Question

Taggart Inc.'s stock has a 50% chance of producing a 25% return, a 30% chance of producing a 10% return, and a 20% chance of producing a -28% return. What is the firm's expected rate of return? What is the standard deviation and coefficient of variation?

Answer 1

To find the expected rate of return for Taggart Inc.'s stock, multiply each possible return by its corresponding probability and sum them up. The standard deviation can be found by calculating the variance and taking the square root. The coefficient of variation can be calculated by dividing the standard deviation by the expected rate of return and multiplying by 100.

Step-by-step explanation:

To find the expected rate of return for Taggart Inc.'s stock, we need to multiply each possible return by its corresponding probability and sum them up. The expected rate of return is found using the formula:

Expected Return = (Probability 1 x Return 1) + (Probability 2 x Return 2) + (Probability 3 x Return 3)

So for this problem, the expected rate of return would be 0.5 x 0.25 + 0.3 x 0.10 + 0.2 x (-0.28).

To find the standard deviation, we need to calculate the variance first. Variance is found using the formula:

Variance = (Probability 1 x (Return 1 - Expected Return)^2) + (Probability 2 x (Return 2 - Expected Return)^2) + (Probability 3 x (Return 3 - Expected Return)^2)

Once we have the variance, we can find the standard deviation by taking the square root of the variance.

The coefficient of variation can be calculated by dividing the standard deviation by the expected rate of return and multiplying by 100 to obtain a percentage.