Using the Z Score to Trade Foreign Exchange and Other Financial Instruments: The Step by Step by Twomey Brian

Author:Twomey, Brian [Twomey, Brian]
Language: eng
Format: epub
Publisher: Unknown
Published: 2012-12-17T16:00:00+00:00

C

hapter 5: Z Score Correlation Coefficients

The slope of the regression line of Y on X in Z-Score form answers how many Standard Deviations Y changes when X changes 1 SD, a positive relationship equates to an increase in X is an increase in Y, a negative relationship is a decrease in X and decrease in Y and a negative correlation between X and Y is an X increase, Y decrease. The Z correlation formula is Sum of Zx X Zy / N and Z Scores on X and Y to chart results is Zx=price minus mean divided by SDx and Zy=y minus mean Y / divided by SDy.

This slope formula alone accomplishes first Pearson r correlations which doesn't change in the manner its calculated since the correlation results will remain the same.

By taking each Zx and Zy Score for each of 8 moving averages and dividing by 8, a standard deviation for each Zx and Zy moving average was correlated against each other since the Z Score was transformed into standard deviations. Essentially a correlation now exists for the entire distribution.

Secondly, the slope of the regression line is formally termed the beta coefficient or standardized coefficient due to the transformation of Z Scores. The slope formula is b= r X SDy / SDx. The beta indicates the amount of change of Y for a change in X but the slope and point intercept of the line has also been established.

Each Z Score has been correlated by a standard deviation so each Zx, Zy equals a beta weight and each can factor to a regression line at any point of Standard Deviations. This point is mentioned for those that trade other markets, other financial instruments. But by virtue of the correlation between the EUR/USD x and USD/CHF y for example, the entire distribution of correlations is known therefore price movements are known. What remains is to plot the points on a chart. The point intercepts are those points that establish price points on a chart. For example, a correlation of a slope of r 1 says prices move on a one for one basis between each other's standard deviations. A slope of 2 says a regression line is steep and not steep if the correlation was say .50.

Monday's correlations: EUR/USD vs. EUR/JPY r=0.810, EUR/USD vs. USD/CHF r = minus 0.91 and EUR/JPY vs. USD/CHF r=0.20.

The X, Y relationship should be viewed pair to pair in the context of each nation's interest rates since interest rates trade in increments of 0.025 or 25 pips.

Probabilities and Percent s

Probabilities and percents factors to an x axis Z Score to reveal percent areas under the curve, probability/percent confidence intervals and tail areas for either one or both sides of the mean. Probabilistic boundary lines are calculated above and below the mean as another trade reinforcement since both sides, 50%, reveals different yet vitally important information and because the general lines of the overall bell curve doesn't move due to its fixed mesokurtic/standard normal shape, a

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