Calculate the return and standard deviation for the following stock, in an economy with five possible states. If a Boom (Probability=25%) economy occurs, then the expected return is 30%. If a Good (Probability=25%) economy occurs, then the expected return is 15%. If a Normal (Probability=20%) economy occurs, then the expected return is 8%. If a Bad (Probability=20%) economy occurs, then the expected return is 5%. If a Recession (Probability=10%) economy occurs, then the expected return is -15%. Show your work for partial credit.

Question

Calculate the return and standard deviation for the following stock, in an economy with five possible states. If a Boom (Probability=25%) economy occurs, then the expected return is 30%. If a Good (Probability=25%) economy occurs, then the expected return is 15%. If a Normal (Probability=20%) economy occurs, then the expected return is 8%. If a Bad (Probability=20%) economy occurs, then the expected return is 5%. If a Recession (Probability=10%) economy occurs, then the expected return is -15%. Show your work for partial credit.

Answer 1

Calculate the return and standard deviation for the following stock, in an economy with five possible states. If a Boom (Probability=25%) economy occurs, then the expected return is 30%. If a Good (Probability=25%) economy occurs, then the expected return is 15%. If a Normal (Probability=20%) economy occurs, then the expected return is 8%. If a Bad (Probability=20%) economy occurs, then the expected return is 5%. If a Recession (Probability=10%) economy occurs, then the expected return is -15%. Show your work for partial credit.

Answer 2

To calculate the return and standard deviation for the given stock in an economy with five possible states, we will use the formula for expected return and standard deviation.

1. Calculate the expected return:
Expected Return = (Probability of State 1 * Return of State 1) + (Probability of State 2 * Return of State 2) + ... + (Probability of State 5 * Return of State 5)

Expected Return = (0.25 * 30%) + (0.25 * 15%) + (0.20 * 8%) + (0.20 * 5%) + (0.10 * (-15%))
Expected Return = 0.075 + 0.0375 + 0.016 + 0.01 + (-0.015)
Expected Return = 0.1235 or 12.35%

Therefore, the expected return for the stock is 12.35%.

2. Calculate the standard deviation:
First, we need to calculate the variance for each state.

Variance for State 1 = Probability of State 1 * (Return of State 1 - Expected Return)^2
Variance for State 1 = 0.25 * (30% - 12.35%)^2

Variance for State 2 = Probability of State 2 * (Return of State 2 - Expected Return)^2
Variance for State 2 = 0.25 * (15% - 12.35%)^2

Similarly, we calculate the variance for States 3, 4, and 5.

Variance for State 3 = 0.20 * (8% - 12.35%)^2
Variance for State 4 = 0.20 * (5% - 12.35%)^2
Variance for State 5 = 0.10 * (-15% - 12.35%)^2

Next, we sum up the variances:

Variance = Variance for State 1 + Variance for State 2 + Variance for State 3 + Variance for State 4 + Variance for State 5

Finally, we take the square root of the variance to get the standard deviation:

Standard Deviation = √(Variance)

By following these calculations, you will be able to find the return and standard deviation for the given stock in an economy with five possible states.

234

1.35

To calculate the return and standard deviation for the given stock in an economy with five possible states, we will use the formula for expected return and standard deviation.