The profitability of the moving average strategy in the French stock market

requires a trade frequency of 2.5%, whereas, that figure of the 100-day MA and the 200-day MA strategy is only 0.3% of the total number of days. Finally, we address the issue of transaction costs by setting the average returns of MAPs to zero to test if the generated abnormal return could compensate for the transaction costs. In this research, we assume that the impact of a R an k H ol di ng T ra di ng B E T C H ol di ng T ra di ng B E T C H ol di ng T ra di ng B E T C H ol di ng T ra di ng B E T C H ol di ng T ra di ng B E T C M A (1 0) M A (2 0) M A (5 0) M A (1 00 ) M A (2 00 ) Lo w 45 .0 7 0. 02 2 62 .2 0 69 .8 1 0. 01 4 84 .8 8 13 6. 68 0. 00 7 13 4. 19 32 8. 36 0. 00 3 34 8. 63 44 9. 70 0. 00 2 39 4. 54 2 47 .3 4 0. 02 1 76 .3 5 77 .9 5 0. 01 3 12 2. 73 17 8. 73 0. 00 5 26 3. 97 25 5. 39 0. 00 4 32 4. 99 89 9. 40 0. 00 1 72 0. 41 3 41 .4 8 0. 02 4 14 6. 18 64 .0 7 0. 01 5 21 1. 12 11 9. 15 0. 00 8 27 7. 10 15 8. 52 0. 00 6 30 4. 42 20 4. 41 0. 00 4 21 1. 34 4 49 .8 6 0. 02 0 26 2. 48 60 .7 4 0. 01 6 29 5. 60 12 5. 59 0. 00 8 44 8. 54 18 3. 88 0. 00 5 52 2. 49 37 4. 75 0. 00 2 78 4. 91 H ig h 39 .3 9 0. 02 5 12 0. 07 64 .0 7 0. 01 5 23 0. 63 11 9. 15 0. 00 8 21 4. 89 27 0. 41 0. 00 3 22 0. 63 28 1. 06 0. 00 3 10 8. 16 Ta bl e 4: T ra di ng fr eq ue nc y an d br ea k- ev en tr an sa ct io n co st N ot e: T ab le 4 re po rt s t he es tim at ed a ve ra ge h ol di ng d ay s ( H ol di ng ), tr ad in g fre qu en cy a s a fr ac tio n of tr ad in g da ys (T ra di ng ) a nd th e b re ak -e ve n tr an sa ct io n co st s i n ba si s p oi nt (B E T C ) of th e M A P s ac ro ss d if fe re nt la g le ng th s. T he b re ak -e ve n tr an sa ct io n co st s ar e ca lc ul at ed o n th e co ns tr ai nt th at th e av er ag e re tu rn s of th e M A P s eq ua l z er o. T he s am pl e pe ri od is fr om J an ua ry 1 , 1 99 5 to D ec em be r 31 , 2 01 2. Journal of Economics and Development Vol. 16, No.2, August 201434 1-month treasury bill transaction cost is neg- ligible and could be ignored. This assumption is highly consistent with the arguments of Bal- duzzi and Lynch (1999), Lynch and Balduzzi (2000), and Han (2006). Table 4 reports the results of the break-even transaction costs2 in basic points (bps) in column “BETC” with two remarkable features. First, break-even trans- action costs increase across the lag lengths, which is consistent with the tendency of aver- age holding days. For instance, in term of the lowest volatility quintile, the 10-day MA has a break-even transaction cost of 62.2 bps while that figure for the100-day MA and the 200-day MA is 348.63 bps and 394.54 bps, respective- ly. Second, the break-even transaction costs increase as portfolios become more volatile, except for L ≥ 100. This result is contrary to what Han, Yang, and Zhou (2011) observe in the US where financial markets are well-devel- oped and highly liquid. Overall, the break-even transaction costs are substantially positive, im- plying that the MA strategy is very economi- cally effective in the French market even after taking into account the cost of transactions. 5.3. Sub-periods The effect of the time-scale factor on the in- vesting strategy is one of our greatest concerns. To avoid serious problems of data snooping and other possible bias, we examine the profitabili- ty of MAPs out of the sample by simply divid- ing the sample period into 2 equal sub-periods, from January 1995 to December 2003 and from January 2004 to December 2012. Table 5 reports the performance of the 10-day MA timing strategy in two equal sub-periods. Overall, the abnormal returns and beta coeffi- cients from the CAPM model in the sub-peri- ods are highly consistent with the results of the previous tests. First, abnormal returns, reflected by CAPM alphas, are positively correlated with the portfolio’s volatility, except for the highest volatility quintiles in the second sub-period. More specifically, in the first sub-period, the alphas turn from a negative number to a posi- tive one across the volatility quintiles with the abnormal return appearing from the 3rd volatil- ity quintile. The high-low spread, reported in the last row of Table 5, is 18.79% per annum and at 5% significance. Similarly, in the second sub-period, alphas are significantly positive and follow an upward trend across the volatility quintiles, except for the highest volatility quin- tile where the alpha turns to negative, -0.25% per annum. Compared to previous results, on average, the CAPM alphas in the first sub-peri- od (-0.07% to 19.2%) are higher than those of the second sub-period (-0.25% to 13.6%) and the entire sample period (3.87% to 15.92%). Second and finally, all market betas, reported in column “βmkt” in Table 5, are significantly negative across time and volatilities, indicat- ing that MAPs are less exposed to market risks compared to buy-and-hold portfolios. In brief, the results in sub-periods do support the abnor- mal performance of the MA timing strategy. In summary, the abnormal returns and beta coefficients from the CAPM model in different lag lengths as well as in sub-periods are highly consistent with the results of the previous tests. The break-even transaction costs are substan- tially positive, implying that the MA strategy is very economically effective in the French market even after taking into account the cost of transactions. Robustness tests, therefore, do support the profitability of MA timing strategy Journal of Economics and Development Vol. 16, No.2, August 201435 Pa ne l A : P er io d Ja nu ar y 1, 1 99 5 - D ec em be r 31 , 2 00 3 Pa ne l B : P er io d Ja nu ar y 1, 2 00 4 - D ec em be r 31 , 2 01 2 R an k α β m kt A dj . R ² α β m kt A dj . R ² P an el A : C A PM M od el Pa ne l B : C A PM M od el Lo w -0 .0 7 -0 .0 5* ** 11 .4 8 7. 61 ** * -0 .1 1* ** 30 .5 8 (-0 .0 6) (-1 7. 45 ) (5 .9 4) (- 32 .1 1) 2 -0 .4 2 -0 .1 5* ** 24 .5 6 11 .3 6* ** -0 .2 1* ** 38 .1 1 (-0 .2 1) (-2 7. 61 ) (5 .5 5) (- 37 .9 6) 3 7. 01 * -0 .2 0* ** 21 .1 5 13 .0 6* ** -0 .3 2* ** 44 .4 3 (2 .4 3) (-2 5. 06 ) (4 .6 7) (- 43 .2 5) 4 19 .2 0* ** -0 .2 8* ** 22 .2 2 12 .4 8* ** -0 .3 4* ** 40 .5 2 (4 .8 8) (-2 5. 87 ) (3 .9 3) (- 39 .9 2) H ig h 18 .7 2* * -0 .2 8* ** 11 .1 1 -0 .2 5 -0 .2 0* ** 15 .1 9 (3 .2 1) (-1 7. 13 ) (- 0. 07 ) (- 20 .4 9) H ig h - L ow 18 .7 9* * -0 .2 3* ** -7 .8 5* -0 .0 9* ** (-3 .2 2) (-1 3. 95 ) (- 2. 22 ) (- 9. 82 ) Ta bl e 5: S ub -p er io ds N ot e: * , * *, * ** in di ca te s ig ni fic an ce a t 0 .1 0, 0 .0 5 an d 0. 01 le ve l, re sp ec ti ve ly . Ta bl e 5 re po rt s th e pe rf or m an ce o f th e 10 -d ay M A t im in g st ra te gy i n tw o eq ua l su b- pe ri od s: f ro m J an ua ry 1 , 19 95 t o D ec em be r 31 , 20 03 (P an el A ) an d fr om J an ua ry 1 , 20 04 t o D ec em be r 31 , 20 12 ( P an el B ). T he a lp ha s ar e an nu al iz ed a nd i n pe rc en ta ge . W e us e th e ro bu st t- st at is ti cs o f N ew ey a nd W es t ( 19 87 ) fo r te st in g th e si gn ifi ca nc e. Journal of Economics and Development Vol. 16, No.2, August 201436 in the French stock market. 6. Conclusion In this paper, we study the cross-sectional profitability of a moving average timing port- folio in the French stock market over the pe- riod from January 1, 1995 to December 31, 2012. Following the methodology suggested by Han, Yang, and Zhou (2011), we find that moving average timing portfolios generate an abnormal return of 3.72% per annum, on aver- age, and outperform the buy-and-hold portfo- lios with higher returns and less risk exposure. These findings are robust across different lag lengths and in two sub-periods. The analysis of the break-even transaction costs also support the superior performance of a moving average strategy over a buy-and-hold strategy. The central contribution of this research is that we not only examine the excess return of moving average portfolios (MAPs) over cor- responding buy-and-hold portfolios across volatility quintiles but also employ the CAPM regression model to test the risk-adjusted re- turn as well as market betas. As previous stud- ies provide no evidence on the cross-sectional profitability of moving average trading rules, our paper contributes to the existing literature by examining the abnormal returns on volatil- ity quintile portfolios in the French stock mar- ket. We also address the common problems of previous studies when dealing with time-series data by robustness testing. This research has some limitations. First, we employ the CAPM model to test abnormal re- turn for MAPs. Since the CAPM model does not take into account other risk factors and thus, may not fully explain the abnormal return of moving average portfolios, we suggest future research should employ other approaches to dig deeper into this issue. Second and finally, we overcome the limitations of previous research when dealing with time-series data by robust- ness testing. To fully correct the serious prob- lem of data snooping and other possible biases when doing empirical research with time-series data, we suggest future research should com- bine robustness tests and other approaches for comprehensively assessing the performance of technical trading rules. Notes: 1. Trading Frequency = (total trading days)/ (total holding days + total trading days). 2. Break-even transaction costs are the costs upon which average return of MAPs turn to zero (Han, Yang, and Zhou, 2011). Acknowledgements We thank Nuttawat Visaltanachoti, Giang T. H. Nguyen, Huong. D. Vu, Lan Anh Nguyen and conference participants at the 1st Paris Financial Management Conference at Ipag Business School, Paris, France, Massey University, New Zealand, and Saint Mary’s University, Canada for their generous comments. We thank anonymous reviewers for their useful comments. We thank Thomson Reuters for providing access to the Datastream. Journal of Economics and Development Vol. 16, No.2, August 201437 References Abeyratna Gunasekarage and David M Power (2001), ‘The profitability of moving average trading rules in South Asian stock markets’, Emerging Markets Review, 2(1): 17-33, S1566-0141(00)00017-0. Alexandru Todea, Adrian Zoicaş-Ienciu, and Angela-Maria Filip (2009), ‘Profitability of the Moving Average Strategy and the Episodic Dependencies: Empirical Evidence from European Stock Markets’, European Research Studies, 7(1): 63-72. Balduzzi, P., and Lynch, A. W. 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