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# Return Calculations and Returns Distributions

1..Return Calculations

A particular stock had a return last year of 4 percent. However, you look at the stock price and notice that it actually didnĂ˘??t change at all last year. How is this possible?

2.Returns Distributions
What is the probability that the return on small stocks will be less than 100 percent in a single year ( think about it)? What are the implications for the distribution of returns?

#### Solution Preview

1. There are two cases that this is possible. Let us look at them one by one.

case a) The stock price remained constant for the entire year, but stock paid an annual dividend of 4%. In this case, you would have an interest/dividend return of 4%.

case b) This is a bit of a tricky case, so we illustrate it with an example. Suppose Jan. 1st 2010 the stock was trading at \$1, and Jan 1st 2011 the stock is also at \$1. The price did not change in the year, but the price flunctuated. So let us say we recorded the following data.

Date Price Change from last period
Jan 1st. 2010 \$1
Apr 1st. 2010 \$2 +100%
Jun 1st. 2010 \$1 -50%
Sep 1st. 2010 \$2 +100%
Jan 1st. 2011 \$1 -50%

The average return is (100% - 50% + 100% - ...

#### Solution Summary

Return Calculations and Returns Distributions

\$2.19