Question

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.)

Answer 1

Answer:

SD = 0.0740270 or 7.40270 percent rounded off to 7.403 percent

Explanation:

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