based on the expected trading signals which are as follows: +1 if E(ret t,t+3 ) > 0 Signal i,t {. (2) 1 if E(ret t,t+3 ) < 0 where the company could take short positions on three-month zinc futures if the expected threemonth futures realized returns are negative and no position otherwise. If the predictive model could correctly predict the direction of three-month futures realized returns, the selective hedging strategy is a profitable strategy for the produced company. In the next section, we will discuss in more detail the numeric results to support our predictive model. III. Empirical results Because of the worldwide presence of its storage facilities and deep liquidity, the LME is considered as the de facto price discovery venue for industrial metals. During the recent two decades, 3-month futures were the most traded contracts among all maturities (Fernandez, 2016). Thus, we gather from Bloomberg spot and 3-month futures prices of zinc in daily basis. On its maturity date, a 3-month futures contract is settled against the official settlement price, which is defined as the last cash offer price of a midday trading session. We calculate the realized futures

8 7 returns from the futures price on the daily basis from 01/01/1995 to 05/31/2016 and its spot price on the maturity date. We firstly run the full sample predictive regression to evaluate the fit information of our kitchen-sink predictive model. Furthermore, we use the dynamic predictive regression to test whether the predicted direction is consistent with the full sample fit information and the previous literature. Finally, we report the P/L of our selective hedging strategy based on the predictive model compared with that of the no hedge and full hedge strategies. Table I Full Sample Kitchen-sink regression estimation Predictor Slope coefficient T-statistic Predictor Slope coefficient T-statistic TED Spread *** TED * MA (3,9) VIX *** VIX * MA (3,9) *** Basis * Basis * MA (3,9) *** BDI *** BDI * MA (3,9) *** S&P 500 Ret S&P 500 * MA (3,9) Term Spread *** Term * MA (3,9) *** MA (3,9) *** # of Observations 5,269 Deg. of Freedom 5,256 Adjust R % Note: The sample period starts from 1/1/1995 and goes to 5/31/2016. Columns two and five are the slope coefficients for all predictors. We use the Hansen-Hodrick standard errors, correcting for overlapped intervals, to calculate t-statistic, as reported in columns three and six. We also winsorize the detrend return and macro/financial predictors at 5- and 95-percentiles to mitigate the outlier effects without excluding any observations. For ease of interpretation, we normalize all predictors. *, **, and *** indicate statistical significance at a 10%, 5%, and 1% level, respectively. Table I clearly depicts that most of the predictors show significant predictability, with the exception of S&P 500 daily returns. The VIX could positively predict the three-month futures realized returns, which are consistent with previous literature, while it is convincing that the greater uncertainty leads to higher futures premium and higher expected futures returns the

9 8 expected three-month futures realized return increase by 1.158% with one standard deviation increase in VIX. On the other hand, the basis also showed significantly negative futures returns predictability which is consistent with previous literature. The TED spread and term spread both have significantly negative futures returns predictability, which means the lower risk aversion or the yield curve would lead to a higher risk premium and higher expected futures returns. Furthermore, the BDI negatively predicts the expected futures realized return, which is the lower BDI creates higher expectation of future spot price. However, the S&P 500 daily returns do not show significantly positive futures returns predictability. The MA(1,9), a moving average technical indicator, shows significant positive futures returns predictability the three-month futures realized returns increase by 3.35% if use the MA(1,9) as the trading signal or in the bull market. The whole sample period predictive regression test provides more promising results for the predictability of three-month zinc futures realized returns. However, we cannot rely on the full sample period regression results because of the very long period used, and the coefficient might time variate. Therefore, we use the dynamic rolling regression to test whether the predictability still holds and provides the stable selective hedging outcome. We construct the dynamic predictive model by using a two-year rolling window. Firstly, we use the first 24 months period to predict the expected three-month futures realized returns of the 25 months and then use the 24 months period between month 2 and month 25 to predict the expected three-month futures realized return for the 26 months and so on and so forth. Finally, we arrive at the monthly coefficients and the monthly expected three-month futures returns from Jan 1997 to May 2016.

10 9 Figure III. Coefficient β 1 plot plus confidence interval for all predictors in kitchen-sink specification model As we mentioned in the model specification section, we are more interested in both the β 1 and β 1 + β 2. Figure III and Figure IV show the coefficient plot of both β 1 and β 1 + β 2 for all macro/financial predictors. The two figures also include the 95% confidence interval to track significance of each predictor in each month. The red line is the coefficient plot; the black vertical line is the confidence interval for the specific coefficient. On the other hand, we define the significant correct direction if the sign of coefficient is significantly consistent with that of whole sample results, or the sign of the coefficient is insignificantly inconsistent with that of whole sample results.

11 10 Figure IV. Coefficient β 1 + β 2 plot plus confidence interval for all predictors in kitchen-sink specification model Figure III illustrates that most predictors show consistent predictability with that of the whole sample regression no matter what the predict direction or the significance. For example, the VIX (+), the TED spread (-) and the basis (-) shows correct significantly predictability in most time even though the coefficients have some jump risk. Therefore, in a bear market, these three predictors show consistent predictability for zinc futures realized returns. However, the BDI, term spread, and S&P 500 returns do not show significant predictability even though the signs of these are consistent with the whole sample regression. Similarly, Figure IV shows that

12 11 the coefficients plot of β 1 + β 2, the bull market predictability, are also consistent with that of β 1, which means no matter what the market condition is, the macro/financial predictors show consistent predictive power for three-month zinc futures realized returns, especially for VIX with positive predictability and basis with negative predictability. Afterward, we can carry out the dynamic selective hedging strategy. We generate the first trading signals in Jan. 1997, and realize gain/loss three months later. In other words, the first gain/loss starts in April 1997 and ends in May 2016 (230 months gain/loss). To calculate the Sharpe Ratio, we calculate the excess gain/loss in each month, which is the difference between the realized gain/loss and the three-month risk-free rate investment. Table II indicates the summary statistics of the 230 months gain/loss along with the Sharpe Ratio for the three different strategies. The full hedge strategy provides lower volatility during the testing period but higher Kurtosis because the full hedge strategy only bears the basis risk. The selective hedging strategy has a highest mean and median gain/loss among the three hedging strategies even though the selective hedging strategy still bear high uncertainty, additionally, it dominates the no hedge strategy and full hedge strategy by generating a highest Sharpe Ratio. Table II Summary statistics of P&L for three trading strategies Selective Hedging No Hedge Full Hedge Mean ($/ton) Standard Error Median ($/ton) Sharpe Ratio % 0.072% % Standard Deviation Kurtosis Skewness Range Minimum Maximum Months We also compare the growth of fund for the three different hedging strategies. We simply assume that the company only long or short one contract into position. And the starting fund is

13 12 three times that of the three-month futures price in the first month. Figure V shows the growth of fund comparison of the three hedging strategies. It emphasizes that the full hedge strategy is the more stable or safer hedge strategy compared with the other two, but that the gain/loss of each period is quite small. It again clearly depicts that the selective hedging strategy dominates the no hedge strategy and has higher gain most of the time compared with the full hedge strategy. Figure V. Growth of fund comparison for hedging strategies IV. Discussion Overall, the no hedge strategy is a bad strategy for the company to continue operating even though it generates more profit in certain periods (e.g., commodity expansion period). In other words, the no hedge strategy is more volatile and has more up and down through the sample period because it heavily relies on the spot price. Furthermore, the commodity markets are uncertain and are more likely to be affected by the economic shocks. Taking the no hedging strategy was more harmful for business during the two financial crises (the 1999 tech bubble and the 2008 great financial crisis). On the other hand, the full hedge strategy is not a bad strategy even though the payoff is quite small. It appears that the risk-free rate plays a safety role for companies and for business. In other words, the full hedge strategy can be treated as a fair strategy, being effective in the bear

14 13 market while helping business rid itself of economic shocks (the great financial crisis period), whereas it is a very costly and unnecessary strategy in the bull market. Finally, the numeric results clearly show how good the selective hedging strategy is. However, the selective hedging strategy is riskier than the full hedge strategy. If the model is not carefully implemented, it could cause the reverse effect and become ineffective. Specifically, if the predictive models are carefully implemented, the selective hedging strategy is not a bad strategy. In other words, the selective hedging strategy can not only help business reduce a huge economic shock effect in the bear market but also help business minimize the risk management cost in the bull market. Therefore, selective hedging would be a very effective way if the manager carefully chooses the right predictive model. V. Conclusion Even though the notions of theory of storage and hedging pressure, the debate of the predictability of macroeconomic variable in commodity futures markets is still very much flourishing today. Since zinc market is important in global economy as well as financial economics, movements in zinc prices can therefore be seen as an early indicator of global economic performance. Indeed, the relatively inelastic supply of zinc, because of the technical and resource lags in expanding production, makes the metal react quite promptly to global demand cyclicality. Meanwhile, zinc-processing firms have been increasing dramatically in recent years because of the thriving of steel makers and highly correlation between zinc and steel. Forecasting changes in zinc futures prices is therefore an important task for forward-looking policy-makers, and the company s decision-maker or shareholders to implement hedging strategy. From the LME zinc futures data, we construct a kitchen-sink dynamic predictive model to identify predictors for three-month zinc futures returns among various macroeconomic and financial variables as well as technical indicators. Using a technical indicator, moving average, as a proxy for identifying up (bull) and down (bear) market condition, we find that the TED spread, VIX, futures basis, BDI and term spread show up as statistically and economically significant in our kitchen-sink dynamic predictive regression. Additionally, we use such predictability as to implement dynamic selective hedging strategy for commodity end-users no matter who the zinc-processing firm or the firm use zinc product, comparing the profitability with another two typical hedge strategies: no hedge strategy and full hedging strategy. We find that the selective hedging strategy not only yields higher profits but also shows a higher Sharpe Ratio during our test period than those of other two strategies. Overall, these macroeconomic/financial variables reveal substantial economic information content in zinc futures risk premium forecast, and the selective hedging strategy, implementing by such predictability, could help the commodity end-users do a better risk management.

15 14 This article may open an avenue of new research. Our results suggest that both chartist perspectives (technical indicators) and the fundamentalist perspectives (macroeconomic/financial predictors) work well in the zinc futures market. Motivated by our findings, an economist may want to investigate the role of market efficiency in the theory of storage, the theory of normal backwardation, and the theory of economic activities, to increase our knowledge about pricing of commodity futures contracts. The expected returns coming from technical rules and macroeconomic/financial predictors may give a new insight into how the market is efficient or inefficient relative to what financial economists know. References: 1. Bahmani-Oskooee, M., Harvey, H., & Hegerty, S. W. (2013). The effects of exchangerate volatility on commodity trade between the U.S. and Brazil. The North American Journal of Economics and Finance, 25(August), Bernanke, B. S., Gertler, M., & Watson, M. (1997). Systematic monetary policy and the effects of oil price shocks. Brookings Papers on Economic Activity 1, Bodie, Z. (1983). Commodity futures as a hedge against inflation. Journal of Portfolio Management 9(3), Brennan, M. (1958) The supply of storage, American Economic Review 48, Bhar, R., & Mallik, G. (2013). Inflation uncertainty, growth uncertainty, oil prices, and output growth in the UK. Empirical Economics, 45(3), Brunnermeier, M. K., Nagel, S., & Pedersen, L. H. (2009). Carry trades and currency crashes. In D. Acemoglu, K. Rogoff, & M.Woodford (Eds.), (Vol. 23) NBER macroeconomics annual 2008 (pp ). University of Chicago Press. 7. Campbell, J. Y., & Thompson, S. B. (2008). Predicting excess stock returns out of sample: Can anything beat the historical average? Review of Financial Studies, 21(4), Chan, K., Tse, Y., & Williams, M. (2011). The relationship between commodity prices and currency exchange rates: Evidence from the futures markets. In T. Ito, & A. K. Rose (Eds.), (Vol. 20) Commodity prices and markets, NBER East Asia seminar on economics (pp ). University of Chicago Press. 9. Chen, Y., Rogoff, K., & Rossi, B. (2010). Can exchange rates forecast commodity prices? Quarterly Journal of Economics, 125(3),

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18 17 Appendix The appendix includes the coefficient β 1 plot plus confidence interval of univariate dynamic regression and the same graph for the coefficient β 1 + β 2. Recall the univariate predictive regression: ret t,t+3 = α + α 1 MA t + β 1 X i,t + β 2 X i,t MA t + ρ i ret t 3i,t 3i+3 + ε t. (1) 8 i=1 where the X i,t represents the macro/financial predictors we mentioned in the report. The MA t represents the moving average indicator which is the MA(3,9) indicator, and this indicator is a dummy variable which is the bull market if it equals to 1, and 0 otherwise. Additionally, we include eight historical three-month realized futures returns in our regression as the control variables.

19 Appendix. Figure I. coefficient β 1 plot plus confidence interval for each univariate dynamic regression 18

20 Appendix. Figure II. coefficient β 1 + β 2 plot plus confidence interval for each univariate dynamic regression 19