What is a Z-score and how to use it when trading?

As a new investor, you may have come across a slightly intimidating term called the 'Z-score' while searching for analytical tools used for stock picking. Understanding what this statistical measure means and how it can guide your investment decisions is a great way to enhance your financial literacy.

Read on to understand everything you need to know about the Z-score in simple terms. Learn what it signifies, how to calculate and interpret it, and most importantly, how you can harness this knowledge to make smarter investment choices.

Understanding the basics

The Z-score is a numerical measure that tells you how far a company's financial ratios are from the average ratios of similar companies in that sector. In simple words, it shows if the company is an outlier from its peers, in terms of financial performance.

For example, you can calculate a company's P/E ratio (share price/earnings per share) Z-score to know if its P/E is unusually high or low compared to industry standards. This may indicate the share is overvalued or undervalued relative to peers.

So, if the Z-score is low, it signals the ratio is below average, which could mean undervaluation. If the Z-score is high, it indicates an above-average ratio and potential overvaluation.

Now let's move on to understanding how this calculation is actually done. No need to worry as there is no rocket science involved!

Calculating the Z-score

The Z-score formula seems complex at first glance but is actually quite straightforward:

Z-score = (x - μ) / σ

Where

x is the company's financial ratio being measured e.g. P/E ratio

μ (mu) is the industry average for that financial ratio

σ (sigma) is the standard deviation of the ratios in the industry

Let's say there are 20 similar companies including XYZ Ltd in the textile industry.

XYZ has a current P/E ratio of 18. The average industry P/E ratio is 12. The standard deviation of P/E ratios is 4.

Plugging this into the formula:

Z-score = (XYZ's P/E - Average Industry P/E) / Standard Deviation = (18 - 12) / 4 = 1.5

So XYZ's P/E ratio Z-score is 1.5 - this means it is 1.5 standard deviations higher than the sector average.

Now comes interpreting what the Z-score implies.

Making sense of the Z-score

The Z-score in itself has no meaning unless you know how to decipher its implications. Typically,

• A Z-score between -2 and +2 indicates the ratio is close to industry norm, i.e. fairly valued.
  
• A Z-score less than -2 suggests the ratio is significantly below average. This may signal undervaluation.
  
• A Z-score greater than +2 implies the ratio is well above average. This could mean overvaluation.
  

In the above example, XYZ Ltd.’s Z-score of 1.5 indicates its P/E is slightly above industry average, hinting at probable overvaluation.

But you should not base decisions on just one ratio's Z-score. Check P/B, P/S ratios too. If most Z-scores signal over/undervaluation, then it is a stronger signal.

Using Z-scores for smarter investing

Now that you understand Z-scores, let's look at how you can actually use them to make better investing decisions.

1. Screen for value picks

One of the key applications of Z-scores is to screen for potential undervalued stocks meriting further research. Look for companies with low Z-scores, say below -1.5 or -2, for metrics like P/E, P/B, and P/S ratios. This indicates their ratios are well below sector averages, signaling possible underpricing.

For instance, a stock with P/E Z-score of -2.1 and P/B score of -1.8 could be worth evaluating. Combine with other filters like high ROE to create a shortlist of value prospects worth analysing further through detailed financial statements study, management evaluation etc.

2. Optimise your sell decisions

On the flip side, high Z-scores can assist you in identifying overvalued stocks nearing their peak. Stocks with P/E, P/S or P/B Z-scores above +2 or +2.5 could be precariously overpriced vis-à-vis their peers.

3. Backtest investing strategies

You can use historical Z-scores to backtest customised investing approaches you plan to deploy. For instance, you could simulate a strategy of going long on stocks with P/E Z-score below -1.5 and booking profits once it reaches +1.

Analysing historical returns from such a Z-score strategy can help refine thresholds and holding periods before implementing it with real money.

4. Build quantitative screens

Z-scores can be included as one of the parameters in automated quantitative screens along with metrics like ROE, EPS growth etc. to filter undervalued or overvalued stocks.

Based on backtesting and correlation analysis, assign appropriate Z-score thresholds and weights within the screening models to shortlist high-probability prospects.

5. Customise for sector nuances

Rather than using overall market Z-score averages, use sector-relative Z-scores to account for industry-specific peculiarities. Doing so improves the relevance of comparisons for stocks within cyclical sectors.

Exercising caution with Z-scores

While very useful, the Z-score has some limitations that you should keep in mind:

• It relies solely on financial ratios without qualitative factors.
• Data inputs may be skewed for cyclical sectors.
• Currency fluctuations can affect income statement data for global firms.
• Changes in accounting policies may reduce cross-firm comparability.

So, use the Z-score as just one of the tools in your investor toolkit, not the only tool. Combine it smartly with other analysis techniques for the best results.

Conclusion

The Z-score is a useful statistical tool for analysing stocks but should not be used in isolation. Qualitative factors also need to be considered before making investment decisions. Use the Z-score as an initial screening tool, in conjunction with other metrics like earnings quality and competitive position. With prudent use alongside fundamental analysis, the Z-score can aid investors in shortlisting prospects and optimising entry and exit points. Ultimately, it serves as one important input, rather than the sole determinant, for intelligent stock picking.