# Estrategia martingala para forex converter

- 16.12.2020
- Felmaran
- Forex glazov vladimir
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You just need to enter an app and choose the most suitable strategy for yourself, which will help you to receive a steady and high profit at the International Forex currency market. Welcome to the Forex club of the successful traders who know how to earn money on the difference in the currency exchange rate. With the install of the application a trader also receives a special bonus. Safety starts with understanding how developers collect and share your data. Data privacy and security practices may vary based on your use, region, and age.

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Data is encrypted in transit. You can request that data be deleted. I really like this app and find it useful for a beginner like me. I just wish I could somehow print or export the strategy with the pictures, so they can be read more easily.

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Forex Course - Trading Basics. Forex Signals. Forex Signals PIP in week. Fxhours: Forex,Crypto,Minerals. Forex - signals and analysis. LiteFinance mobile trading. Forex fundamental analysis. There are several ways to measure the previous performance of the portfolio; the most common is using the previous returns or an average of the returns.

Barroso, suggest that there is evidence that the three months average contains information about the future behavior of the currency and that longer periods are not useful as was observed in Menkhoff, ; this period was also used by Kroencke Other periods that we find in literature, as in Burnside, and Rafferty, , are just one month lag or twelve months, for which we found that they contain relevant information.

The first task to construct the portfolio is to establish how many past lags in the returns we will use to determine if we should take a long or short position in the currency. Generally, the momentum strategies that use the most recently observed returns produce profits, which is expected if we assume that the foreign exchange rate accomplishes the Markov property. Only 10 of the 52 currencies have negative returns in average, which suggests that this strategy takes advantage from the abnormalities observed in the foreign exchange market.

However, we analyzed if we could find significant information including more lags. According to the augmented Dickey -Fuller test, the majority of currencies may be stationary with p-values lower or equal to 0. From this observation, in particular for the autoregressive part of the model, we may conclude that the number of lags should be between one and four.

Furthermore, we compare the results with different numbers of lags and maintenance periods 5 for each currency assuming all transaction costs. Table 7 Momentum strategy for individual currencies Source: own elaboration. In the previous table it is possible to appreciate that the strategies that use three lags have better performance and one of the best maintenance periods is one month; for longer maintenance periods the efficiency decreases.

These findings are supported by other papers such as Menkhoff, Following the methodology exposed in Menkhoff, the momentum strategy sorts the available currencies in six portfolios using a cross section ranking. In order to obtain a neutral dollar strategy the first and sixth portfolios will be used to build a strategy in which the investor will take a short position in the first portfolio and a long one in the sixth portfolio HML portfolio. It is worth mentioning that even though all foreign currencies appreciate at the same time we can take a short position in those with less significant appreciations, and long in those with greater appreciations, obtaining a benefit due to the differential between them.

The analogous case is that all currencies depreciate, which allows the use of this strategy, which is dollar-neutral in any situation. Table 8 Average Returns Source: own elaboration. Table 9 Average hit ratio Source: own elaboration.

Table 10 Developed and Emerging currencies Source: own elaboration. In the tables 11 and 12 we show the performance of the HML portfolios using one, three, six, and twelve months and with one, three, six, and twelve holding periods to corroborate our previous observation that three months for the average and one month holding period produces better results. Furthermore, as with the Carry trade, we present the performance of the six portfolios and the HML portfolio.

The monotonicity in the mean of return is less clear than in the carry trade and will be tested in the next chapter. Also, the results for the HML are compared with the portfolios including all transaction costs, a portfolio without transaction costs, and finally a portfolio that only includes developed currencies.

Table 11 Momentum Portfolio Source: own elaboration. Table 12 Momentum Source: own elaboration. Finally, we compare the performance of the HML portfolio for the whole set of currencies and for the developed currencies G10 with the Momentum Index 6 of Deutsche Bank. Figure 8. Figure 9 Source: own elaboration. In the figure 9 it is possible to appreciate that the momentum strategy performs well during the crises, which is one of the main differences in the behavior between the momentum and the carry trade.

For the value strategy the principle is to determine using the real exchange rate instead if the manager will buy sell currencies based on under over -valuation relative to equilibrium exchange rates. The real foreign exchange rate considers the relative prices and is adapted according to the international commerce of each country. To show if a currency is undervalued or overvalued, we use the Hodrick-Prescott filter HP.

This filter decomposes the time series in its trend and cycle, the trend is used to determine if the real foreign exchange rate is above or below its trend line. In Barroso, they use the standardized real exchange rate using its historical moments, they comment that this standardization is necessary as the real exchange rates are close to a unit root process.

Applying the Dickey-Fuller test for the real exchange indexes, all of them reject the hypothesis to be stationary with p-values bigger than 0. The HP filter identifies the cycle and trend by balancing a trade-off between smoothness and trend adjustment:. To calculate the trend and the signal, the real exchange rates are used with a lag of one month because they are published fifteen days after the end of each month. When this signal is positive it indicates that the real exchange rate is undervalued and it should appreciate.

The appropriate strategy in this case is to take a long position. On the other hand when the signal is negative, the real exchange rate is overvalued and the investor should bet to a depreciation of the currency taking a short position. In this kind of strategy the fact that we use the signal with one lag does not imply a huge disadvantage as usually the signal stays for several months before and during the mean reversion of the real exchange rate.

For the Hodrick-Prescott filter all the information available will be used as data for each currency. The pay-off of this strategy for the i-th currency is:. The blank spaces in the next tables correspond to currencies for which the calculations could not be made. Once again we sort the currencies from those that showed greater overvaluation to those which presented greater undervaluation using the value signal, dividing the currencies in three portfolios. Two of them are considered: The first one PS contains the currencies which are over its trend line and present the biggest value signal in absolute terms, and the second portfolio PL contains the currencies which are below its trend line and have the biggest difference.

With these two portfolios the strategist should take a short position in PS and a long position in PL, building a dollar neutral portfolio. The third portfolio, PM, is also included in the tables 14 y In the following plots the performance of the value strategy is contrasted against the Deutsche Bank PPP index 7. Table 13 Individual Value Strategy Source: own elaboration.

Table 14 Value Strategy Source: own elaboration. Table 15 Value Strategy transaction cost effect Source: own elaboration. Figure10 Source: own elaboration. Figure11 Source: own elaboration. The reversal strategy is based on the idea of taking advantage of the misalignment of the currency for its long term mean expecting a correction; this phenomenon is called the mean reversion property.

In this strategy the manager takes a long position in the currencies that are undervalued and a short position in the currencies that are overvalued. This strategy was implemented in papers such as Asness et al. For our purposes we use the nominal exchange rates and follow Asness et al. Then we can define the reversal signal as:. If l o g S t i S t i , U I P is positive, it implies that the currency is depreciated and it should appreciate; then the investor should take a long position in this currency.

However, if l o g S t i S t i , U I P is negative, the currency is overvalued and it should depreciate, so the investor should take a short position. Thus the pay-off of this strategy is:. In order to determine the period that we need to consider for the reversal strategy we consider three alternatives: three, four, and five years.

First of all, the regression:. However by observing the hit ratio, this statistic indicates that in average the three years period has more accuracy anticipating the direction of the movement of the interest rate than the four-year and five-year periods.

Table 16 Regression and Hit ratio obtained from the signal and hit ratio Source: own elaboration. Once we define the three-year period as a reference for this strategy, five portfolios are built by a cross sectional rank which divides the portfolios in five quantiles using the empirical cross section distribution based on the reversal signal. Then, the asset manager takes a long position in the portfolio with currencies with bigger reversal signal and a short position in the set of currencies with lower reversal.

Ideally, for portfolio P5 reversal signals are positive for all the currencies and greater than the signals for other currencies. This indicates that the currencies in that portfolio should appreciate. Conversely, for portfolio P1 reversal signals are negative for all the currencies and lower than the signals for other currencies, which indicates that they should depreciate. Table 17 Reversal Strategy Portfolios Source: own elaboration. Table 18 Reversal Strategy Source: own elaboration. Only in seven months the signal is negative for all the currencies; in the other cases there is at least one currency for which it is was either positive or negative.

However, if this does not happen, the strategy can also make a profit if the signal is correct, anticipating bigger returns for the currencies in P5 and lower returns for the currencies in P1. Figure 12 Source: own elaboration. In this strategy the losses generated for the short P1 portfolio drive the bad performance of the strategy and the monotonicity observed in the carry trade is not observed as the returns generated by a long position in P1 are bigger than the other long investments in the other portfolios in average, which contradicts the idea of the reversal strategy.

This section includes two subsections, both involving hypothesis tests. The first one is for the monotonicity of the returns for the trade and momentum portfolios, and the second is to test that the mean is different from zero for different portfolios of each strategy. In order to test the monotonic relations between the returns in the carry trade portfolios and in the momentum portfolios, the approach proposed by Patton, , which uses the Bootstrap methodology for the proof, will be utilized.

For the sorted portfolios we have the population differences between the means of the P i portfolio and the P i - 1 :. Let define the hypothesis. The idea is to reject the null hypothesis and then not rejecting the alternative hypothesis that. Patton, avoided the problem of estimating the covariance matrix of the asymptotic multivariate normal distribution N for a large sample T :. We apply the test for the 5 carry trade portfolios assuming for this test that P1 is also a long position, and not a short position as explained in the previous chapter.

P3 and P4. When the tests were made without P3 or without P4, they were accepted with p-value of 0. The most important relation is that the mean of returns in P1 is lower than the mean of returns in P5, which implies that taking a short position in P1 and a long position in P5 will have a positive mean of returns. In the case of the momentum strategy, the monotonicity relation is rejected. However the monotonicity relation that the returns in P1 are lower than the returns in P6 is not rejected for the returns calculated with or without transaction costs with a p-value of 0.

When the transaction costs are omitted, the hypothesis of monotonicity relation is rejected. This suggests that the transaction costs play an important role for this strategy. For the reversal and value, the High Minus Low strategy does not generate profits in average, but the portfolios with the currencies that have the higher signal showed positive returns in average. These portfolios will be used for the next test and in the next chapter to construct a portfolio that includes the five kinds of portfolios.

Using the same approach as in the test before, the p-value J can be calculated using the bootstrap samples:. For the Wilcoxon test the hypotheses tested are:. In the table the answers presented for this test are related to H 0. An important remark is that the Wilcoxon test assumes the symmetry of the distribution while the test made using the bootstrap did not assume so.

Table 19 Mean and Median test Source: own elaboration. When the returns do not consider transaction costs, all the strategies reject the hypothesis that the mean is less than or equal to zero and the same applies for the median according to the Wilcoxon test. However, when the transaction costs are taken into account, only the tests for the sign and the HML Carry Trade reject the hypothesis, while in the other cases there is not enough information to reject it.

In the standard causality test, k lags are established arbitrarily, and the following regression is performed with ordinary least squares:. The null hypothesis is that the coefficients are equal to zero and this implies that Y does not cause X. The proof also requires the following statistic:. The test is performed for each of the characteristics, trying to identify if these have relevant information about the future returns of the currencies.

Each one is standardized by its cross-sectional mean and standard deviation to make the series stationary. Although the results of the test show how the characteristics are relevant for some currencies and not for others, the carry trade strategies sign and implied interest differential are significant for a bigger number of currencies in comparison with the other three characteristics. This observation, along with the significance obtained from the mean and median tests in the last subsection, suggests that the carry trade signals contain some information that may be complemented with the other signals to construct a portfolio that takes advantage of the information contained in the four signals.

After the statistical analysis of the currency strategies in the last sections, which suggests that the characteristics of each currency contain information it is possible to construct a portfolio taking advantage of this information based on the approach of a parametric portfolio developed by Barroso and Santa-Clara, who implement a model for a currency portfolio using characteristics for the currencies similar to those that was analyzed previously.

The presented portfolios include the modification suggested by Barroso and Santa-Clara, for the transaction costs that implicitly include information about the liquidity of each asset according to each period, which Beardsley et al. Furthermore, in order to adapt the model for conservative funds such as pension funds, we propose to include a restriction in the leverage of the portfolio which may be replaced with a restriction that considers some risk budget.

For the construction of the portfolio, we use the Constant Relative Risk Aversion Utility function, also known as the power utility function. While we can apply the methodology presented in this section with other utility functions, the CRRA utility function penalizes the skewness and kurtosis as was mentioned by Barroso and Santa-Clara, and it is explained below.

For this exercise, without loss of generality, we consider:. The main assumption of this approach is that the characteristics of the currencies contain all the information available. This investment is zero cost if we assume that it is not required to post collateral. The characteristics of the currency x i , t that will be used for the construction of the portfolio are the following: 1 the Sign of the carry trade, 2 the Implied interest differential, 3 the Momentum signal, 4 the Reversal Signal and 5 the Value signal.

Each characteristic is standardized by its cross section mean and standard deviation. Then the distributions of the characteristics are stationary because for each month their distribution has zero mean and variance one. The standardisation also allows us to compare the relative signal among the periods; its most relevant contribution for the portfolio optimization is the guarantee that the sum of the weights w i , t is zero.

If the first order approximation is good enough, it indicates that the manager should only invest in the long short contingency portfolio if and only if it has a non-negative mean. This is a desirable condition that the optimal portfolio should fulfil. This factor reflects the risk aversion of the asset manager, in particular their crash risk aversion. For this reason it is desirable to have a utility function that penalizes negative skewness and high kurtosis, this property is relevant at the moment of performing the optimization.

Simplifying the notation, we can write E t instead of E F t :. From the previous expansion it is easy to notice that for the CRRA utility function the factors in the last equation penalise the high volatility, the negative skewness, and the high kurtosis. Probably this assumption is not a problem as optimization should provide the best that generates the best returns. The optimization suggested above does not take into consideration the effect of the transaction costs that also constitute a proxy of the liquidity in the market.

From the analysis in the previous section it can be observed that the transaction cost and liquidity are a valid concern for the asset managers; the relevance of the transaction cost in portfolios was also reported by Menkhoff et al. In order to incorporate the transaction cost into the optimisation, the approach of Barroso and Santa-Clara, was followed.

The modification from the previous objective function is simple, as it only needs to incorporate the forward transaction cost of each currency c i , F , t inside the utility function in the following way:. These equations are useful according to Brandt et al.

In the next section we calculate the standard errors using the bootstrap technique which was also suggested by Brandt et al. For the optimisation we used the following formulation in which the next constraints were included when not considering the transaction cost:. A similar setting is used taking into account the transaction cost in the optimisation:. The signal of each strategy was constructed to be positive when the investor should take a long position and negative when the investor should take a short position.

This observation may not be a problem for the hedge funds but for market participants that take more conservative approaches such as pension funds, sovereign wealth funds, or central banks, the level of leverage necessary could limit the implementation of the optimal portfolio. This restriction can also be useful in scenarios in which the short selling is restricted or when the regulation limits the short position, this limit could be over the average of leverage taken by an institution in a certain period of time.

Thus the restriction contributes to the implementation of this optimization approach for a bigger number of participants. Furthermore at the moment of solving the optimization problem, the following condition is fulfilled:. Finally and probably the most important characteristic of this approach is that it is tractable because it has a parsimonious number of parameters that have to be estimated to determine the investment amount for each currency.

This fact was highlighted by Barroso and Santa-Clara, and Brandt et al. In order to construct the optimal portfolios, we use the same currencies as in previous sections, and use two different windows of time. The first window corresponds to the in-sample period, which covers from October to December The second window is the out-sample period and includes from January to June For the in-sample period, the constrained optimization of the objective that includes the transaction cost in the utility function is performed for 1, bootstrapped samples in order to obtain the estimation of the parameters for each sample.

Furthermore the same exercise is performed individually for each characteristic and for the objective function without transaction costs. The samples obtained by the bootstrap allowed replacement and all of them have the same size as the original sample. The following hypothesis test is performed to determine if the estimated parameters are significant or not:. Table 22 Parameters' covariance matrix Source: own elaboration. Table 23 Standard errors. The estimated parameters for each sample are used to calculate their means, their standard errors, and their p-values.

The results obtained after the bootstrap sampling and after the estimation of the parameters suggest that the momentum, reversal, and value do not characterize well the future returns of the portfolio. This is consistent with the performance and the statistics obtained for each of the portfolios, as these strategies tend to perform better than the carry trade only in stressed periods and this factor makes them valuable when they are combined with the other strategies.

When the optimization is performed taking into account the five characteristics with or without considering the transaction cost inside the utility function, the significance for the momentum, reversal, value increases, and the sign and interest rate differential it decreases slightly in comparison with the high significance obtained with the model which uses only one characteristic.

This is due to the sign and the interest rate differential providing similar information. Rafferty, reported that when the strategies of Carry Trade, Momentum, and Value are combined, the asset allocation efficiency increases. Figure 13 Source: own elaboration. The optimal parameters change through time but in general the changes from one month to another are relatively small.

In the case of the implied interest rate differential and sign strategy, the estimated parameters present an inverse relation which might be explained by the increase in the number of emerging currencies available for investments since From this year onwards, the interest rate differential has provided more information than just the sign, its magnitude has become more relevant.

This is reflected in the currencies with the highest rate differentials outperforming other currencies with lower interest rate differentials even when the currencies have the same sign for the carry trade. The Brazilian Real is a good example as it has had high interest rates for a long time. The returns obtained for the OOS period considering transaction cost and allowing the inheritance of positions clearly show more profits than losses, particularly for the period between April and December During the crisis in the portfolio presented the biggest losses and after that year the returns presented a greater number of fluctuations between the profits and losses, which may be explained by the volatile episodes in the markets observed in the last 5 years.

These episodes have not been anticipated by the used characteristics of the currencies, which might suggest that a new characteristic is required to explain them. This new characteristic might be a global volatility index. The table 29 presents the statistics of the returns obtained for the OOS period for the portfolios that were optimized with the objective function that include the transaction cost.

In the first column is the portfolio that allows the inheritance of the position. The second shows the portfolio in which it is assumed that the positions are closed at the end of each period. Finally, the third column presents the results for the optimized portfolio which does not consider the transaction cost inside the objective function.

Table 24 Parametric portfolios comparison Source: own elaboration. Figura 14 Source: own elaboration. The impact of the transaction costs in the performance of the portfolio is observable in the plot as well as in the table. These costs reduce significantly the potential profits in the long run and also affect the estimations of the performance indicator such as the Sharpe ratio; for this reason the calculation is made taking into consideration the possibility to inherit the positions from one period to the next trying to replicate the behavior of an investor that tries to reduce their transaction cost in each rebalance date.

With respect to the restriction imposed in the leverage, it had a good performance preventing the portfolio from taking aggressive positions. Another advantage of the portfolio is that it prevents taking a short position and a long position in the same currency at the same time. This might happen when an asset manager takes a position in different currency strategies. Figure 15 Source: own elaboration. Figure 16 Source: own elaboration. Figure 17 Source: own elaboration. This performance confirms the results presented by Rafferty, This might explain why it has a better performance, as the difference between the two portfolios increases after the inclusion of more emergent currencies in the year The paper formalizes and analyzes statistically four foreign exchange strategies based on the concept of carry trade, momentum, and mean reversion property.

We propose a methodology to calculate the returns considering the transaction cost and allowing the inheritance of the position for the previous strategies. This method has less assumptions and incorporates the behavior of the managers who try to use their previous positions to reduce their transaction costs, which have a significant impact in the long run. Among the foreign exchange strategies, the carry trade investments table XX computed as in Menkhoff, , which take advantage of the interest rate differential, appear to be the most profitable against the other strategies and also contain valuable information that can be used to predict the future returns.

The sign strategy that is also based on the interest rate differential show a good returns, in order of profitability the reversal and the momentum present in average profits only the value strategy in average has losses but this strategy has low correlation or even negative correlation against the other strategies that increase the diversification in risk events as this strategy tend to have a good behavior in high volatility periods.

A relevant point is that the strategies returns are leptokurtic which increase the risk of big losses however a combination of this strategy that include relevant information about the future behavior of the currency decreases the risk of potential loses as the correlation among the strategies is relatively low. Table 25 Strategies comparison Source: own elaboration.

In order to take advantage of the information contained in these strategies and use it to construct an optimal portfolio, we develop five signals that determine the pay-off of each strategy. These signals become the characteristics of the currencies which are used in the implementation of a version of the parametric optimization proposed by Barroso and Santa-Clara, and Brandt et al. The adaptation of the model by the introduction of the leverage constraint produces portfolios that are more suitable to implement than the portfolios obtained without the restriction.

This constraint also increases the efficiency of the sub-gradient and genetic algorithm routines applied to find the maximum. The model also decreases the risk of in-sample over-fitting since the coefficients will only deviate from zero if the combination of them offers an increase in the expected utility. At least two questions remain to be investigated; the first one is to determine the optimal time for which the parameters theta should be re-estimated and if the causes of different performance is a phenomenon observed only for portfolios that include emerging currencies.

Finally, the performance observed in the portfolios constructed using the parametric method suggests that it could offer profitable investment opportunities that have not been used by the market participants with the exception of quant managers, who only represent a small proportion of the market participants. Asness, C. Value and momentum everywhere.

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### Estrategia martingala para forex converter max and forex

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