If the asset's return distribution is known, then its standard deviation is 1.79%
Investors may find volatility to be both a difficulty and an opportunity. It is a challenge since a significant loss in portfolio value could occur quickly. At the same time, volatility gives knowledgeable investors the chance to profit from brief price fluctuations and buy stocks at a discount to their true worth.
Let,
pi = probability of state i
Ri = return in state i
The weighted average of all returns will yield the expected return:
R = ∑ pi * Ri
R = (0.15 * 0.12) + (0.5 * 0.1) + (0.35 * 0.07)
R = 0.018 + 0.05 + 0.0245
R = 9.25%
Computation of Standard Deviation:
SD = √∑pi * (Ri - R)²
SD = √0.15 * (0.12 - 0.0925)² + 0.5 * (0.1 - 0.0925)² + 0.35 * (0.07 - 0.0925)²
SD = 1.79%
Therefore, the Standard Deviation for the asset's returns = 1.79%
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