Finding Stock Volatility: Calculate the Correct Answer

Calculating Stock Volatility

A single share of stock in a company with a current price of $120 is analyzed for its volatility based on four possibilities for the stock's return over the course of the next year. The table displays the possibilities and their associated probabilities.

Formula

The volatility of a stock is measured through standard deviation, which indicates the extent of variability in the possible returns from the mean return. The formula to calculate standard deviation is as follows:

σ = √( Σ (xi - μ)² / n)

where:

σ: Standard Deviation

μ: Mean Return

xi: Individual Values

n: Number of Values

Calculations

To determine the stock's volatility, we first compute the mean return by multiplying each possible return by its probability and summing the results:

Mean return = (1-18%)(0.19) + (-10%)(0.41) + (16%)(0.23) + (27%)(0.17) = -1.58%

Next, the variance of the possible returns is calculated by determining the squared differences between each return and the mean return, multiplying by the probability, and summing the values:

Variance = (1-18% - (-1.58%))^2(0.19) + (-10% - (-1.58%))^2(0.41) + (16% - (-1.58%))^2(0.23) + (27% - (-1.58%))^2(0.17) = 0.0238

By taking the square root of the variance, we arrive at the stock's volatility:

Standard deviation = sqrt(0.0238) = 0.1524 = 15.24%

Therefore, the stock's volatility is calculated to be 15.24%, indicating the level of risk and variability associated with the potential returns. For further insights into stock volatility, refer to additional resources.