1.8 Calculating Security Returns

With an understanding of efficient markets, we will now discuss how to measure whether prices change in response to information by learning how to calculate security returns. In a general sense, there are two types of returns: dollar returns and percentage returns.

Dollar returns are calculated by taking the difference between the price of the security during the previous time period and the price of the security at the current time period, plus any additional cash flow that came from the security. For instance, bonds pay a coupon (or interest) payment once or twice a year, while stocks will sometimes pay a dividend. Mathematically, dollar returns are calculated in the following way:

$\text{Dollar Returns}=P_t-P_{t-1}+C{F}_t$

In this equation, P_t is the sold price, P_{t − 1} is the bought price, and CF_t is the cash flow (coupons for bonds; dividends for stocks).

Percentage returns are calculated by simply dividing the dollar returns by the price of the security at time t − 1, or the previous time period.

$\text{Percentage Returns}=(\frac{P_t-P_{t-1}}{P_{t-1}}+\frac{C{F}_t}{P_{t-1}})\times 100$

Recall that in the last section, we used two examples to help in our understanding of market efficiency. The first example was a firm announcing unexpectedly high quarterly earnings. Figure 1.2 shows the percentage returns, as calculated above, for a large sample of stocks that announce quarterly earnings. We divide the sample into four groups based on the size of the unexpected earnings. As seen in the figure, firms with the highest unexpected earnings had substantially large positive percentage returns on the announcement day and on the day after the announcement day. Similarly, firms with the lowest unexpected earnings had large negative percentage returns on the announcement day and on the day after.

In our second example, we discussed the possibility that some firm would be named as a defendant in a class-action lawsuit. Using all of the U.S. stocks that fit into this sample, Figure 1.3 shows percentage returns surrounding the lawsuit filing date. As seen in the figure, percentage returns become negative during the four days prior to the filing and remain negative until two days after the filing. These results seem to indicate that the market knew about the information in the lawsuit filing before the lawsuit was even filed. In either case, Figure 1.2 and Figure 1.3 seem to suggest that markets incorporate new information into stock prices.