Saturday, March 2, 2013

Why x% down is not equal to x% up.

Question:  You place $100 in a stock. It goes up 25% one year and down 25% the next.  How much do you have after two years?

Answer:  After one year you have (100)x(1+0.25)=$125.  After two years you have 125x(1-0.25)=$93.75.  

Note the return after two years does not depend on whether the up-year is the first year or the second year.

93.75=(100)*(1+0.25)*(1-0.25) since multiplication is commutative.

Note that even though the market moves up and down the same direction you are worse off.  The combination of a 25% increase and a 25% decrease in the market leaves your account balance at $93.75 which is below your initial investment of $100.

Bonus question:  You have $12,000 in a stock account.  It falls 50% in the first year.  What second-year return will leave you whole after two years.

Show that you need a 100% return in the second year.  To get back to $12,000 you need to have the stock double.

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