You are considering investing in a project with the following possible outcomes: Probability of Investment States Occurrence Returns State 1: Economic boom 20% 16% State 2: Economic growth 40% 12% State 3: Economic decline 20% 5% State 4: Depression 20% -5% Calculate the standard deviation of returns for this investment. Round to the nearset hundredth percent. Answer in the percent format. Do not include % sign in your answer (i.e. If your answer is 4.33%, type 4.33 without a % sign at the end.)

To calculate the standard deviation of the investment, we must first calculate the expected or mean return of the investment. The expected or mean return can be calculated as follows,

r = pA * rA + pB * rB + ... + pN * rN

Where,

pA, pB, ... represents the probability of state occurrence
rA, rB, ... represents return A, return B and so on under each state

r = 0.2 * 0.16 + 0.4 * 0.12 + 0.2 * 0.05 + 0.2 * -0.05

r = 0.08 or 8%

The formula to calculate the standard deviation of a stock/investment is as follows,

SD = √pA * (rA - r)² + pB * (rB - r)² + ... + pN * (rN - r)²

SD = √0.2 * (0.16 - 0.08)² + 0.4 * (0.12 - 0.08)² + 0.2 * (0.05 - 0.08)² + 0.2 * (-0.05 - 0.08)²

SD = 0.0740270 or 7.40270 percent rounded off to 7.403 percent