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Z-Score

It is a statistical tool. It is used mainly to compare performance with the standard one. The data from the output is given as an input and is compared with the standard in this tool. In this method the average mean of the normal data is calculated and is compared with the obtained data to find the standard deviation. This shows how much the obtained data has deviated from the standard data. Then the z-score is obtained by subtracting the numbers in the data with the mean value and then dividing the value with the standard deviation, this is called as Z-score. The algorithm of the Z- score is some what similar to the volatility calculation. The only major difference being in case of volatility calculation the order of deviation is found, which is not found in case of Z- score. Z-scores are often used in the case of market analysis. Z-scores are also termed as Z-values and standard values. The word ‘Z’ is used in this because the normal distribution is usually expressed with the word ‘Z’ and there are a whole lot of similarities between the two. The Z-score are calculated using the formula,

Z-score = (x - µ)/σ

Where x is the value obtained from the observed data, µ is the mean average of the normal data, and σ is the standard deviation value.

The Z-score are used to analyze the fluctuation in the market. If the fluctuations are too high then the investor will shift focus to find out the reason for the fluctuations. Z-score are also widely used to determine whether the bank is going to undergo bankruptcy. It is found that Z-score is 72 % accurate in identifying the bankruptcy of a bank with a time gap of two years before the bankruptcy actually taking place.  If a score is greater than 3.0 then it shows that the bank is at a very lower risk of being bankrupt; whereas if a score is less then 1.8 shows that the bank is in high risk of being bankrupt.  The Z-score value for finding out the risk ness will not be same in all the cases. These values must be regularly updated with the industry standard and other banks.

Question

• What are the various uses of Z-score?
• How is Z-score calculated?
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