Error distribution

Research on probability distributions often use changes in the logarithms of prices. The evidence is mixed on whether price changes are well approximated by the log normal distribution. For example, Hudson, Leuthold, and Sarassoro (1987) find that the log normal distribution is a good approximation for wheat, soybeans, and live cattle for daily prices for the years 1976 through 1982, but not if earlier years are included. Similarly, Hilliard and Reis (1999) observe on every price intraday change for soybeans for the period July 1990 to June 1992, and they conclude that the logarithmic changes are not distributed normally. It is not infrequent that agricultural futures prices, like many other financial series are distributed nonnormally with the fat tails. (Yang and Brorsen, 1993; and Hall, Brorsen, and Irwin, 1989) suggest that the distribution of commodity price changes is not normal, but is leptokurtic. For six agricultural futures, Corazza et al. (1997) find returns are not log-normally distributed, due to fatter tails and instability in

38 _{Academics argue that asymmetries occur due to the effect of price falls on operating and financial}

leverage (see, for example, Nelson, 1991). However, the extent to which these explanations can account fully for the observed asymmetric effect is debatable. In particular, see Braun, Nelson, and Sunier (1991), who argue that these explanations are insufficient in explaining the extent of the observed asymmetries. Thus, the market dynamics argument may well explain, at least in part, the observed asymmetries in volatility.

39 _{Brown (2001) provides further support of the asymmetric information mitigation hypothesis. In an}

examination of the risk practices of a large multinational, he reports that its hedging decisions are in part motivated by attempts to reduce informational asymmetries.

40 _{Dadalt et al. (2002) examine the relationship between derivatives usage and information asymmetry}

using a structural model in which they simultaneously model derivatives usage as a function of information asymmetry and vice versa (see Graham and Rogers, 1999). Coefficients on the asymmetric information variables were generally negative and statistically insignificant.

61 the variance level (accounting for the relatively many outliers). Bera and Garcia (2002) and Manfredo et al. (1999) propose a t distribution after the normal distribution being left with excess kurtosis. Similarly, Bailey and Myers (1991) use a conditional t distribution and find strong evidence of persistent shocks to the volatility. Finally, Poitras (1990) conclude that more “normal” distributions are produced by increasing the differenced data interval from daily to weekly.

An understanding of the probability distributions of futures prices is important to decision makers. First, optimal hedges in futures depend on the parameters of the underlying probability distributions, and the estimates of these parameters depend, in turn, on the analyst’s assumed model of the distribution (McNew and Fackler, 1994). Second, models of options prices make assumptions about the nature of the probability distribution of the underlying asset. In the case of traded agricultural options, the underlying asset is a position in a futures contract (Tomek and Peterson, 2001). In addition, these authors suggest that changes in volatility can pressure the margin level for futures contracts and hence influence the cost of hedging. Moreover, one might expect that with normally distributed data the symmetric GARCH model would exhibit the lowest RMSE. Bracker and Smith (1999) show that the GARCH model rank first compared to the asymmetric EGARCH, AGARCH, and GJR for some futures market.

2.16.3 Forecasting

It is well known that successful hedging and speculative activities in futures markets depend critically on the ability to forecast price movements (Girma and Mougoue, 2002). The econometrics literature is full of studies comparing the forecasting ability of various time-series models.41 For instance, Poon and Granger (2003) list 39 studies comparing the out-of-sample forecasting abilities of the GARCH (1, 1) model and the historical variance. Factors influencing the supply and demand of inventories provide critical information towards making expectation about the value of the month price at

41 _{For an excellent review of existing studies in this area see Poon and Granger (2003). Notable examples}

62 maturity. As time passes, new information comes, and both the price level and the price differences can alter. However, in an efficient market, truly new information is a surprise and is incorporated rapidly into price changes making arbitrage opportunities disappear quickly. Indeed, most traders cannot profit from price forecasts if markets are efficient. Put another way, econometric models in the public domain cannot outperform efficient futures markets as forecasts of the maturity price (Tomek, 1997). Also, consistent with the existing volatility forecasting literature, Manfredo et al. (1999) confirm the difficulty in finding a “best” volatility forecasting method across different horizons and data intervals. Yet, markets may not be strong form efficient, and some traders may profit by having better (private) data and models (Bessler and Brandt, 1992). Moreover, price-forecasting models can have statistical, but not economic significance, that is, returns from using the forecasts are less than transaction costs (Peterson, 2001). Overall, the literature suggests that no one particular method for forecasting the volatility of asset returns performs best over a wide array of data series and alternative forecast horizons. The sensitivity of the forecasts and the forecastibility of volatilities to diverse techniques depend very much on the return series in question (Jackson, Maude and Perraudin, 1997).

One issue addressed by Poon and Granger (2003) is whether volatility forecast errors are best measured in terms of the standard deviation or variance. As they point out, when the RMSFE is measured in terms of the variance, a few outliers tend to dominate the results. In addition, derivative prices are roughly proportional to the standard deviation. Consequently, they define RMSFE in terms of the standard deviation, and find that the GARCH model puts too much weight on recent observations relative to those in the past. This is consistent with prior evidence showing that asset market volatility has a long memory, such as Ding and Granger (1996). They also make mention of the inability of other models to forecast very well out-of-sample due to the cost of added complexity underscoring the argument of Dimson and Marsh (1990).

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