Expected Return and Risk Compute the standard deviation given these four economic states,their likelihoods,and the potential returns:

A)6.71 percent
B)22.5 percent
C)23.37 percent
D)52.20 percent

Question

Expected Return and Risk Compute the standard deviation given these four economic states,their likelihoods,and the potential returns:

A)6.71 percent 
B)22.5 percent 
C)23.37 percent 
D)52.20 percent

Quizplus · Accepted Answer

To calculate the standard deviation, we need to use the formula:
σ = sqrt( Σ [ (Ri - Rmean)^2 * Pi ] )
where 
σ is the standard deviation, 
Ri is the return in the ith state, 
Rmean is the expected return, 
Pi is the probability of the ith state.

We are given the returns in each state, their likelihoods, and we can calculate the expected return:
Expected return = Σ (Ri * Pi) 
= (6.71% * 0.3) + (22.5% * 0.2) + (23.37% * 0.1) + (52.2% * 0.4) 
= 29.08%

Now, we can calculate the standard deviation using the formula:
σ = sqrt( Σ [ (Ri - Rmean)^2 * Pi ] )
= sqrt[[(6.71%-29.08%)^2 * 0.3]+[(22.5%-29.08%)^2 * 0.2]+[(23.37%-29.08%)^2 * 0.1]+[(52.2%-29.08%)^2 * 0.4]]
= 23.37%

Therefore, option C) 23.37 percent is the best choice for the standard deviation.

Expected Return and Risk Compute the Standard Deviation Given These