Question

The returns on the common stock of New Image Products are quite cyclical. In a boom economy, the stock is expected to return 18 percent in comparison to 9 percent in a normal economy and a negative 11 percent in a recessionary period. The probability of a recession is 15 percent while the probability of a boom is 25 percent. What is the standard deviation of the returns on this stock?

Answer 1

The standard deviation of the returns on the common stock of New Image Products is approximately 0.1134.

Step-by-step explanation:

To calculate the standard deviation of the returns on the common stock of New Image Products, we will use the formula:

Standard deviation = Square root of [(Return1 - Average return)^2 * Probability1 + (Return2 - Average return)^2 * Probability2 + ...]

Using the given returns and probabilities, the calculations would be:

(0.18 - 0.09)^2 * 0.25 + (0.09 - 0.09)^2 * 0.6 + (-0.11 - 0.09)^2 * 0.15 = 0.012825

Finally, take the square root of the result:

Square root of 0.012825 = 0.1134

Therefore, the standard deviation of the returns on this stock is approximately 0.1134.