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The results from the simple trading strategy described earlier on the calendar anomalies are documented in Table 4.7 for the full sample and in Table 4.8 for the post publication samples. Table 4.7 reports that using a simple trading strategy over the full sample on the Monday effect does outperform the buy-and-hold strategy for the DJIA, however it cannot outperform the buy-and-hold strategy for the FT30 and TOPIX. Specially, the DJIA outperforms the buy-and-hold strategy by 0.81% per annum. The risk of the trading strategy and the buy-and- hold strategy are broadly similar for the Monday effect. The January anomaly results show that the buy-and-hold strategy outperforms the trading strategy for each market, even though the risk associated with the January effect is substantially less than the risk of the buy-and- hold strategy because the strategy is out of the market most of the time. This shows that the January effect could not be traded on using this simple trading strategy throughout the full sample in each market to gain returns greater than a buy-and-hold strategy. The TOTM anomaly results show that the DJIA and FT30 can outperform the buy-and-hold strategy using this trading strategy, but only by 0.07% and 0.18% per annum respectively. The TOPIX cannot outperform the buy-and-hold strategy for the TOTM, with returns 0.67% per annum less than the buy-and-hold strategy. The previous analysis suggested that the TOTM anomaly was quite strong in all three markets, however these results show that trading on the anomaly is not as successful. The risk of trading on the TOTM is substantially less than the buy-and-hold strategy because the strategy is out of the market most of the time, and may contribute to the success of the anomaly in the DJIA and FT30 markets.

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Although the TOPIX has been in existence for a number of decades, it is relatively new compared to the DJIA which was formed in 1896.

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Table 4.8 presents the results for the simple trading rule since the first publication of each anomaly25. The simple trading rule does not outperform the buy-and-hold strategy for the Monday effect on the DJIA and FT30. The returns are less than the buy-and-hold strategy by 0.08% and 0.04% per annum respectively. This shows that the Monday effect has become less successful since the publication of the anomaly compared to the full sample. However the TOPIX does outperform the buy-and-hold strategy by 0.02% per annum. This shows that since 1973, trading on the Monday effect in the TOPIX has been successful but over the full sample it has been unsuccessful. Thus the Monday effect in the TOPIX has become a lot more successful since the publication of the seminal paper by Cross in 1973. The January results show the simple trading rule did not outperform the buy-and-hold strategy since 1976 for each market with the returns from the trading strategy being 3.13%, 0.03% and 0.03% per annum less than the buy-and-hold strategy. Further, the risk associated with the January effect from the simple trading rule is substantially less than that of the buy-and-hold strategy, further indicating the unsuccessfulness of trading on the January anomaly. The TOTM results show that the implementing this simple trading strategy after 1987 does not outperform the buy-and-hold strategy in the DJIA. However, the FT30 and TOPIX do outperform the buy-and-hold strategy by 0.12% and 0.13% per annum espectively. This shows that since 1987 the TOTM could have gained substantial returns, but over the full sample it generated negative returns. However, the risk associated with the TOTM effect is considerably less than the buy-and-hold strategy. Because of this, the “double or out” trading strategy is also conducted so make the risk of each trading rule fairly similar.

The results from Tables 4.9 and 4.10 document the “double or out” trading strategy to try to form a trading strategy that has comparable risk to that of the buy-and-hold strategy. It clear that the risk of the “double or out” trading strategy is double that of the simple trading strategy, and that the profit achieved from the rule is double that of the simple trading strategy. This is because there are no neutral signals generated so the investor is either out of the market or in the market by double the original amount. The results indicate that the risk of the “double or out” strategy for the Monday effect is now greater than the buy-and-hold strategy showing that the returns from this strategy are not just the result of a strategy with less risk. Even though the risk of the TOTM anomaly is still less than that of the buy-and- hold strategy, they are broadly comparable. However, the January standard deviations from

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the “double or out” trading strategy are still substantially less than that of the buy-and-hold strategy. Thus a “quadruple or out” strategy is now considered for the January anomaly in Table 4.11 to generate comparable risks between a trading strategy and the buy-and-hold strategy. The strategy is similar to the “double or out” strategy but the investor goes in the market with leverage of four times when a buy signal is generated. The strategy generates similar risks to the buy-and-hold strategy for the January anomaly and shows that none of the markets can outperform the buy-and-hold strategy.

The profitability of the three calendar anomalies previously examined through a simple trading strategy and a “double or out” trading strategy. The results show that using the simple trading strategy only the Monday effect in the DJIA, and the TOTM effect in the DJIA and FT30 can outperform the buy-and-hold strategy over the full sample. Further, studying the data after the seminal publication of that anomaly, the results show only Monday anomaly in the TOPIX and the TOTM anomaly in the FT30 and TOPIX can outperform the buy-and- hold strategy. All of the other anomalies cannot beat the buy-and-hold strategy, indicating that although these calendar anomalies are found in the market, they cannot be used to gain returns greater than the market using the simple trading strategy. The results from the “double or out” strategy are similar to the simple trading strategy but only the rule profits have doubled as have the standard deviations of the rules. Finally a “quadruple or out” trading strategy is also conducted for the January anomaly to enable the risk of the trading strategy to the comparable to that of the buy-and-hold strategy. The results show that the trading strategy cannot outperform the buy-and-hold strategy for all three markets. These results show that even though the earlier analysis shows that the calendar anomalies are strong and evident in the markets, it does not always guarantee that the anomaly will generate returns greater than the market.

Anomaly No. Buys No. Sells SD Rule SD B&H Rule Profit B&H Profit Difference Annualised % Difference

Panel A: DJIA Monday Effect 5522 5522 0.96 1.10 1124.00 585.14 538.87 0.81% January Effect 113 113 0.23 1.10 33.81 585.14 -551.33 -0.83% TOTM Effect 1360 1659 0.44 1.10 634.04 585.14 48.90 0.07% Panel B: FT30 Monday Effect 3731 3731 0.95 1.06 69.44 294.40 -224.96 -1.01% January Effect 74 74 0.25 1.06 62.39 294.40 -232.01 -1.05% TOTM Effect 894 893 0.46 1.06 333.65 294.40 39.25 0.18% Panel C: TOPIX Monday Effect 3078 3078 0.87 1.02 432.80 436.15 -3.35 -0.01% January Effect 59 59 0.25 1.02 82.22 436.15 -353.93 -1.40% TOTM Effect 709 708 0.43 1.02 266.96 436.15 -169.76 -0.67%

Table 4.7: Test results for the calendar anomalies using the simple trading strategy on the full sample of each market. The number of trades (No. of buy/sell) are shown as well as the standard deviations associated with the trading rule and the buy-and-hold strategy. The profits from trading on the rule (Rule Profit) as well as the buy-and-hold strategy are shown. Further, the annualised difference between the rule returns and the buy-and-hold returns are also shown.

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Table 4.9: Test results for the calendar anomalies using the “double or out” trading strategy on the full sample data. The number of trades (No. of buy/sell) are shown as well as the standard deviations associated with the trading rule and the buy-and-hold strategy. The profits from trading on the rule (Rule Profit) as well as the buy-and-hold strategy are shown. Further, the annualised difference between the rule returns and the buy-and-hold returns are also shown.

Table 4.8: Test results for the calendar anomalies using the simple trading strategy on the post publication data. The number of trades (No. of buy/sell) are shown as well as the standard deviations associated with the trading rule and the buy-and-hold strategy. The profits from trading on the rule (Rule Profit) as well as the buy-and-hold strategy are shown. Further, the annualised difference between the rule returns and the buy-and- hold returns are also shown.

Anomaly No. Buys No. Sells SD Rule SD B&H Rule Profit B&H Profit Difference Annualised % Difference

Panel A: DJIA Monday Effect 1788 1788 0.93 1.11 225.78 232.47 -6.68 -0.08% January Effect 34 34 0.26 1.10 -7.85 250.42 -258.27 -3.13% TOTM Effect 276 276 0.47 1.19 112.15 170.48 -58.33 -1.56% Panel B: FT30 Monday Effect 1904 1904 1.15 1.28 -43.67 133.92 -177.59 -0.04% January Effect 34 34 0.27 1.18 24.39 162.28 -137.89 -0.03% TOTM Effect 276 276 0.49 1.18 138.32 138.32 101.07 0.12% Panel C: TOPIX Monday Effect 1931 1931 0.96 1.12 143.32 81.51 61.81 0.02% January Effect 34 34 0.27 1.14 -10.77 103.68 -114.46 -0.03% TOTM Effect 276 276 0.54 1.32 101.18 -54.33 155.51 0.13%

Anomaly No. Buys No. Sells SD Rule SD B&H Rule Profit B&H Profit Difference Annualised % Difference

Panel A: DJIA Monday Effect 5522 5522 1.91 1.10 2248.00 585.14 1662.87 2.49% January Effect 113 113 0.46 1.10 67.62 585.14 -517.52 -0.78% TOTM Effect 1360 1659 0.88 1.10 1268.08 585.14 682.94 1.02% Panel B: FT30 Monday Effect 3731 3731 1.90 1.06 138.89 294.40 -155.52 -0.70% January Effect 74 74 0.50 1.06 294.40 294.40 -169.61 -0.77% TOTM Effect 894 894 0.91 1.06 667.61 294.40 372.90 1.69% Panel C: TOPIX Monday Effect 3078 3078 1.74 1.02 865.60 436.15 429.44 1.70% January Effect 59 59 0.49 1.02 164.44 436.15 -271.72 -1.07% TOTM Effect 709 708 0.85 1.02 533.91 436.15 97.76 0.39%

Table 4.10: Test results for the calendar anomalies using the “double or out” trading strategy on the post publication data. The number of trades (No. of buy/sell) are shown as well as the standard deviations associated with the trading rule and the buy-and-hold strategy. The profits from trading on the rule (Rule Profit) as well as the buy-and-hold strategy are shown. Further, the annualised difference between the rule returns and the buy-and-hold returns are also shown.

Anomaly No. Buys No. Sells SD Rule SD B&H Rule Profit B&H Profit Difference Annualised % Difference

Panel A: DJIA Monday Effect 1788 1788 1.87 1.11 451.57 232.47 219.10 2.62% January Effect 34 34 0.53 1.10 -15.70 250.42 -266.12 3.22% TOTM Effect 276 276 0.94 1.19 224.29 170.48 53.81 1.44% Panel B: FT30 Monday Effect 1904 1904 1.90 1.06 138.89 133.92 -155.52 -1.47% January Effect 34 34 0.54 1.19 48.77 162.28 -113.51 -2.12% TOTM Effect 276 276 0.97 1.18 276.64 138.32 239.39 29.21% Panel C: TOPIX Monday Effect 1931 1931 1.93 1.12 286.64 81.51 205.13 6.99% January Effect 34 34 0.53 1.14 -21.55 103.68 -125.23 -3.66% TOTM Effect 276 276 1.08 1.32 202.36 -54.33 256.69 21.48%

Anomaly No. Buys No. Sells SD Rule SD B&H Rule Profit B&H Profit Difference Annualised % Difference

Panel A: Full Sample

DJIA 113 113 0.93 1.10 135.23 585.14 -449.91 -0.67%

FT30 74 74 1.01 1.06 249.58 294.40 -44.83 -0.20%

TOPIX 59 59 0.98 1.02 328.87 436.15 -107.28 -0.42%

Panel B: Post Publication Data

DJIA 34 34 1.06 1.10 -31.39 250.42 -281.81 -3.41%

FT30 34 34 1.07 1.18 97.55 162.28 -64.73 -1.21%

TOPIX 34 34 1.06 1.14 -43.10 103.68 -146.78 -4.29%

Table 4.11: Test results for the “quadruple or out” trading strategy on the January anomaly. The number of trades (No. of buy/sell) are shown as well as the standard deviations associated with the trading rule and the buy-and-hold strategy. The profits from trading on the rule (Rule Profit) as well as the buy-and-hold strategy are shown. Further, the annualised difference between the rule returns and the buy- and-hold returns are also shown.

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