Suppose you invest $100 in a stock that goes down 50% one day and goes up 50% the next day, how much do you have after two days?
If your intuition says A, you are very human and subject to the common mistake that many human beings make.
“Really? But I am rational and good at math.” You pull out a piece of paper, do the math, and find out that B is the right answer. Why? Because at the end of the first day, you have only $50 left. So your 50% return on the second day has a smaller base.
“What if the stock goes up 50% on the first day, and goes down 50% on the second day? Would I be better off?” A very good question indeed. A quick math tells you that you will end up in the same spot. In fact, it can be proven mathematically that the order doesn’t matter. Does it seem unfair? Maybe. But that is how investment works.
If your investment of $100 loses 50% on the first day, how much does it need to go up on the second day for you to break even?
Yes, you got it. The right answer is 100%. That is why it is so important to control your downside risk. You really can’t afford to “stick with it” during the crash.
You invest $100 in a stock that goes up 10% one day, and goes down 10% the next day, and repeat this pattern for a year. How much do you have in a year? Pick the closest number.
You know that after two days, your $100 becomes $99. A year has 252 trading days, so you will have to repeat the two-day cycle 126 times: $100 * (0.99^126) = $28.19
Now you’ve got the correct answer: D.
By J. Helen Yang, CFA, January 23, 2018