1. Introduction

The rate of return that we earn on an asset during a given time period, the so-called holding period return, is:

 

\( Return = \frac{\text{Price end of period}+\text{Cash payments}}{\text{Price beginning of period}}-1 \)

 

If we use the letter P to denote the asset price and C for the cash payments, and if we assume that the holding period lasts from time 0 to 1, we can rewrite the above expression as:

 

\( Return = \frac{P_1 + C}{P_0} -1 \)

 

We can rewrite this as:

 

\( Return = \frac{P_1 - P_0 + C}{P_0} \)

 

Using the greek letter Delta \( \Delta \) to denote the change in the price from the beginning to the end of the holding period, \( \Delta P = P_1 -P_0 \), we can also write:

  

\( Return = \frac{\Delta P + C}{P_0} \)

 

Intuitively, the return an investor earns comes from the change in the asset price (\(\Delta P \)) and the cash distributions (C).

  

Example 1

Suppose an investor bought shares of Procter & Gamble Co. at the beginning of 2018. Back then, the price per share of common stock was $91.24 (P0). At the end of the year, the stock was trading at $92.49 (P1). We also know that, during the year, shareholders of P&G received a total cash dividend of $2.841 (C), split into quarterly dividends.

 

The following figure summarizes the stock price development of P&G during 2018. The symbols   D  indicate dividend payments (source: Marketwatch).

  

Stock price of PG 2018

 

With this information, we can compute the 2018 holding period return of the P&G stock. For simplicity, we assume no reinvestment of the dividend payments during the year, so that the total cash payout is simply equal to the sum of all dividend payments. During 2018, shareholders of P&G earned a total return of 4.48%:

 

\( Return = \frac{P_1 + C}{P_0} -1 = \frac{92.49 + 2.841}{91.24} - 1 = 0.0448 = 4.48\%\)

 

To better see the sources of the return (price change vs. cash distribution), we can also write:

 

\( \Delta P = P_1 - P_0 = 92.49 - 91.24 = 1.25 \)

 

So that:

 

\( Return = \frac{\Delta P + C}{P_0} = \frac{1.25+2.841}{91.24} = 0.0448 = 4.48\% \)

 

As one can see, the largest part of the P&G's return in 2018 came from dividend payments (2.841 vs. 1.25).