Weekly Return Distribution

Weekly Return Distribution: Euro Currency CU

Our distribution analysis provides a two-part perspective on weekly returns over the past three years. The first part reviews the characteristics of the market as it describes the distribution of returns using the skewness and kurtosis measures. This section is used to evaluate the personality of the market to help match it with the characteristics of an appropriate trading system. The second part quantifies various extreme levels of returns to determine current risk levels associated with the market. Historical measures, such as average monthly returns, standard deviation and conditional VaR, provide perspective on potential turning points.

Weekly Return Distribution:

Part One: Description of Returns

• The skewness measure indicates the level of non-symmetry. If the distribution of the data is symmetric, then skewness will be close to zero. The further from zero, the more skewed the data. A negative value indicates returns are skewed to the left, while a positive value indicates returns are skewed to the right. In trader talk … a high skew suggest that a return surprise is more likely to occur on the upside rather than from the downside. Traders will need to properly protect themselves from these potential moves. More
• Kurtosis is a measure of the peakedness of a distribution. In other words, it measures if outcomes produce a “tall and skinny with thin tails” or “short and squat with fat tails” curve. In trader talk … a high kurtosis suggests that more standard deviation risk is coming from the extremes (fat tail). Traders might look for high kurtosis markets expecting to see profit come from strong trends. More

Key Weekly Return Levels:

Part Two: Extreme levels of returns:

• Average Positive Week (APW), as its name suggests, measures the average positive weekly returns for those weeks that ended up. Its counterpart, Average Negative Week (ANW), measures the average of all weeks that ended down. Both of these measures provide potential targets for the week. Once we move past these levels, the markets are added to our watch list, which monitor standard deviation and conditional VaR targets.
• Standard Deviation (STD) is our first major extreme level. Markets have a tendency to gravitate toward these +/- levels and then possibly reverse. Keep a watchful eye on markets near their +/- standard deviation levels.
• Conditional VaR (CVaR) is our second major extreme level. CVaR is a statistical measure portfolio managers use to define risk. In the case of CVaR, if it’s broken, something major has occurred in the market. Individuals new to trading should look at CVaR as a reference point to determine if they can handle the risk associated with being on the wrong side of a strong market. If the market should hit +/- CVaR, it will either find a point of consolidation or accelerate even further in the same direction. In trading terms, it’s a decision point -do you exit or add to positions?
• The Best/Worst performance over the testing period is the third major extreme level. These are the most extreme returns over the past 3+ years. Note: unless the market is above or below its CVaR level, the best/worst returns will not appear on the chart. These extreme returns, with dates, do however appear on the distribution chart.