A stock will provide a rate of return of either –20% or +28% .
1. If both possibilities are equally likely, calculate the expected return and standard deviation.
How can you find the expected returns, if you don't know the principal?
Do you want the "standard deviation" or merely the deviation?
Repost with more specific phrasing and data.
By the way, you subject is math.
To calculate the expected return, we need to calculate the weighted average of the possible returns, where the weights represent the probabilities of each outcome.
In this case, the two possibilities are -20% and +28%, and they are equally likely. Therefore, the probability of each outcome is 0.5.
Expected Return = (Probability of -20% return * -20%) + (Probability of +28% return * +28%)
= (0.5 * -20%) + (0.5 * +28%)
= -10% + 14%
= 4%
So, the expected return is 4%.
Next, let's calculate the standard deviation.
Standard deviation measures the dispersion or volatility of returns. To calculate it, we need to find the variance first and then take the square root of the variance.
Step 1: Calculate the variance
Variance = (Probability of -20% return * (-20% - Expected Return)^2) + (Probability of +28% return * (+28% - Expected Return)^2)
= (0.5 * (-20% - 4%)^2) + (0.5 * (+28% - 4%)^2)
= (0.5 * (-24%)^2) + (0.5 * (+24%)^2)
= (0.5 * 576%) + (0.5 * 576%)
= 288% + 288%
= 576%
Step 2: Calculate the square root of the variance to find the standard deviation
Standard Deviation = Square root of Variance
= Square root of 576%
= Square root of 5.76 (since 1% is equivalent to 0.01)
= 2.4
So, the standard deviation is 2.4.
Therefore, the expected return is 4% and the standard deviation is 2.4.