Forecasting Return and Volatility

Backed by Tomek and Peterson (2001) who argued that forecasting models have statistical but not economic significance, a graphical representation is used for forecasting purposes. The sample for forecasting is set from January 2000 to Dec 2000 and a static forecasting technique is used115. Supported by Jackson, Maude and Perraudin (1997) who argued that the forecastability of volatilities and the sensitivity of the forecasts to different techniques depend very much on the return series in question, graphs 4.8–4.11 in Appendix 6.14 show the forecasted returns of hedgers and speculators under both GARCH and PARCH models, and under both normal and t probability distributions. Actual futures returns complement each graph to compare actual with forecasted returns.

178 Findings in graphs 4.8–4.11 show that both returns for hedgers and speculators, under GARCH and PARCH models, follow nearly the same close trend in all 29 markets. This is further supported by the fact that 95% confidence intervals of the forecasted returns under GARCH and PARCH models are calculated for all 29 markets, and all of them are wide enough to include the actual returns within the intervals range116. Moreover, for hedgers’ forecasted returns, the (GARCH, normal) underestimates (overestimates) in 13(8) markets, while under (PARCH, normal), hedgers’ forecast returns are underestimated (overestimated) in 11(8) markets. For speculators’ returns, the (GARCH, normal) model underestimates (overestimates) the forecast in 14(9) markets while under PARCH model in 13(9). Under (GARCH, t), hedgers’ forecast returns are underestimated (overestimated) in 12(9) markets, and under (PARCH, t) in 15(8). For speculators, the (GARCH, t) underestimates (overestimates) the forecast returns in 17(8) markets. While the highest number of underestimated forecasts is 17 under (PARCH, t) for speculators’ forecast returns, the number of overestimated forecasts are generally the same across all four models. This suggests that the GARCH and PARCH models are generally more affected by increasing actual returns compared to decreasing actual returns. This is analogous to the decreasing trend in net positions observed in December 1999 just before the forecast of January 2000. In line with Ding and Granger (1996), the GARCH model under normal distribution puts too much weight on recent observations relative to those in the past. Further, under t distribution, the PARCH model with its high number of underestimated returns forecasts can be attributed to high sensitivity of standard deviation over returns. This is in line with Poon and Granger (2003) who found that standard deviation is more proportional to derivatives prices than variance models.

In deciding which of the four models of graphs 4.8–4.11 better predict the actual returns, the first month forecast returns is compared with the actual futures returns, and only those markets’ returns which have been correctly forecasted are reported. For hedgers, the (PARCH, normal) model ranks first with ten good forecasts of one-month

179 return117. The (GARCH, normal) and (GARCH, t) rank equally 2nd with eight good forecasts118. (PARCH, t) ranks last in predicting the one-month actual returns. As for speculators, the best models are (PARCH, normal) and (GARCH, t) which rank equally 1st with seven good forecasts119. (GARCH, normal) ranks 3rd with six good forecasts120, while (PARCH, t) ranks again last with only four good forecasts. The reason for (PARCH, t) ranking last is due to the high number of underestimated forecast returns. The (PARCH, normal) ranks first by producing also the least number of underestimated forecast returns. In comparing the number of good forecasts achieved under hedgers’ and speculators’ returns, it can be observed that hedgers’ returns are better forecasted than speculators’ returns. Further, the (PARCH, normal) model appears to work better in forecasting hedgers’ one-month return than speculators’ one-month return121.

Having looked at the forecasted returns under GARCH and PARCH models, it is also worthwhile to consider the conditional standard deviation under PARCH model and the conditional variance under the GARCH model. Due to the volatile characteristics of standard deviation and variance, it is better to have an outlook of the whole sample data rather than just for the forecast sample. The idiosyncratic volatility used before in this study is also included as a proxy of actual volatility, for comparison with the conditional variance and conditional standard deviation. Based upon the good one-month forecast returns obtained above, it is interesting to know whether the idiosyncratic volatility

117 _{These markets were live hogs, lumber, coffee, cotton, corn, soybean oil, soybean meal, S&P500, sugar}

and soybean.

118 _{Under (GARCH, normal), these markets were lumber, coffee, corn, soybean oil, soybean meal, S&P500,}

sugar and soybean. Under (GARCH, t), in addition to live hogs, the markets were same as (GARCH, normal) except for coffee.

119 _{Under (PARCH, normal), these markets were wheat (Minnesota), lumber, copper, crude oil, soybean oil,}

S&P500, and sugar. Under (GARCH, t), in addition to Eurodollars, these markets were the same as under (PARCH, normal) except for wheat (Minnesota).

120 _{These markets are the same as under (PARCH, normal) except for S&P500.}

121 _{It is important to know that only one-month forecast return (January 2000) has been analysed here.}

Tables 4.3-4.6 show the forecasted returns under December 2000. To check the robustness of that one- month forecast, the same exercise as above can be undertaken over more months. A comparison of actual RMSE with forecast RMSE can be valuable in comparing the models further. Only one-month forecast is studied to analyse the effect of the January 2000 bust where net positions dropped significantly.

180 measures the corresponding volatility quite accurately or not. Full sample results are reported in the Appendix 6.15.1 and 6.15.2122.

Graphs 4.7.1 and 4.7.2 in Appendices 6.15.1 and 6.15.2 support that idiosyncratic volatility tends to be more volatile among the three volatility measures. Also as expected, variance ( 2

t

σ ) is larger than standard deviation (σ ) since theoretically _t

2

t

σ >0. Under t distribution, the PARCH model, as seen before, is much more sensitive than the GARCH model. Markets where variance (σ ) or standard deviation (t2 σ ) of t

hedgers are smaller than those of speculators support Smith’s (1922) price insurance theory where hedging enables hedgers to insure against the risk of price fluctuations and also Hoffman’s (1932) view that hedging is shifting risk. On the other hand, markets where variance ( 2

t

σ ) or standard deviation (σ ) of hedgers are bigger than those of _t speculators support Telser (1981) that the motivation to use futures contracts is not primarily driven by the firm’s desire to reduce risk, but by the institutional characteristics of the futures exchange itself like regulation ensuring liquidity. Hedgers who wish to avoid price risks of holding inventories can do so without an organized futures market, namely by entering into forward transactions in the cash market. Panel A in both appendices also support that the variance tends to be much more volatile in currency and financial markets. This is analogous to currency and financial markets known to be the most volatile markets in the US.

In comparing the idiosyncratic volatility with the standard deviation and variance in one-month forecast, only in S&P500 futures market does idiosyncratic volatility provide a good measure of volatility for the one-month forecast returns123. Panel B, which magnifies the results of Panel A, shows that idiosyncratic volatility is a good measure of volatility to forecast one-month futures return in S&P500, under either

122 _{Only markets in footnotes 116-119 are included to compare idiosyncratic volatility with GARCH and}

PARCH volatility.

123 _{This is obviously based on the assumption that the GARCH and PARCH models have provided a good}

forecast return. Only then can the idiosyncratic volatility be compared with that specific standard deviation and variance.

181 normal and t distribution. For the remaining 28 markets, idiosyncratic volatility fails to provide a good measure of volatility for one-month forecast returns, where volatility is measured as standard deviation and variance, which provides good one-month forecast returns. Consistent with the existing volatility forecasting literature and specifically Manfredo et al. (1999), the poor measure of idiosyncratic volatility confirms the difficulty in finding a “best” volatility forecasting method across alternative data sets and horizons. Importantly too, graphs from Appendices 4.7.1 and 4.7.2 show that the hypothesis that the variance rate on the market remains constant over any appreciable period of time can be rejected. This is consistent with Merton (1980) and Rosenberg (1972).