Sunday, May 5, 2019

Adjusted Stock Prices



This post takes information on dividend payments and information on actual closing stock prices to obtain an adjusted closing stock price on the date a stock is purchased.   the adjusted stock price for the purchase of the stock is  used to calculate the average annual rate of return on a stock under the assumption all dividends are reinvested in the stock.


Adjusted Close Stock Prices

Question:  The table below contains stock dividend payment information and stock closing price information for IBM.   Use this information to calculate the adjusted closing price for IBM on March 15, 2017.  What is the average annual rate of return for a person who purchases IBM stock on March 15, 2017 and  sells all share on February 7, 2018, under the assumption all dividends are reinvested?


Dividend and Stock Close Price for IBM
?Date
Dividends
Date
Close
8-Feb-18
1.5 Dividend
7-Feb-18
153.85
9-Nov-17
1.5 Dividend
8-Nov-17
151.57
8-Aug-17
1.5 Dividend
7-Aug-17
143.47
8-May-17
1.5 Dividend
7-May-17
155.05
15-Mar-17
175.81


Discussion:   The adjusted closing price accounts for payments of dividends and stock splits.   A comparison of price today to adjusted closing price in the past will accurately measure returns after stock splits and accounting for the reinvestment of all dividends. 

The adjustment of closing prices for dividend payments requires the analyst to multiply the actual close price by (1-D/SP).   Here D is Dividend and SP is stock price on dividend payment date.

The adjustment is made to all stock prices prior to the payment of the dividend.


The Calculation of Adjusted Stock Price on March 15, 2017:


March 15, 2017 is prior to all four dividend payment dates listed in the table.   We must adjust the actual closing price on March 15, 2017 by multiplying by the adjustment factor.


The adjustment factor is


ADJ = (1-1.5/153.85) x (1-1.5/151.57) x (1-1.5/143.47) x (1-1.5/155.05)



Multiplying the adjustment factor by the actual closing stock price I get 168.92 for the adjusted closing price.   This is in fact the value of the adjusted closing price on March 15, 2107 listed in YAHOO FINANCE.


Rate of Return Calculation:

The rate of return calculation is presented in that chart below. 

Rate of Return Calculation
Sale date
8-Feb-18
Purchase Date
8-May-17
Holding Period in Days
276
Holding Period In Years
0.7562
Sale date Closing Price
153.85
Purchase Date Adjusted Closing Price
168.92
Average Annual Return
-11.62%


The average annual rate of return is (S/AP)(1/t)   - 1

Where S is sale price, AP is adjusted purchase price and t is the holding period in years.

Concluding Thought:  The adjusted share price is very convenient when analyzing returns from stock when dividends are reinvested in the original asset.  However, when dividends are spent or invested in a different asset class the analyst must follow the money and account for returns from the reinvestments in the second asset.

  



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