Two years ago you purchased a share of stock for $24.375. The first year that you owned the stock you received an 80% return; over the second year, however, the stock fell by 51%. What was your average rate of return and your holding period return?

24.375 x 1.8 = 43.875
next year it was
43.875 x .49 = 21.49875

profit for 1st year = 19.5
less loss for 2nd year =2.8775
net profit = 16.6225

total return for the period = 16.6225/24.375=68.19%
Average = 68.19/2 = 34.1%

Nyet, comrade Haider. You are correct that at the end of the two-year holding period the investment was worth 21.49875. But given that the original investment was 24.375, the overall holding period return was clearly negative (i.e. a net loss).

Oksana, when you're asked for an "average" return, it usually refers to the geometric mean of the holding period return, rather than the simple arithmetic mean. The arithmetic mean can be misleading. To see why, consider an initial investment of $100 which gains 20% in the first year, then loses 20% in the second year.

Run the numbers and you'll see that you've ended up with $96; clearly a loss overall. Yet the simple average of +20% and -20% is 0%--suggesting that you had a zero overall return.

The geometric mean, on the other hand, tells the accurate story:

\sqrt{\frac{96}{100}} \ - \ 1 \ = \ -0.0202041. Do the math and you'll see that an investment of $100 that loses 2.02041% per year, for two consecutive years, ends up at $96.

So compute the geometric mean of your holding period return to get an accurate "average" return for your question.