Yahoo! Finance stock data gives different result from their graphs online

Question

I'm downloading stock data directly from Yahoo! Finance.

I compare "Adj Closed" for two dates to get the growth rate. For example, on 7/20/1987 KO (Coca-Cola) had an adjusted closing value of 1.71, and on 7/1/2013 it had a value of 40.46. The rate therefore is 2366%; my program gets this correct. But it doesn't agree with the graph at Yahoo! Finance, and it's easy to see why: the graph has the 7/20/1987 value at 3.0238. But why is it different on their graph than in their data?

I get a worse problem when comparing VFINX (an index fund) to ^GSPC (Standard & Poor, which is what it's indexed to). The graph shows them in lockstep, as they should be, growing around around 400%. VFINX grows from 16.14 to 156.14 over that period (adjusted closing). But ^GSPC grows from 302.94 to 1692.39, which gives a very different ratio.

What's wrong with my data? Am I misinterpreting something, or looking in the wrong place?

Here's ^GSPC. The last field is Adjusted Closing.
7/23/2013 1696.63 1698.78 1691.13 1692.39 3096180000 1692.39
7/1/1987 303.99 304 302.53 302.94 157000000 302.94
and here's VFINX
7/23/2013 156.14 156.14 156.14 156.14 0 156.14
7/1/1987 30.41 30.41 30.41 30.41 0 16.14

Answer 1

The reason for the discrepancy is because the graph plots the closing price (adjusted for splits), but you're comparing it to adjusted price, which accounts for splits and dividends.

None of the columns in the historic dump show closing price, adjusted for splits only. Think of "adjusted price" as including dividend re-investment. Example:

Jan 12, 2006    $10 (price)
Jan 12, 2006    $2  (dividend)
Jan 13, 2006    $9  (price)

One way of looking at this is that between Jan 12 and 13, you lost 10%. This is what would be shown on the graph, with a little tick to show a dividend happened.

But, a better way of looking at this is to include the value of the dividend. So, at the end of Jan 12, the $2 dividend was used to "purchase" 0.2 units of stock. Consequently, on Jan 13 you own 1.2 units at $9, which has a value of $10.80, an 8% gain from the previous day!

However, saying that today's adjusted price is $10.80 would be confusing since it doesn't match today's actual price. To fix this, just divide all the numbers by 1.2. This makes Jan 13 go back to $9, but it changes Jan 12 to $8.33. All the ratios are maintained, and it's a better reflection of the value of the share over history. This is how adjusted price works.

Here's the source: https://ca.help.yahoo.com/kb/finance/historical-prices-adjusted-close-sln2311.html

Answer 2

I believe you and Yahoo are not making the same distinction here between Rate of Interest and Compound Average Rate of Return.

If you have $10, and 10 years later you have $100, the interest required to make that $10 into $100 is 100% (100% * $10 * 10Y = $1000).

However, the Compound Average Rate of Return in this case is 23.247%. Calculating compound interest is complicated. You may end up with a different value if you assume the cycle started at the end of the month, vs. the beginning.

Since it is a complicated calculation, two sources might come up with different answers for compound average rate of return, both being correct under a different set of assumptions.

This tool can help you work with Compound Rate of Return: http://danielstern.ca/calculator/