There is a 20% chance we will get a 16% return, a 30% chance of getting a 12% return, a 40% chance of getting a 8% return, and a 10% chance of getting an 4% return. The standard deviation for the above investment would be:

SD = 0.03666 or 3.666%

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,

r = 0.2 * 0.16  +  0.3 * 0.12  +  0.4 * 0.08  +  0.1 * 0.04

r = 0.104 or 10.4%

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 - 0.104)²  +  0.3 * (0.12 - 0.104)²  +  0.4 * (0.08 - 0.104)²  +  0.1 * (0.04 - 0.104)²

SD = 0.03666 or 3.666%

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