Why are stock prices Lognormally distributed?

While the returns for stocks usually have a normal distribution, the stock price itself is often log-normally distributed. This is because extreme moves become less likely as the stock’s price approaches zero.

What happens when stock price decreases?

If the stock price falls, the short seller profits by buying the stock at the lower price–closing out the trade. The net difference between the sale and buy prices is settled with the broker. Although short-sellers are profiting from a declining price, they’re not taking your money when you lose on a stock sale.

What probability distribution do stock returns follow?

The basic assumption that stock price returns follow normal distribution itself is questioned time and again. There is sufficient empirical proof of instances where values fail to adhere to the assumed normal distribution. Basing complex models on such assumptions may lead to results with large deviations.

Are stock returns Lognormally distributed?

Real life stock returns are not normally distributed. They aren’t exactly lognormal at any time horizon. However it is true that log returns have more stable distributions than arithmetic returns. So it makes more sense to work with logs.

What does a lognormal distribution tell you?

A lognormal distribution is a continuous probability distribution of a random variable in which logarithm is normally distributed. Thus, if the random variable has a lognormal distribution, then has a normal distribution. Likewise, if has a normal distribution, then has a lognormal distribution.

How do you determine if a distribution is lognormal?

A random variable is lognormally distributed if its logarithm is normally distributed. Skewed distributions with low mean values, large variance, and all-positive values often fit this type of distribution. Values must be positive as log(x) exists only for positive values of x.

What is Lognormally distributed data?

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. A random variable which is log-normally distributed takes only positive real values.

Why can’t normal distribution be used to model stock prices?

Normal distribution cannot be used to model stock prices because it has a negative side, and stock prices cannot fall below zero. Another similar use of the lognormal distribution is with the pricing of options. The Black-Scholes model—used to price options—uses the lognormal distribution as its basis to determine option prices.

What is the lognormal distribution used for in finance?

Another similar use of the lognormal distribution is with the pricing of options . The Black-Scholes model—used to price options—uses the lognormal distribution as its basis to determine option prices. Conversely, normal distribution works better when calculating total portfolio returns.

What is the distribution of stock prices and returns?

For example, a 10-cent price change corresponds to a hefty 5 percent if the stock is only $2. So the stock’s return is normally distributed, while the price movements are better explained with a log-normal distribution. The distribution of stock prices and returns will help you determine the probable gains and losses in your portfolio.

Is the future of the stock price always positive?

The future stock price will always be positive because stock prices cannot fall below $0. The preceding example helped us arrive at what really matters to investors: when to use each method. Lognormal is extremely useful when analyzing stock prices.