The Mathematics of Overcoming Negative Returns

My last post got me to thinking about the mathematics involved in overcoming negative returns. In that post, I mentioned that 15 of the ETFs listed in the Wall Street Journal are down over 10% so far in 2008 (and that’s after just 3 days of trading!).

If a stock goes down 10%, it takes a return greater than 10% just to get back to the original price. To illustrate that point, take a look at this graphic:

So, if an investment goes down 10%, it takes a return of 11.11% just to get back to the original amount.

Now let’s say at the beginning of the year you were looking for a 10% return on your investment over the next year. But, on January 4th, you already found yourself down 10% on the year. What kind of return would you need to get so that you still received a 10% rate of return over the year? The answer is a whopping 22.22%!

Pretty amazing isn’t it? It will be interesting to see where some of those ETFs finish for the year.

6 thoughts on “The Mathematics of Overcoming Negative Returns”

1. Ever noticed that sometimes on CNBC when Kernen is talking about stocks on the move he will say, this stock has fallen 90%, but its risen 50% back from its low so things aren’t so terrible? I hate when these kind of comments are made because when you see a drop like that, its going to take a lot more than that to make much of a difference to that investor that lost 90%.

2. Dave says:

There’s a subtle difference between JLP’s and Aaron’s language. In JLP’s case, after a \$10 stock falls 90% to \$1, a 50% rise would take it to \$1.50. In Aaron’s case, it probably means that the stock fell, say, from \$10 to \$1, and now has risen halfway back to \$10, i.e., to \$5.50. That’s certainly a huge loss, but it definitely is not as terrible as the original loss to \$1.

3. Your post is very interesting.
I just don’t understand in spite of best brains why mutual funds and other institutions engaged in share investing miserably fail towards making profits.Is it a failure to understand the maths of stock investment or greed to make money?