Daily Log Return Calculator (Excel LN Method)

Calculate the continuously compounded daily return of an asset using the same LN() function method found in Excel. This tool is essential for accurate financial modeling and time-series analysis.

Return Sensitivity to Ending Price Changes

Ending Price	Price Ratio	Log Return (%)

What is calculating daily returns in Excel using LN?

Calculating daily returns in Excel using the LN function refers to the method of determining the continuously compounded return, also known as the logarithmic return (log return). Unlike a simple percentage change, a log return represents the rate of growth if compounding were happening infinitely many times over the period. It’s a cornerstone of modern financial analysis, risk management, and quantitative modeling because of its desirable statistical properties.

This method is preferred by analysts for its time-additivity, which means you can sum daily log returns to get the total log return over a longer period (like a week or month). The Excel formula is elegantly simple: =LN(Ending_Price/Starting_Price). Our calculator automates this exact process. For a deeper dive into time-series analysis, understanding the volatility calculation is a natural next step.

The Daily Log Return Formula and Explanation

The formula for calculating the daily logarithmic return is precise and powerful. It captures the true, continuously compounded rate of change between two price points.

Daily Return = LN(P₁ / P₀)

Here, the LN function represents the natural logarithm, which is the inverse of Euler’s number (e). This mathematical structure is what allows log returns to be summed over time.

Variables Table

Variable	Meaning	Unit	Typical Range
P₁	The ending price of the asset.	Currency (e.g., USD, EUR)	Greater than 0
P₀	The starting price of the asset.	Currency (e.g., USD, EUR)	Greater than 0
LN	The natural logarithm function.	Unitless	N/A
Daily Return	The continuously compounded return.	Percentage (%)	-∞ to +∞ (typically -10% to +10%)

Practical Examples

Let’s walk through two scenarios to see how calculating daily returns in Excel using LN works in practice.

Example 1: A Positive Return

An investor is tracking a stock that closed at $150 yesterday and closes at $152 today.

• Inputs: Starting Price (P₀) = $150, Ending Price (P₁) = $152
• Calculation: LN(152 / 150) = LN(1.01333) ≈ 0.01324
• Result: The daily log return is approximately +1.324%. This represents the continuously compounded growth for the day.

Example 2: A Negative Return

Another stock in the portfolio had a less fortunate day, falling from $50 to $48.50.

• Inputs: Starting Price (P₀) = $50, Ending Price (P₁) = $48.50
• Calculation: LN(48.50 / 50) = LN(0.97) ≈ -0.03046
• Result: The daily log return is approximately -3.046%. Knowing the difference between simple vs log returns is crucial for interpreting this result correctly.

How to Use This Daily Log Return Calculator

Our tool simplifies the process of calculating daily returns, making it fast and error-free.

1. Enter Starting Price: In the first field, input the price of the asset at the start of your period (e.g., yesterday’s closing price).
2. Enter Ending Price: In the second field, input the price at the end of the period (e.g., today’s closing price). The currency must be the same as the starting price.
3. Analyze the Results: The calculator instantly provides the daily log return as a percentage. It also shows intermediate values like the price ratio and the raw natural log result for advanced analysis.
4. Review Visuals: The sensitivity table and chart automatically update to show how the return would change with different ending prices, offering a quick risk assessment.

Key Factors That Affect Log Returns

The calculated log return is directly influenced by several factors:

• Magnitude of Price Change: The larger the difference between the starting and ending price, the larger the absolute log return.
• Direction of Price Change: An increase in price yields a positive log return, while a decrease yields a negative one.
• Starting Price Level: A $1 price change has a much larger percentage impact on a $10 stock than on a $1000 stock. Log returns inherently account for this scaling.
• Time Period: While this calculator is for a single period, the interpretation depends on the period’s length (daily, weekly, etc.). The time-additivity of log returns makes them perfect for multi-period analysis.
• Volatility: High-volatility assets will naturally exhibit larger daily log returns (both positive and negative) compared to stable, low-volatility assets.
• Dividends & Splits: For a truly accurate return, you should use adjusted closing prices that account for dividends and stock splits. This calculator processes the prices you provide as-is.

Frequently Asked Questions (FAQ)

1. Why use the LN function instead of a simple percentage change?

The primary reason is time-additivity. The sum of daily log returns equals the total log return for the entire period. This property does not hold for simple percentage returns, making log returns far superior for statistical modeling and time series analysis.

2. What’s the main difference between simple returns and log returns?

A simple return is `(P₁/P₀) – 1`, while a log return is `LN(P₁/P₀)`. For small price changes, their values are very similar. However, as changes become larger, they diverge. Log returns are always slightly smaller than their corresponding positive simple returns. This is key to understanding the logarithmic return formula.

3. Can the log return be negative?

Yes. If the ending price is lower than the starting price, the ratio (P₁/P₀) will be less than 1, and the natural logarithm of a number less than 1 is always negative.

4. How do I calculate a weekly return from daily log returns?

Thanks to time-additivity, you simply sum the five daily log returns for the week. To convert the total weekly log return back to a simple return for reporting, you would use the formula `EXP(total_log_return) – 1`.

5. Does the currency (USD, EUR, etc.) matter?

No, as long as you are consistent. The calculation is based on the ratio of the two prices, so the currency unit cancels out. You must use the same currency for both the starting and ending price.

6. What is the benefit of a “continuously compounded” return?

It represents a theoretical limit where returns are compounded at every instant. This makes it a more accurate and standardized measure for comparing asset performance, removing ambiguity about the compounding frequency (daily, monthly, etc.).

7. Why are log returns preferred for financial modeling?

Besides time-additivity, the distribution of log returns is often closer to a normal distribution (bell curve) than simple returns. This makes them much more suitable for many statistical models used in finance, such as those for an Excel for finance guide.

8. What does a 0% log return mean?

A 0% log return means the starting price and ending price were identical. The ratio is 1, and LN(1) is 0.