Stock prices are quoted in many places. However, prices neglect the value of owning a certain stock or mutual fund. As an investor, I’m more interested in “pocket book value” (PBV), or how much money really increases or decreases in my pocket book. PBV includes stock price subsequently corrected for stock splits, dividend payments. This article describes how to calculate PBV.
Historical stock prices can be obtained from web sites such as http://www.yahoo.com or http://www.google.com/finance after you type in a ticker symbol. However, what the closing price was on any day is not enough information to compare the value gain of a stock over time.
Correcting for Stock Splits
If a stock price runs about $100 and the company does a 2:1 split, you’ll instantly own twice as many shares, but they’ll be worth only $50 each. Although the price has done a big change, the value you hold has not. We want this event to show as no change in value.
A specific example would be Steven Madden, Ltd (ticker SHOO). On May 31, 2011, SHOO closed at $55.74, then issued a 3:2 stock split. If you owned 10 shares, you held a value of $557.40. After the stock split, you owned 15 stocks, each worth 2/3 of the original value, or $37.16.
Notice the value you hold is the same: 15 x $37.16 => $557.40. We would expect the opening price a day later, on June 1, 2011 to be $37.16. Because of market-maker activities while the market is closed the first sale of the next day actually occurred 25 cents higher, but this has nothing to do with the split.
So, how can one show old prices before the split (in the $50’s) with any ability to compare on a chart with the new price (in the $30’s)? It would not work to show a huge drop in price because it has nothing to do with real value changes. Look at the tabular historical prices for SHOO, and you’ll see that common practice is to change all previous historical prices, multiplying prices before the stock split:
The historical stock charts showing prices in the $30s do not report the true $50-ish prices the stock used to sell for. However, the adjustment does give a comparison that is useful. Also remember this process can happen more than once. Changing all historical prices happens for each stock split, accumulating back into history where the oldest historical prices may have been corrected 2 or 3 or many more times.
Correcting for Dividend Payments
If a stock price runs about $100 and the company does a $3 dividend payment, the stock price instantly becomes $97 and you hold $3 cash. I’m not including subtleties of whether you actually take the cash or automatically reinvest it into the stock, in which case you’ll automatically buy an additional 0.0309 shares, so that your total value will also remain at $100. We want this type of an event to show as no change in value.
A specific example would be Best Buy, (ticker BBY). On April 11, 2011, BBY closed at $30.51, then issued a $0.15 dividend per share. If you owned 10 shares, you held a value of $305.10. After the dividend payment, you owned 10 stocks, each worth $0.15 less per share or, or $30.36. But you also hold an additional $1.50 in cash. Notice the value you hold is the same: 10 x $30.36 (stock) + 10 x $0.15 (cash) => $305.10. We would expect the opening price a day later, on April 12, 2011 to be $30.36. Because of market-maker activities while the market is closed the first sale of the next day actually occurred 13 cents lower, but this has nothing to do with the dividend payment.
Like the SHOO example above, look at a chart for BBY, and you’ll see that common practice is to change all previous historical prices. In this example, the historical prices are adjusted:
The historical stock charts showing slightly lower prices do not reflect the prices the stock used to sell for. But it does give a comparison that is useful. Changing all historical prices that have been reported happens for each dividend payment, accumulating back into history where the oldest prices may have 2 or 3 or many more adjustments built in.
Displaying on a Logarithmic Scale
If a stock price goes up by $10 is that a good or bad gain? Well, you don’t know until I tell you the prior stock price. For Google, currently running about $518/share, that’s a 1.9% gain. For Best Buy, currently running about $29/share that’s a 34.5% gain. Big difference.
In order to compare percentage gains instead of dollar gains, you need to view price charts on a logarithmic scale. A linear scale shows a move from $10 to $12 as the same visual distance on the vertical axis a move from $20 to $22. A Logarithmic scale does not. Instead it shows a 20% gain from $10 to $12 as the same visual distance on the vertical axis as 20% gain from $20 to $24.
Once you have a chart plotted on a logarithmic scale that corrects historical prices for stock splits and dividends, you are able to do real value change calculations from any point in time to any other point in time. In Part II, I’ll show you how to do this with pencil and paper, no fancy computer spreadsheet, using only a $5 calculator. I don’t mean simple gain calculations such as “it went up 20%”, because that could have happened over a day, or month, or decade. What you need is a for-real annualized return that can be compared.
Being able to calculate comparable annualized percentage yields yourself from adjusted price charts is valuable because you are not limited to periods of time such as traditional “last month” gains, or “last year gains”, or “last 5 year gains”. Instead, you can calculate APR across any range of time like “during my last job” or “during the school semester” or “during the presidential campaign”. Additionally, you can do the calculation in a way that averages out small daily perturbations.