# Calculating Yield with Adjusted Closing Price

I have a data set with stock prices and all stock events through time (with adjustment factors for all events). I'm trying to calculate the yield of holding this stock for a period of time (without dividend reinvestment) using the adjustment factors (as I read they should be used) and the numbers I'm getting don't make sense (IMHO)

Specific example

Company distributed dividends as follows:

• Ex date 16/01/2018, dividend $188.94, adjustment factor 0.96305 • Ex date 30/05/2018, dividend$188.94, adjustment factor 0.9572

Historical prices:

• 2017/12/31 closing price: $4988 • 2018/06/21 closing price:$4658

I now want to calculate the YTD (until 21/6/2018) return of the stock. Without using adjustment factors this would be:

$$YDT Return = \frac{final price + dividends}{initial price} - 1 = \frac{4658+188.94+188.94}{4988} - 1 = 0.96%$$

But in most cases I won't have all the dividends or other events like splits, but I do have the adjustment factor, therefore I tried using it to calculate the YTD return as follows:

$$YTD Return = \frac{final price}{adjusted initial price} - 1 = \frac{4658}{4988*0.96305*0.9572} -1 = 1.30%$$

What is the problem with my calculations?

Assuming that your adjustment factor numbers are correct, I don't think the problem is your calculations because I think that the problem arises in the data itself.

I can't explain the mathematical cause of it so the best I can do is observational. Look at some historical data (close and adjusted close), perhaps at Yahoo Finance. If the adjusted close was a linear adjustment, for the past quarter, they'd simply subtract the dividend from the close and the adjusted close would be exactly that amount less than the actual close every day. For the previous quarter, two times the dividend would be subtracted (assuming dividend unchanged), and so on. If you look the difference of the close and adjusted close, it varies day to day so the yield calculation will also vary for any time period.

In the case of unadjusted data, you'd take the current price, subtract the purchase price and add the dividends received to determine a gain of "X" . Divide by purchase price to determine the yield. In your example, it would be .96% which is correct.

However, if you go through the motions of adjusting the data then once done, one should be able to subtract the adjusted close of the purchase date from the current price and the amount should be equal to "X" . But it's not (when looking at Yahoo data) and that is supported by your second calculation of 1.30%. So my guess is that there's a different formula for working with adjusted data to determine yield.

• I’ve double checked the data, including the adjustment indexes and they all seem right, so something else is wrong... – vainolo Jun 24 '18 at 19:33
• For each day, subtract the adjusted close from the close. Is the day to day difference constant or does the difference vary? If it varies then that's where your problem lies. – Bob Baerker Jun 24 '18 at 20:11

Found the problem! The difference between my calculations in the question is taht adjusted prices automatically imply dividend reinvestment, so after the first dividend is distributed, this means that instead of having 1 stock, I now have ~1.038 stocks, so on the second distribution I don't get $188.94 but$196, which reinvested again turn into ~1.084 stocks. This way the return is

$$\frac{1.084*4658}{4988} ~= 1.3%$$

Problem solved!