# 2 – M1L5 02 Returns V6

Say we’re looking at a time series of prices for a stock. The ups and downs are interesting if we’re vaguely curious about how the company is doing. But more likely than not, we’re looking at the price series because we own some of the stock or we’ve invested money in the stock on someone else’s behalf. What we care about is how our investment has increased or decreased in value. So, how do we measure that increase or decrease? There are actually several metrics we might use to quantify changes in price over time. One is the simple difference in price. P_t minus P_t minus one. This might represent the difference between the price of a stock this month and it’s price one month ago for example. Another is the percentage return or raw return. This is the difference divided by the starting price, P_t minus P_t minus one divided by P_t minus one. Imagine you bought a $1,000 of stock one month ago and sold it this month for$1050. Your return on your initial investment of $50 is five percent of your original investment. If you buy$5,000 of stock this month and sell it for $5,300 next month, you might want to compare the success of this new investment to the previous one. Instead of comparing$300 to \$50, you can calculate the return and compare six percent to five percent to see that as a proportion of your original investment. You did slightly better with the second investment. That’s the advantage of using returns. Prices are normalized and thus similar in scale. This is actually a requirement for many statistical and machine learning techniques.