- #1

Peter G.

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## Homework Statement

Find the VaR for an investment of $500,000 at 1% given that the investment is expected to grow 10% every year with standard deviation of 35% and that the investment is held for two years.

## Homework Equations

E(X + Y) = E(X) + E(Y)

E(X*Y) = E(X) * E(Y) (for independent random variables)

var (X + Y) = var (X) + var (Y) (for independent random variables)

## The Attempt at a Solution

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So, at first, I thought that the expected return if the investment were held for two years would be:

E(X+[(1+X)*Y])

Although I can compute that, if that were the case, then the variance for the two year investment would be given by:

var (X + [(1+X)*Y]) = var (X) + var (Y) + var (Y*X)

But that cannot be the case I do not know how to calculate that last term.

Upon doing some research, it appears that I should be computing E(X + Y) and var (X + Y) instead. However, that does not make much sense to me. For example: if I were to invest 100 dollars on a stock that yielded a return of 10% with SD = 0% every year, then my return on the 100 dollars after two years would be 21%, not 20%, right?

Can anyone shed some light on this for me please?

Thank you in advance!