What Is a Log-Normal Distribution?
Let me explain to you what a log-normal distribution is: it's a set of data that follows a normal distribution once you apply logarithms to its values. You might be more familiar with the bell curve of a normal distribution, but the log-normal one is crucial in financial analyses, particularly for modeling stock prices and returns. I'll show you how to transition between normal and log-normal distributions and use them effectively, including in Excel, to gain deeper insights into financial data patterns.
Key Takeaways
- A log-normal distribution comes from logarithmic values of a normal distribution and can be converted back using logarithmic calculations.
- Unlike a normal distribution, which can include negative values, a log-normal distribution only has positive values.
- Log-normal distributions appear frequently in finance, especially when analyzing stock prices and expected compound returns.
- In Excel, you can use the LOGNORM.DIST function to model log-normal distributions by inputting the value, mean, and standard deviation of the logarithmic values.
Differences and Connections Between Normal and Log-Normal Distributions
You know a normal distribution as a symmetrical probability distribution forming a bell curve, where 68% of results fall within one standard deviation and 95% within two.
Most people recognize normal distributions, but log-normal ones are less familiar. When you apply logarithms to a normal distribution, it turns into a log-normal one, because log-normal distributions stem from normally distributed variables.
I often see log-normal distributions used with normal ones. They typically involve the natural log with base e=2.718, though a different base alters the distribution's shape.
A log-normal distribution plots the log of random variables from a normal curve. Here, the log is the exponent required to raise a base number to yield a normally distributed random variable (x).
Practical Applications of Log-Normal Distribution in Financial Analysis
Normal distributions can include negative values, but log-normal distributions address this by only covering positive values.
In finance, you use log-normal distributions to analyze stock prices. Potential stock returns follow a normal distribution, whereas stock prices themselves fit a log-normal distribution, which helps identify expected compound returns over time.
Keep in mind that log-normal distributions are positively skewed with long right tails, resulting from low mean values and high variances in the random variables.
Lognormal Distribution in Excel
You can handle lognormal distributions in Excel through the statistical functions, specifically LOGNORM.DIST.
Excel defines it this way: LOGNORM.DIST (x,mean,standard_dev,cumulative) returns the lognormal distribution of x, where ln(x) is normally distributed with parameters mean and standard_dev.
Parameters for LOGNORM.DIST in Excel
- x = value at which to evaluate the function
- Mean = the mean of ln(x)
- Standard Deviation = the standard deviation of ln(x), which must be positive
The Bottom Line
The log-normal distribution is vital in finance, especially for analyzing stock prices and potential returns. Unlike a normal distribution, it handles only positive variables, providing a more accurate view of outcomes like stock prices. By understanding how to apply log-normal distributions conceptually and in tools like Excel, you equip yourself with better insights into potential financial outcomes, such as compound returns over time.
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