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«VOLUM E 1 1, N UM B E R 1 I S SN 2 1 6 8 - 0 6 1 2 F L ASH DR I V E I S SN 1 9 4 1 - 9 5 8 9 ON L I N E T h e In s t it ut e f o r Bu s i n e s s an ...»

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Further, although open prices have the highest correlations with FRAMA models, closing prices are used to be consistent with the use of the closing price in the FRAMA model. Daily frequency is used henceforth since they reflect less noise in the correlations when the frequency interval changes across different lag periods. As part of the initial process towards a robust trading strategy, the FRAMA model is tested over the three respective lag periods used in the initial part of the study, i.e. 10, 100, 200 days. The annualized return and annualized risk are calculated, followed by the Sharpe performance measure. The risk free rate of short and long trades are also calculated. On any given day, if the value of / is greater than is based on a 30 year Treasury bond yield at 4.42% p.a. The return over the whole period and the number the value of , and the value of /−1 is less than the value of −1, a buy (long) trade is initiated. Similarly, if the value of / is less than the value of , and the value of /−1 is greater than the value of −1, a sell (short) trade is initiated. If none of these conditions are met, the previous day trading strategy (long or short) is held. Findings are reported in Table 1.

Table 1: Risk and Return For FRAMA Models with Lag Periods of 10, 100 and 200

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Findings tend to support that the shorter the lag period under consideration, the lesser the number of trades.

However, the annualized return was the highest with the longest lag period of 200 although all of the annualized returns were valued around 24%. Annualized risk was stable under all three scenarios around 11%. With the highest annualized return and stable risk, the Sharpe performance measure was the highest for the longest lag period used among the three. However, due to the small incremental increase in the return for the 200 period case, it is important to investigate further lag period to detect any possible change

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in the trend of the return over different lag periods since the use of a longer lag period reduces the availability of data within a specific time frame analysis. This will also shed further light if the number of extra trades can be justified for such an incremental return. Trading strategies with lag intervals of 25, 50, 75, 125, 150 and 175 are also tested to shed further light on any such possible relationship between annualized return and lag period under the FRAMA model.

As the lag period is increased from 10 to 200, the annualized return increases by a small increment of 0.5% overall. The annualized risk still remained stable over the other different lag periods, resulting in a higher Sharpe value when using the longest lag period in the trading strategy. The number of trades tends to increase in a similar fashion as the annualized return, with an additional 70 trades when using the 200 days FRAMA model compared to the 10 days FRAMA model. Noticeably too, the number of trades dropped to 303 long and 302 short trades when using the 125 lag period, accompanied with a Sharpe measure of 1.781 and annualized return of 24.6%. Due to the fall in the annualized risk from 11.4% to 11.3% when comparing lag periods 75,100 and 125, it is interesting to investigate if the drop persists at other lag periods between 125 and 150, while sustaining the relatively high return of 24.6%.

Due to the fact the annualized returns and total number of trades can be two distinct decision making factors, the use of a relative ratio between them allows the comparison which model has a relatively higher annualized return to trade value. In a similar fashion, since the Sharpe measure takes into account both the risk and return factors, the Sharpe to Total Trades ratio as per equation (1) is used to allow for comparison between the model having different Sharpe values relative to the total number of trades. The annualized return/ total trades and Sharpe/total trades ratios reported higher values when using the 135 lag period model. While the Annualized return/ total trades increased from 0.041% to 0.042%, together with an increase in the Sharpe measurement value from 0.297% to 0.3%, it is important to acknowledge a drop in the number of trades on both the long and short sides, when comparing the 130 lag model to the 135 counterpart. As part of robust testing, lag periods between 130-137 are tested in regards to the total number of trades, annualized risk and returns, Annualized return/ total trades and the Sharpe/total trades values.

Figure 2 provides a graphical representation of the results.

Figure 2: Optimized FRAMA Model

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Findings tend to support the optimal lag number occurs when using the 131 day FRAMA model, with 291 long and 292 short trades over the January 2000 to June 2015 period. While the annualized return was not the highest among all, the annualized return/ total trades, which factors in the total number of trades, resulted in 0.042%. Similarly, the Sharpe/total trades ratio was the highest at 0.305%. The declining trend in the Sharpe/total trades values as the lag period is increased can be attributed to higher number of trades, accompanied with relatively similar annualized risk and returns. A comparison with a naïve buy and hold GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 375 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 strategy over the 15 year period, would have resulted in an annualized return of 0.84% p.a. and an annualized risk of 12.34%. In both instances, the fractal adaptive based model yielded a higher annualized return of 24.53% and a lower annualized risk 11.32%. Assuming that a naïve buy and hold strategy is based on a long and a short trade, the Sharpe/Total trades ratio would have been -14.5% compared with the optimized FRAMA model yielding 0.305%.


The emergence of behavioral finance can be explained through many facets, including the use of technical analysis techniques such as the moving average. The use of historical representations during the time in which investors make decisions, whether informed or not, whether short run or long run remains valid.

This paper adds to the existing literature by demonstrating that a moving average technique based on adaptive fractals can yield superior annualized returns, lower annualized risk, and a relatively higher Sharpe ratio. The paper sets the tone initially by comparing the strength of the relationship between the FRAMA model with open, high, low and closing values of the EUR/USD currency pair, compared with the widely used EMA and SMA model. Minute-wise, daily, weekly and monthly data are tested and the FRAMA model tends to hold a leading hand particularly for the closing EUR/USD values under the daily frequency interval. This paper also introduces the Sharpe to Total Trades ratio which takes into account the fact that different trading strategies are compared while having different number of long and short transactions. The Sharpe to Total Trades ratio extends on the existing Sharpe measure by adjusting it to the number of total trades. The optimized FRAMA model in the study is based on daily data using 131 lags. The annualized return of the market timing strategy yielded 24.53%, an annualized risk of 11.32%, a total number of 583 trades, and a Sharpe/total trades value of 0.305% compared with a buy-and-hold strategy which yielded a negative Sharpe/total trades value of -14.5%. One important area of future research would be to relax the assumption that the fractal adaptive moving average model moves between a fast moving average of 1 day and a slow moving average of 198 days, and as such test other daily boundaries.


Anghel, D.G. (2013). How reliable is the Moving Average Crossover Rule for an Investor on the Romanian Stock Market? Review of Finance and Banking. 5(2), pp. 89-115.

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GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 376 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 Gurrib, I. (2015). The Moving Average Crossover Strategy: Does it Work for the S&P500 Market Index?

SSRN Journal SSRN Electronic Journal, p1-24.

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Characterization of Atrophic Changes in the Cerebral Cortex Using Fractal Dimensional Analysis. Brain Imaging and Behavior, 3(2), 154-166.

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Hong Kong evidence. Journal of International Money and Finance, 17(3), pp. 535-545.

Mandelbrot, B. (1967). How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science, 156(3775), 636-638. doi:10.1126/science.156.3775.636 Mandelbrot, B. (1982). The fractal geometry of nature. San Francisco: W.H. Freeman.

Mandelbrot, B., & Hudson, R. (2004). The (mis)behavior of markets: A fractal view of risk, ruin, and reward. New York: Basic Books.

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GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 377 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 Zweig, M., & Goldfischer, M. (1986). Martin Zweig's winning on Wall Street. New York, NY: Warner Books.


The author would like to acknowledge the invaluable feedback from Dr. Saad Alshahrani from International Monetary Fund (IMF), and the dedicated motivation of Professor Stefane Kabene from the School of Postgraduate Studies at the Canadian University of Dubai.

GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 378 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1

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The recent scandal of Volkswagen AG (VW) has demonstrated one of the weaknesses of Corporate Social Responsibility (CSR)—how much people can trust CSR reporting. At a time when CSR is moving from voluntary initiative to a required component for businesses in many countries, sustainability and the environmental standards of Environmental/Social/Governmental (ESG) CSR have gained importance because there are existing regulations, especially in the emissions area. However, this focus has meant that CSR reporting can lack strategic focus and neglect profit reporting (ESGP). This paper will briefly describe the history of CSR and its movement toward the Environmental focus based on the current Cone, LLC consumer research on CSR. It will then describe the current reporting organizations and the current CSR focus of different companies and the value of adopting integrative reporting. As the number of organizations that act as third-party assessors and that announce awards for being social responsible grows, the fact that there is an Integrated model on the horizon may be the solution to standardizing what is meant by being socially responsible.

JEL: M140 KEYWORDS: Corporate Social Responsibility (Csr), Sustainability, Global Reporting Initiative, Accountability, Third Party Assessors


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