Total returns (tutorial #2)

In the previous tutorial, we presented the general formula for calculating the (net) return over a single period t:

R_t = ( P_t - P_t-1 ) / P_t-1

This formula has to be modified slightly if the stock makes a dividend payment during your holding period. To explain this modification, let us give you another example. Imagine buying 1 share of Microsoft's common stock on October 31, 2011 at the closing price of $26.63 with the intention of holding it for a month. Then, you could sell your share on November 30, 2011 at a price of $25.58. Using the equation above this would imply a return of:

($25.58 - $26.63) / $26.63 = -3.94%. 

Due to the decrease in stock price you would realize a loss. The calculation is incomplete, however. Because, Microsoft paid a dividend of $0.20 on November 15. We have to take this payment into account, since it is part of the stock's return. Luckily, the adjustment is quite straightforward. We just need to add the dividend to the numerator. Then, the correct return is:

($0.20 + $25.58 - $26.63) / $26.63 = -3.19%

which is still negative, but now it is a smaller loss. With dividend payments, the general formula becomes:

R_t = ( D_t + P_t - P_t-1 ) / P_t-1

where D_t is the total dividend payments made during period t. We can rewrite this equation as follows:

R_t = ( D_t / P_t-1 ) + ( P_t - P_t-1 ) / P_t-1

In this form, the equation has a nice interpretation. It says that the stock's total return R_t is equal to its dividend yield ( D_t / P_t-1 ) plus its capital gains rate ( P_t - P_t-1 ) / P_t-1. In our example, Microsoft 's dividend yield was $0.20 / $26.63 = 0.75%, and its capital gains rate was -3.94%, yielding a total return of -3.19% in November.

Next tutorial: Stock splits
Previous tutorial: Net and gross return calculations

• Tweet