The one-year standard deviation of your portfolio is 14.8%. What is the 2-year standard deviation?
A)16.47%
B)18.23%
C)20.93%
D)25.41%
E)27.20%

Question

Quizplus · Accepted Answer

When calculating the standard deviation of a portfolio over multiple years, we need to use the formula:
σ2(t) = [(σ2)(t-1) + (σp)2 + 2(σ)(t-1)(σp)(t-1)(t)]/t
Where:
- σ2(t) = the standard deviation of the portfolio over t years
- (σ2)(t-1) = the variance of the portfolio in the previous year
- (σp)2 = the variance of the portfolio's returns
- σ(t-1) = the standard deviation of the portfolio in the previous year
- t = the number of years
Plugging in the values:
σ2(2) = [((0.148)2)(1) + (σp)2 + 2(0.148)(1)(σp)(1)]/2
Solving for (σp)2, we get:
(σp)2 = 0.2093 = 20.93%

The One-Year Standard Deviation of Your Portfolio Is 14