α–Perfect Forecasting

Tables 6.4, 6.5 and 6.6 contain the relative returns of obtained by the strategies in the set of experiments A. Each row contains the relative returns of the strategies for one test case. The first column is the asset price series used in the corresponding test case. From the second column, each column contains the relative returns for the different strategies that participated in the market. For each row, the highest return is highlighted. The test cases in the tables are grouped by the value of the forecasting parameter α.

The results from the stock market price series (Microsoft, Dell and IBM price series) show that the OTMinR strategy obtains higher returns than the other strategies participating in the market. The OTMinR strategy also obtains higher returns than the other strategies in most of the test cases where the Random A price series is used as the asset price.

When the Random B price series is used as the asset price, the OTMaxW strategy out- performs the other strategies in most of the test cases. The test case when α = 0.6 is the only case (using the Random B price series) where the OTMix strategy outperforms the OT- MaxW. The only test case where the ATSpec strategy outperforms the other strategies is when the Random A price series is used and α = 1.

It is of special interest, the fact that for the test cases of the Microsoft asset price, the performance of the OTMinR is more than 100% higher than the average for the experiments with high and uncertainty (when α = 0, 0.2) shown in Figure 6.4, and medium uncertainty (when α = 0.4, 0.6) shown in Figure 6.5.

It should be recalled that, the Microsoft price series is characterized by a market crash where the price decreases abruptly in one time step. Considering this fact along with the high returns of the agents gives the intuition that the agents using the OTMinR strategy were able to prevent much losses due to the market crash. This phenomena is investigated furtherly in Section 6.3.

In the same way, the IBM price series is characterized by a similar market crash where the price decreases by a high in one time step. This may be the reason of why the returns of the OTMinR are more than 50% higher than the average.

From Table 6.5, it is possible to see that the advantage of the OTMinR strategy decreases when the forecasting accuracy is high (i.e., when α = 0.8, 1). And in the case of the Random

Aprice series, it is outperformed by the ATSpec strategy.

a) Relative returns when α = 0

Price Series OTMinR OTMaxW OTMix OTRnd ATSpec ATNoise Dell 0.231 -0.131 0.096 -0.046 -0.084 -0.066 Microsoft 1.165 -0.530 0.280 -0.054 -0.430 -0.430 IBM 0.655 -0.232 0.037 -0.090 -0.186 -0.184 Random A 0.191 -0.060 -0.037 -0.036 -0.027 -0.032 Random B -0.324 0.162 -0.087 0.042 0.113 0.093 b) Returns when α = 0.2

Price Series OTMinR OTMaxW OTMix OTRnd ATSpec ATNoise Dell 0.225 -0.126 0.086 -0.043 -0.083 -0.060 Microsoft 1.166 -0.522 0.265 -0.062 -0.431 -0.417 IBM 0.665 -0.230 0.047 -0.093 -0.195 -0.194 Random A 0.230 -0.066 -0.035 -0.042 -0.041 -0.045 Random B -0.324 0.158 -0.026 0.028 0.095 0.069

Table 6.4: Relative Returns of the different strategies for the experiments with different price series using α–Perfect forecasting with α = 0 and α = 0.2. The highest values for each row are emphasised.

Further information is obtained by comparing the dispersion of the relative returns for one test case. This comparison is done obtaining the standard deviation of the relative returns for each test case (denoted by each row from Tables 6.4 to 6.6). The standard devia- tions are shown in Table 6.7. From these standard deviations it is possible to see that, in the test cases where the forecasting accuracy is high (when α = 0.8 and α = 1) the dispersion of the relative returns is lower than in the experiments where the forecasting accuracy is medium (α = 0.4 and α = 0.6) and when it is low (α = 0 and α = 0.2). This pattern indicates that as the uncertainty decreases in the market (i.e., as α → 1), the difference between the returns obtained by the use of the strategies is lower and consequently agents may have fewer opportunities to profit from the market. This may be due to the fact that as the forecast accuracy increases, all the agents will tend to make offers that lay on the same side of the market.

The differences in the returns of the Option trading strategies shown so far suggest that under the experimented conditions, trading Option contracts may provide an advantage to an agent by yielding higher returns than the non-Option trading strategies. Specifically, when the traders face more uncertainty in their forecasting (i.e., as α → 0), trading Options can give greater advantage over non trading Options. Figure 6.1 shows a chart with the stan- dardised relative returns (scaling the values from Tables 6.4, 6.5 and 6.6 to make their mean 0 and standard deviation 1) for each strategy under the experimented scenarios. The results are grouped by the price series used as the price of the asset. For each group, the horizon- tal axis in the figures represents the standardised relative returns obtained by the strategies participating in the market. The vertical axis represents the different values of α. From this figure it is possible to see that the returns of the agents follow certain trends as the value

6.2. STRATEGY RETURNS PERFORMANCE ANALYSIS 111

a) Relative returns when α = 0.4

Price Series OTMinR OTMaxW OTMix OTRnd ATSpec ATNoise Dell 0.214 -0.123 0.066 -0.035 -0.070 -0.051 Microsoft 1.174 -0.498 0.200 -0.050 -0.418 -0.408 IBM 0.637 -0.219 0.029 -0.079 -0.185 -0.183 Random A 0.235 -0.068 -0.027 -0.041 -0.048 -0.051 Random B -0.349 0.154 0.069 0.029 0.059 0.038 b) Returns when α = 0.6

Price Series OTMinR OTMaxW OTMix OTRnd ATSpec ATNoise Dell 0.187 -0.124 0.022 -0.024 -0.034 -0.026 Microsoft 1.177 -0.461 0.027 -0.011 -0.375 -0.357 IBM 0.570 -0.191 -0.005 -0.053 -0.160 -0.161 Random A 0.154 -0.060 0.005 -0.025 -0.034 -0.040 Random B -0.289 0.150 0.156 0.008 -0.014 -0.010

Table 6.5: Relative Returns of the different strategies for the experiments with different price series using α–Perfect forecasting with α = 0.4 and α = 0.6. The highest values for each row are emphasised.

a) Relative returns when α = 0.8

Price Series OTMinR OTMaxW OTMix OTRnd ATSpec ATNoise Dell 0.157 -0.135 -0.020 -0.010 0.009 -0.001 Microsoft 0.775 -0.465 -0.436 -0.003 0.084 0.046 IBM 0.268 -0.138 -0.095 0.031 -0.030 -0.036 Random A 0.043 -0.028 0.035 0.003 -0.022 -0.031 Random B -0.260 0.152 0.149 -0.007 -0.018 -0.016 b) Returns when α = 1

Price Series OTMinR OTMaxW OTMix OTRnd ATSpec ATNoise Dell 0.174 -0.139 -0.043 -0.002 0.020 -0.009 Microsoft 0.759 -0.468 -0.447 -0.026 0.129 0.054 IBM 0.205 -0.142 -0.131 0.043 0.010 0.017 Random A -0.001 -0.012 -0.008 0.015 0.021 -0.016 Random B -0.264 0.154 0.153 -0.006 -0.013 -0.024

Table 6.6: Relative Returns of the different strategies for the experiments with different price series using α–Perfect forecasting with α = 0.8 and α = 1. The highest values for each row are emphasised.

α Microsoft Dell IBM Random A Random B 0 0.59 0.12 0.30 0.08 0.16 0.2 0.58 0.12 0.31 0.10 0.15 0.4 0.57 0.11 0.29 0.10 0.16 0.6 0.55 0.09 0.26 0.07 0.14 0.8 0.41 0.08 0.13 0.03 0.13 1.0 0.41 0.09 0.11 0.01 0.14

of α is varied among experiments. Specifically, the OTMinR strategy is the top performing strategy in the experiments using the Microsoft, IBM and Dell price series. In the same experiments, the OTMaxW strategy is the worst performing strategy. Also, the performance of the ATSpec strategy (asset-only trading speculator) improves as the uncertainty decreases (i.e., as α → 1).

Figure 6.1: Standardised Relative returns of the different strategies for the α–Perfect forecasting experiments.

In the test cases where the Random B price series is used, the OTMinR performs worse than all the other strategies. However, in this same case, both the OTMaxW and the OTMix strategy have the best performance.In the cases where Random A price series is used, the OTMinRstrategy performs better than the other strategies for the high and medium uncer- tainty test cases, however in the cases where the uncertainty is low, the difference between the returns of all the strategies is very low.