Consider an asset with a one-day volatility of 1. Assume that the asset is trending with an auto- correlation (serial correlation) of 0.5, i.e. the correlation between todays return and the day after is 0.5. Under this scenario, what is the five-day volatility?

Hint: Let Xi denote the change of the asset value at day i, such that the five-days change in the portfolio value is given by

Y =X1 +X2 +X3 +X4 +X5 Note that Y can be written as a function of vector X, such that

Y =X1 with 1 denoting 5 1 column vector of ones and

X1 X2

X = X3

X 4

X5 The question asks for the standard deviation of Y .

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