Question

Consider the following probability distribution for stocks a and b: state probability return on stock a return on stock b 1 0.15 8 % 8 % 2 0.20 13 % 7 % 3 0.15 12 % 6 % 4 0.30 14 % 9 % 5 0.20 16 % 11 % the standard deviations of stocks a and b are _____ and _____, respectively.

Answer 1

To find the standard deviations of stocks A and B, calculate the expected return, the squared deviations, weight them by the state probabilities, sum these to get the variance, and take the square root for the standard deviation.

Step-by-step explanation:

To calculate the standard deviations of stocks A and B, we need to follow these steps:

1. Calculate the expected return (mean) for each stock.
2. For each state, compute the squared deviation of the stock's return from its mean.
3. Weight these squared deviations by the probability of each state.
4. Sum the weighted squared deviations to get the variance for each stock.
5. Take the square root of the variance to determine the standard deviation for each stock.

Unfortunately, without the actual return data, I cannot provide the numerical standard deviations for stocks A and B. However, you can apply these steps using the provided return percentages and probabilities to compute the variance and subsequently the standard deviation for each stock.