Question

the rate of return on the common stock of kang distribution is expected to be 13.5 percent in a boom economy, 8 percent in a normal economy, and only 2.5 percent in a recessionary economy. the probabilities of these economic states are 11 percent for a boom and 26 percent for a recession. what is the variance of the returns on this common stock?

Answer 1

To find the variance of the returns on Kang Distribution's common stock, calculate the expected return, the squared deviations for each economic state, and sum the products of these deviations with their respective probabilities. Since the probability of a normal economy is not provided, assume it to fill the remaining percentage to 100%.

Step-by-step explanation:

The student is asking how to calculate the variance of the returns on Kang Distribution's common stock, given the expected rates of return in different economic conditions and the probabilities of those conditions occurring. To find the variance, we would use the formula for the expected value of the squared deviations from the expected return, weighting each squared deviation by the probability of its associated economic state.

First, calculate the expected return (mean) by multiplying each possible return by its probability and summing these products. Then, for each economic state, calculate the squared deviation from this mean (i.e., subtract the mean from the return for that state and square the result). Multiply each squared deviation by its probability, and sum these to find the variance.

However, since we don't have the probability of a normal economy given, we cannot complete the calculation. We assume that the probabilities must add up to 100%, so the missing probability can be calculated as 100% - 11% (boom) - 26% (recession) = 63% (normal).

Using this information, we can carry out the calculation for the variance:

1. Calculate the expected return (E(R)): E(R) = (0.11 × 13.5%) + (0.63 × 8%) + (0.26 × 2.5%).
2. Calculate the squared deviations and multiply by their probabilities: (13.5% - E(R))² × 0.11, (8% - E(R))² × 0.63, and (2.5% - E(R))² × 0.26.
3. Add these values together to find the variance.

Answer 2

To calculate the variance of the returns, first find the expected return by weighting each return by its probability, then compute the squared deviations of each possible return from the expected return, weigh these by their probabilities, and sum them up.

Step-by-step explanation:

To calculate the variance of the returns on Kang Distribution's common stock, we first need to find the expected return. This involves multiplying each possible rate of return by its probability and summing these products. The probabilities of the economic scenarios not provided must sum to 100%, so the probability of a normal economy is 100% - 11% - 26% = 63%. Thus, the expected return (ER) is calculated as follows:

ER = (0.11 × 13.5%) + (0.63 × 8%) + (0.26 × 2.5%)

Next, we compute the squared deviations of each return from the expected return, multiply each by its respective probability, and sum these values to obtain the variance.

Variance = (0.11 × (13.5% - ER)^2) + (0.63 × (8% - ER)^2) + (0.26 × (2.5% - ER)^2)

In terms of investment risk, variance is a measure used to quantify the dispersion of possible returns around the expected return, which reflects the investment's volatility. A higher variance indicates a wider range of possible returns and thus greater risk.