Stock Price Normalization: Returns, Rolling Ranges, and Relative Prices

Summary

The discussion collects several ways to transform stock prices for analysis. Suggested measures include log prices, price deviations from a mean, standardized deviations using a standard deviation, log-price deviations from a mean, log returns, percentage price changes, and a position within the rolling high-low range. These transformations express price movement or level on different scales and can be used for comparison or modeling.

A second answer notes that dividing one instrument’s price by a base instrument’s price can represent relative performance when both series begin at the same time; the author reports using this in pairs-strategy backtesting. The exchange does not recommend one normalization as universally best. Instrument choice, time horizon, and the intended use matter, and the question lacks those details, so the suggestions are starting points rather than a validated method.

Key ideas

• Log returns measure the change between consecutive closing prices on a logarithmic scale.
• Percentage changes express price movement relative to the prior close.
• A rolling high-low range can scale a price according to its position within recent extremes.
• Standardized deviations and log-price deviations express prices relative to a mean and, in one case, dispersion.
• Ratios between synchronized instruments can represent relative prices for pairs analysis.

Tags

# How to normalize stock data


# How to normalize stock data












Please advise how can i normalize stock prices.

Recently, I've been using such formulas:

- Log prices = Ln(Close(t))

- Close(t)-Mean

- (Close(t)-Mean)/(StdDev)

- Ln(Close(t))-Mean

Is there any other ways?

## Answer by htrahdis (score 7)

https://quant.stackexchange.com/a/9220

Here are some more :

- Ln(Close) - Ln(Close1) : Close1 is previous close.

- (Close-Close1)*100/Close1

- (Close-LowN)/(HighN-LowN) : LowN and HighN are the low and high within the last N values.

Some more information about the problem would help.

## Answer by NN1983 (score 3)

https://quant.stackexchange.com/a/9193

This answer can certainly be improved with more information: like which instruments, what time scale etc.

If you can assume one instrument to be the 'base' instrument then the ratio of the prices is a good measure with both time series beginning at the same time. This is similar to calculating relative return. I have used this when backtesting a pairs trading system.

More information might help me improve the answer.

Happy to help.

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