Antecedentes de la Teoría del Crecimiento Económico

A relation between the number of standard deviations and the summated returns found, can be identified. On average, a lower summated return is seen alongside a higher the number of standard deviation. This is reflected by figure 2 (chapter 5.1), where the combinations including 3.0 standard deviations are found at the bottom of the y-axis, while the combinations with a lower value for standard deviations are, on average, found higher up the y-axis. The combinations including 1.0 standard deviations returned, on average, the highest summated returns.

This underlying relationship can be caused by a number of reasons. The ranges of 2.4 to 3.0 standard deviations are not capable of generating summated positive returns that exceed 20% for any given year (as seen from table 4). The losses, however, for the range of 2.4 to 3.0 standard deviations do not return summated losses that exceed 20% either (as seen from table 5). A possible explanation as to why only profits smaller than 20% and losses smaller than 20% are reported within the range of 2.4 to 3.0 standard deviations could be the relatively low frequency of trades that the combinations with this range of standard deviations returns (as seen from table 6). The combinations including 2.4 to 3.0 standard deviation have on average 6.2 to 2.4 trades per year respectively. This frequency is lower than the frequency found for the combinations including 0.8 to 2.2 standard deviations, which have 14.8 to 7.6 trades on average per year respectively. The low frequency found for the combinations including 2.4 to 3.0 standard deviations may cause the inability for these combinations to generate profits and losses that exceed the 20% mark, and therewith fail to yield an overall higher summated return than the combinations with 0.8 to 2.2 standard deviations.

The combinations including 2.2 to 1.4 standard deviations were all capable of returning, and are the only combinations that returned, a summated return in excess of 30% profit within a one year time span (as seen from table 4). This range, however, also results in the highest losses found for an individual year (as seen from table 5). The range of 1.4 to 2.2 standard deviations managed to generate a higher frequency of entry signals than the combinations with 2.4 to 3.0 standard deviation, and is therefore capable of generating larger positive and negative summated returns than combinations with 2.4 to 3.0 standard deviations. However, the range of 1.4 to 2.2 standard deviations did, despite its ability to generate larger positive returns, not yield larger summated returns on a 15-year horizon than combinations including 0.8 to 1.2 standard deviations.

A possible explanation, as to why 0.8 to 1.2 standard deviations yield a higher summated return on a 15-year horizon, may be found in the losses that are being generated by the combinations with 1.4 to 2.2 standard deviations. For the combinations including 1.4 to 2.2 standard deviations the MOPOI levels are low enough to signal overreaction in moments in which the market sell offs. However, the MOPOI levels are high enough to signal an entry position at times when the market takes a moment to breath during a sell off. For the combinations including 0.8 to 1.2

40 standard deviations, the MOPOI values are lower, and the WVF values will thus have to decline more in order to generate a signal that signals an entry position. In moments of strong market sell-offs, such as in 2008, the combinations with 1.4 to 2.2 standard deviations, will generate more entry signals than combinations with 0.8 to 1.2 standard deviations. On average the MOPOI algorithm yields a higher summated return when a larger upward movement is seen in markets, then in markets in which large sell-offs take place, such as in 2008. The combinations including 0.8 to 1.2 trigger less often in markets which experience a sell-off, and are often more reliable in markets experiencing a sell-off than the triggers of combinations including 1.4 to 2.2 standard deviations. Several combinations including 0.8 and 1.0 standard deviations even returned a positive summated return for 2008, due to the low frequency and higher accuracy in markets with a long downward movement. This is ought to be the primary reason as to why 1.0 standard deviations is the most successful number of standard deviations found for the MOPOI algorithm. Appendix I, II and III provide more insight in the year-to-year returns for every tested combination of variable y and z.

SD: Days – MA: Year: Summated profit (in %): 0.8 18 1998 27.85% 1.0 19 1998 26.85% 1.2 17 1998 26.91% 1.4 25 2009 34.05% 1.6 25 2009 33.94% 1.8 22 2009 33.08% 2.0 20 2009 33.27% 2.2 18 2009 31.72% 2.4 22 / 23 / 24 2009 18.90% 2.6 17 2009 9.56% 2.8 22 2009 9.35% 3.0 25 1995 5.13%

Table 4: Largest summated profits found for a year in the period 1991 – 2015 for 0.8-3.0 SD

SD: Days – MA: Year: Summated loss (in %): 0.8 19 2001 9.03% 1.0 20 2002 25.82% 1.2 18 2002 35.05% 1.4 17 2008 42.11% 1.6 21 2008 51.16% 1.8 25 2008 48.28% 2.0 21 2008 30.55% 2.2 21 2008 24.14% 2.4 18 2008 18.69% 2.6 19 2008 18.75% 2.8 17 / 18 / 19 2008 10.77% 3.0 17 / 18 2008 4.09%

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SD: Average frequency per combination for 1991-2015

Average frequency per combination per year

0.8 371 14.8 1.0 343 13.7 1.2 338 13.5 1.4 328 13.1 1.6 305 12.2 1.8 271 10.8 2.0 231 9.3 2.2 190 7.6 2.4 156 6.2 2.6 119 4.7 2.8 87 3.5 3.0 61 2.4

Table 6: Average frequency distribution for 0.8-3.0 SD

The number of days used for the moving average seems to have little influence on the summated return found for the MOPOI trading algorithm, before the inclusion of transaction costs. This is illustrated by the flat lines of standard deviations in figure 2 (chapter 5.1). The higher end of the tested range of the number of days, used to calculate the moving average, generates higher summated returns after the inclusion of transaction costs. This effect can be explained by the lower frequency of trades found for combinations with a higher number of days for the moving average, compared to combinations including a low number of days for the moving average (see appendix II for a year to year frequency of trades distribution for all combinations). Before transaction costs the higher frequency, of the lower spectrum of days to calculate the moving average, is offset by an increase of the accuracy when the moving average is calculated by the higher number of days for the moving average. This is a clear illustration of the equilibrium problem that has been described in chapter 4.1.1.