Stock Price Adjustment

A guide on how to adjust stock prices using forward and backward adjust factors for accurate quantitative analysis.

TL; DR

• Backward adjust factor is used for real-time applications and ensures the most recent data is unaltered.

• Forward adjust factor is preferred for historical analysis as it reflects the actual historical trading prices.

• The relationship between forward and backward adjust factors is inverse.

• Information services use backward adjusted prices, while quant backtesting uses forward adjusted prices.

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Adjusting Stock Prices for Corporate Actions

When conducting quantitative research on stock prices, it's crucial to account for corporate actions such as dividends, stock splits, and reverse splits. These events can distort the true performance of a stock if not adjusted for. There are two primary methods for adjusting stock prices: backward and forward adjustment.

Backward Adjusted Prices

Backward adjusting is a method where historical prices are adjusted from a specific point in time moving backward. This method ensures that the most recent data is unaltered, which is particularly useful for real-time applications and maintaining the integrity of the most current data.

How to Apply Backward Adjust Factor

To backward adjust prices, we use a factor that is applied to all historical prices before the corporate action. The formula for the backward adjust factor is:

$$\text{Backward Adjust Factor} = \frac{\text{Previous Close Price}}{\text{Adjusted Close Price}}$$

This factor is then multiplied with historical prices to obtain the adjusted prices.

Example:

Let's say a stock undergoes a 2-for-1 split. The closing price before the split is $100. The backward adjust factor would be:

$$\text{Backward Adjust Factor} = \frac{100}{50} = 2$$

All historical prices before the split would be divided by 2 to reflect the split.

Here is a time-series table illustrating the backward adjustment:

Date	Original Close Price	Backward Adjust Factor	Adjusted Close Price
Pre-Split	$100	2	$50
Post-Split	$50	-	$50

More on Backward Adjusting

When backward adjusting, all historical data points are recalculated as if the investor held the stock through the corporate action. This method is less intuitive for historical analysis because it does not reflect the actual prices at which securities traded in the past.

Forward Adjusted Prices

Forward adjusting is a method where historical prices are adjusted from a specific point in time moving forward. This is the preferred method for historical analysis because it reflects the actual prices at which securities traded in the past and maintains the historical price series as accurate and unaltered.

How to Apply Forward Adjust Factor

To forward adjust prices, we use a factor that is applied to all historical prices after the corporate action. The formula for the forward adjust factor is:

$$\text{Forward Adjust Factor} = \frac{\text{Adjusted Close Price}}{\text{Previous Close Price}}$$

This factor is then multiplied with historical prices to obtain the adjusted prices.

Example:

Using the same 2-for-1 split example, the forward adjust factor would be:

$$\text{Forward Adjust Factor} = \frac{50}{100} = 0.5$$

All historical prices after the split would be multiplied by 0.5 to reflect the split.

Here is a time-series table illustrating the forward adjustment:

Date	Original Close Price	Forward Adjust Factor	Adjusted Close Price
Pre-Split	$100	-	$100
Post-Split	$50	0.5	$100

More on Forward Adjusting

Forward adjusting ensures that the price series reflects actual transaction prices, which is essential for accurately presenting historical data. However, it can make recent data appear more volatile if a significant corporate action has occurred.

Relationship Between Forward and Backward Adjust Factors

The relationship between forward and backward adjust factors is essentially an inverse one. If you have one, you can easily calculate the other using the following formula:

$$\text{Forward Adjust Factor} = \frac{1}{\text{Backward Adjust Factor}}$$

And vice versa:

$$\text{Backward Adjust Factor} = \frac{1}{\text{Forward Adjust Factor}}$$

Preferred Methodologies in Information Services and Quant Backtesting

• Information Services: Typically use backward adjusted prices because they prioritize the most current price data, which is crucial for real-time decision-making and analysis.

• Quant Backtesting: Generally prefer forward adjusted prices because they aim to preserve the historical price series without alteration, which is vital for accurate backtesting and analysis of historical performance.

Understanding and applying these adjustments is essential for accurate quantitative analysis and modeling. By adjusting historical prices, researchers and analysts can eliminate distortions caused by corporate actions and maintain the integrity of their data.