I need some help with this statistics/finance problem:

Imagine you own an asset over four periods and the value of it is affected by market price movements. You know the standard deviation and the position that will be held during each period. To complicate the problem, these are different in each period. All of this information is known at inception.

(Standard deviation is the standard price change for one period, not the entire four)

How do you calculate the standard deviation and the Earnings@Risk across the sum of all four periods?

If the StDev and position never change I believe you can do StDev*sqrt(4) to get the StDev for 4 periods. Multiply this by some Zstat (i.e. 1.96) and by the size of the position to get an Earnings@Risk (95%) in Euros.

However, I do not know how to correct for the fact that StDev and position changes in each period. I have attached an excel with a clear example, and two guesses in G12 and J12.

Any ideas on how to do this properly? Thank you