Forex trading外汇交易

Optimal risk and money management choice in FX tradingReport for FIN255Bo LiMarco BucciAbstractThe report talks about the optimal choice of stop loss/ take profit level and the proportion of risky asset in support and resistance trading. The data we used is from the demo trading of GBP against USD in Metatrader. We first fixed support and resistance levels in everyday trading, based on which, as well as the historical change of exchange rate between sterling and US dollar, then we choose two pairs of take profit and stop loss level to define our trading in some sense. The real-time price of exchange rate will either hit take profit or stop loss level, so in this way we derive the outcome of every trading. As a result, we can set the proportion of risky asset in every trading which to great extent affects the value of our portfolio. By optimizing the portfolio in terms of different criteria, we obtain optimal ratios of risky asset to whole portfolio. And finally we try to reconcile the ideas and implications behind such different optimal proportion.I IntroductionBy engaging ourselves in real-time trading in foreign exchange market, we try to get an optimal trading strategy based on the support and resistance analysis. Put it specifically, when trying to construct the optimum trading portfolio, we need to address two important problems which determines the volatility and return of our portfolio--- determination of take profit/ stop loss level and risk per trade.To begin with, we would like to present some introductory knowledge about exchange rate, foreign exchange trade and support resistance, take profit and stop loss, as well as money management to understand our issue. Explaining it in a few words, exchange rate is the price of one country's currency expressed in another country's currency ( Investopedia, 2008), and it follows naturally that foreign exchange trade is the trading in terms of exchange rate for speculation or hedging the foreign exchange risk. In this trading, one of the most frequently used method of technical analysis is resistance/support level which means the price at which a stock or market can trade, but not exceed/ fall below, for a certain period of time and is applied by us. Another important concept is take profit and stop loss. Take profit order is an order used by currency traders specifying the exact rate or number of pips from the current price point where to close out their current position for a profit And the understanding ofstop loss is close to it. Lastly, money management indicates the process of budgeting, saving, investing, spending or otherwise in overseeing the cash usage of an individual or group. So with such understanding, we unfold the introduction of our work.The first and foremost problem is the selection of take profit level and stop loss level. This is a fairly important issue in trading. Based on our comprehension, it largely determines the outcome of every trading, either winning or loss because if we fix a low take profit level in trading, it is easier for us to win in this trading for the price only needs to go a little distance toward the favourable direction. Easy to win as it is, the draw back is that profit in every likely winning is limited. Likewise, if we set a low stop loss level, it is more likely for us to lose in this certain trading, although it is true that the actual loss in every losing trading is little. And the same reasoning can be extrapolated to high take profit level, which indicates a low probability to win yet a big gain in winning, as well as big stop loss level, which suggests a low probability to lose however a huge cost when losing. In a word, the selection of take profit and stop loss level is a trade-off between the probability and amount of winning/loss. To get a sensible take profit and stop loss level, we try to draw on the historical fluctuation of exchange rate between sterling and US dollars, along with a quasi-scenario analysis conducted in subsequent parts of the reports.Another equally, if not more important problem arising is the determination of the risk per trade whose definition is the percentage of total asset that is risk being lost in the trading. That is to say, whenever the price of exchange rate hits the stop loss level, the loss of the trading is risk per trade times the current position of our account. It seems plausible to set a risk per trade as low as possible following logic. However, when considering that with a low risk per trade, we can only make a restricted amount of profit when winning, it is easy to conclude that the previous inference is not true. In effect, this problem is the issue of the amount of investment. It is quite straightforward that less invested in the portfolio, less we win or lose. So it is also a problem of risk allocation, close to the first problem we point out.Our report presents the answers for the two problems through which make a reasonable risk choice and optimal portfolio. In section II, we try to shed light on the methodology we use, including general demonstration and some specific quantitativemethods and criteria we used. Section III is the main body of the report, interpreting the result and explaining the choice of stop loss, take profit level and the risk per trade via the maximization of the account through Excel. Besides, we try to extend our direct results, and give more advice on the risk management of investment and trading. As the last part of our report, section IV briefly summarized our finding and suggests some directions for further research.II MethodologyThe general methodology adopted by us is an experimental method and optimization via Excel, which refers to that we apply different candidate take profit and stop loss level into the account so that get varied return and volatility of the value of the account, and then we judge the return and volatility in terms of different quantitative criteria. Finally by comparing different results, we get the final result. This method is reflected in solving both of the core problem presented in the beginning of the report.In picking up the stop loss and take profit level, we first delve into the statistical characteristic of the historical data of the exchange rate level, in particular getting a idea of its volatility. According to it, we get four pairs of candidate stop loss and take profit levels, then by using the experimental method mentioned above, we try to select the best one pair and explain the idea behind this level. The same logic is well extrapolated into solving the second problem: choosing the preferable level of risk per trade.A key issue in the experiment is to evaluate the return and volatility of the different results influenced by our choice of stop loss, take profit level and risk per trade. The following quantitative criteria are adopted by us to measure the performance of different strategies.Net profit. / Average returnNet profit is one of the most widely quoted performance statistics. Simply put, net profit is the dollar earned or lost during the life of the back-test. And average returnjust measure the profit in another lens. We use geometric average return here, here is the formula:0(/)^(1/1)1n R R R n =+−Profit to DrawdownThe ratio of net profit to maximum drawdown is also a popular measure of performance. A drawdown occurs when net profits falls from its highest point. This drawdown is calculated each trading day, and the maximum value is recorded as the maximum draw down. In our analysis, we first measure the drawdown, and then try to get the profit to drawdown.The Sharpe RatioDeveloped by Nobel Laureate William Sharpe, the Sharpe ratio is a standard in the money management industry. The ratio is calculated using two statistical measures: mean and standard deviation. The formula is like this:R R SR σ=Calmar RatioGenerally speaking, the higher the Calmar ratio, the better. Some funds have high annual returns, but they also have extremely high drawdown risk. This ratio helps determine return on a downside risk-adjusted basis. Most people use data from thepast three years.( Investopedia, 2008)The utility function analysisDifferent criteria give rise to different optimal choice of the take profit, stop loss level and risk per trade? The further question is which the best one among these relatively optimal choices is. In fact, those different results are just the varied answers to a same question from different perspectives. So perhaps the desirable way to deal with the problem is not to pick out the so-called best but to interpret the implications behindthe different results. And after that, we will try to find the preferable one based on our own judgment and experience.III Trading DataAs mentioned above, we try to accomplish our analysis in a real-time environment, so the trading result on which our analysis based on is gained through the operation of our group from 27/10/2008 to 14/11/2008 during which we have completed 97 trading. We admit that the period of experiment and numbers of trading is limited yet considering the time span of the course, we are trying to get the final result in limited experimental period.Our trading is based on the platform of Alpari Metatrader, and we committed ourselves into the trade of GBP/ USD. The reason why we choose it is that first we are located in London, and GBP has the most important position in the foreign exchange market of London which guarantees the practical benefit of the report, second GBP/USD is one of the most well-established trading instrument, which means the existence of a mature market condition.The initial asset of our account is $100,000. We intend to observe the final balance of our account in different scenario.IV Analysis and FindingsWe try to solve the problem posted in part of introduction one by one, first to fix a take profit/ stop loss and second set the risk per trade.Determine take profit/ stop loss levelThe first step to fix a take profit/ stop loss level is to examine the historical return and the volatility of the exchange rate of the pound sterling against US dollar. The period we examine is from 1/7/2008 to 21/10/2008, three months before our experiment. We examine the average of the daily logarithm change and standard deviation of daily level. The result is like this: the average is – 0.00294, indicating a declining trend of GBP, and the standard deviation is 0.156187. Considering the average level of GBPis 1.79 in this period, the standard deviation, which implies a change in one day is relatively high. So we should adopt a comparatively high level of both take profit and stop loss level.Apart from considering the historical profit, we should take the current economic and financial environment into account. First and foremost, billions of capital have been spent buying the dollar over the past a couple weeks, motivated by a risk-aversion tendency in financial turmoil. We need to adjust in order to suit it. Needless to say, most of our trading should be placed on the side of short, moreover, it also affects our choice of take profit/stop loss level. For example, in a so-called heavy trending environment, like now, when we are trading long, we should take profits quickly and do not look to hit a homerun. And ‘ trending environment= more pips in line with the trend’ (Ironman, 2008). In addition, we stick to some rules of thumb, for example, ‘1st take profit level should be set on the nearest trend line or resistance level’),and ‘ As long after determining the S/L and T/P points, calculate the risk reward ratio. Trade only when the R:R ratio is at LEAST 1:1’(Forex Ebooks,2008).Therefore, we try to fix take profit/ stop loss level more risky in such a trending environment, meaning a bigger take profit level than stop loss level. Besides, we seek to place more bets on the declining side of the exchange rate and now that we are in a trending environment and decline is the obvious trend in this time, a wider range in both stop loss and take profit is adopted.Four pairs of take profit/ stop loss level are set by us to make a comparison between them. We try to compare the final payoff of the four pairs and answer which is the best one. Thereby take profit and stop loss levels are set as follow: 75/-30, 25/-10, 35/-20, 50/-20.With the se take profit/ stop loss level, we get the outcome of our trading as in the table below. Since in every pair of stop loss/take profit, we fix a higher take profit level, so generally speaking the numbers of winning is less than those of loss. It seems that in every case, the wider win is offset by the fewer time winning, however, a close examine can shed light on the efficiency of different pairs of take profit/stop loss levels. As is demonstrated in the Hit rate column and W/L column, with a same W/Lratio, the 25/-10 level gain a higher win/loss ration than the other three one, but the 50/-20 is the most inefficient one. So in this perspective, 25/-10 seems to be the optimal one. In terms of the ratio between points gained ( equals to take profit level times the winning time, for example 75*36) and points lost ( similar to the definition of points gained), we should also choose the 25/-10 for it gives us the highest ration of Points gained( Pg)/ Points lost(Pl).Win Loss Hit rate W/L Points gained Points LostPg/Pl75/-3036 61 37.11% 2.5 2700 1830 1.48 25/-1047 50 48.45% 2.5 1175 500 2.35 35/-2040 57 41.24% 1.75 1400 1140 1.23 50/-2034 63 35.05% 2.5 1700 1260 1.35 Table 1: the win and loss of different levelsDesirable as it is in terms of winning and loss points, 25/-10 should be further investigated to see whether it stands the test of asset. The result is encouraging for the 25/-10 voters. From a conservative risk per trade 3% to a aggressive one 10%, 25/-10 outrun the other three for the final asset in the account after 97 trading is much more when adopting 25/-10, as is showed by the following chart.Chart 1 the performance in risk per trade 0.25%Even using a more complicated criteria, Sharpe ratio, the choice is the same, as is illustrated by the following table.Sharpe ratio Calmar RatioReturn StandardDeviation75/-30 0.0094 0.0511 0.1572 4.513905725/-10 0.0214 0.0528 0.3762 23.89786135/-20 0.00750.0410 0.1612 5.107838650/-20 0.0080 0.0505 0.1334 2.46449Table 1 the return, standard deviation of different levels Therefore, after standing the test of winning times, account performance and the sharpe ratio, it is safe to say that 25/-10 is the optimal choice for us when we try to fix a take profit/stop loss level.Set the risk per tradeWhen setting the risk per trade, scenario analysis used by the part of determining take profit/ stop loss level is no longer feasible. Instead, we use the ‘ solver’ in Excel to find the optimal choice of risk per trade.Based on the result we derived in the previous part, we choose the 25/-10 as our take profit and stop loss level. In this level, we try to optimize the balance of our account.The so-called optimize may be different when adopting varied criteria and indicator to judge. And we seek to use 4 indicators, intending to give a comprehensive answer and drawing some comparison among them.First is the Average Return. In short in this case, we try to maximize the account in the last trading, so the result is that 29%, which is the so-called Kelly Ratio, is the optimal risk per trade, leading to a amazing 694449557 balance after the trading. After examine the increase of the asset, we find that it is a series of 11 consecutive winning from trading No, 80 to 90 that give the exponential skyrocket of the account. Besides, this winning series result in a one-side increase, instead of huge volatility, which tend to accompany huge return.When making such a big profit, it is better to investigate its risk, which is measured by dropdown by us in this case. Even in dropdown inspection, 25/-10 further benefits from its 11 consecutive. From the chart we see that although in the middle of theexperiment, the dropdown ratio is pretty high, indicating a huge slump of credit in our account from its previous maximum level. However, in the end, the dropdown is pretty low as showed in the chart. Even offset by the consecutive winning, the average of the dropdown when using a 29% risk per trade, the figure maximize the account in the last trading, is 50.6%, is still pretty high. So when considering volatility, 29% is not a very good choice. To reduce the average of dropdown, the obvious method is to set the risk per trade as 0% or extremely close to 0%, which is more feasible. Nevertheless, it sacrifices the return of the trading.Chart2 the dropdown of 25/-10 in different trading The next criterion is unsurprisingly Sharpe ratio, which is a key measure of risk and reward. To maximize the Sharpe ratio, we get the Risk per trade to be 1.5E-8, roughly equal to 0.This is a weird result, indicating a extreme risk- aversion, however, noticing the fact that the extent to which the standard deviation of return determine the Sharpe ratio, it is no wonder there comes the extreme result. In this case, if a person is risk-avert, enough for him to take Sharpe ratio as the reasonable standard, the best strategy for him is to take a 0% risk per trade.However, risk-avert as we are, we do not count standard deviation that much as in using Sharpe ratio, so perhaps Calmar ratio makes more sense.Likewise, we use ‘ Solver’ in excel to maximize the Calmar Ratio of the performance of 25/-10. The result is roughly 19%, which signifies a relatively risk-taking attitude.To interpret the result, the point is to observe that the to extreme case of maximum of dropdown, acting as the denominator when calculating the Calmar Ratio. That is to say, volatility plays a limited role in determining Calmar Ratio, however, return have infinite potent in some sense.V Recommendations in tradingIn short several recommendations can be composed after the analysis of the report.First, try to get informed of everything before trading. As mentioned in the analysis above, one should first have an idea of the asset one holds, the risk attitude and market condition, both historical and current. For example, when trading these days, in a serious financial turmoil, one should place more bets on the short position and adopt the take profit and stop loss level based on the trending environment. Also, if the investor is some kind of risk-aversion, he or she should sidestep the current market.Second, when using S/R trading, fix a reasonable stop loss/ take profit level. We should avoid qualitative trading when using S/R. Since human is irrational, if we let the price go and keep our position in foreign exchange market, the final result is likely to be not encouraging. And numerous empirical study shows that the quantitative method gives a much better than qualitative one.Third, using Sharpe ratio, Calmar ratio can be misleading if we have no idea of the implication behind such ratios. We should be aware of the meaning the these ratio and resort these indicators to get an idea on the risk and return selection in our trading.More specifically in this experiment, we recommend the varied choices based on the risk attitude of individual investor:Risk-take:We strongly recommend the pair 25/-10 if you have enough courage to take the volatility.PairAnnual return DropdownrateLoss capitalprobabilityRisk pertrade25/-10 2.59287081369939E+63%96.6718%51.5464% 27.6641%It is showed from the graph that having the 27.66%risk per trade will lead you to have a amazingly 2.6E+63% annual return! In the meantime, high return means high risk, the probability of losing your capital is 51.55%, which is relative high. And the drawdown rate is 96.67%, which shows the volatility is extremely high. Considering the high return, it’s really a good choice to bet your money, once succeed, you will be not merely a billionaire!Risk- aversionPair Annualreturn Drawdown rateLoss capitalprobabilityRisk per trade35/-20 23376.5871% 0.1562% 19.5876% 6.4046%This pair 35/-20 is quite profitable as well, but compared with last one, 23376.5871% annual return seems so little. We recommend as the reason the probability of losing your capital and drawdown rate are much lower, which are 19.59% and 0.1562%. As the whole market does not perform well, having the 6.40% risk per trade and get a 23376.5871% profit is definitely a good deal.VI ConclusionOur report successfully address two key problems posted above, the first uses the scenario analysis method, comparing different take profit and stop loss level, and finally set 25/-10 as the optimal take profit/ stop loss level. After that, based on the choice of 25/-10, we seek to find the best risk per trade. However, from differentviews, the concept of best may vary so we find four criteria to be the touchstone. And then we compare the implication of the different criteria and based on our risk-attitude, we give our own selection.Besides, some recommendations are provided in the report by summarising the tricky points when carrying out the experiment and the lessons we have draw from the real-time trading procedure.One deep implication of outcome of our real-time trading research can further disprove the so-called EMH hypothesis (i.e. Efficient Market Hypothesis). Now that we have derived an optimal proportion of risky asset, as well as a reasonable take profit and stop loss level into trading, which in effect make the portfolio of value in foreign exchange market maximal, one significant corollary of EMH can not be convincing that any technical analysis using historical price data makes no sense.ReferenceInvestopedia92008 ( 2008), /terms/e/exchangerate.asp Ironman, 2008, BRV’No Brainer’ S+R trading.Forextrade,(2008) /index.php/Lessons/take-profits.html Investopedia(2008),http://w/terms/c/calmarratio.asp?viewed=1。