AAPL Stock Price Almost Returns to Attractor Path

In a post last Friday (here), I argued that Apple stock (AAPL) was way overvalued. The opinion was based on the dynamic attractor plot (dashed red line in the graph below) for the stock. Early this morning, when AAPL was around 490 (after being above 520 yesterday), it seemed pretty clear that the stock was reverting to the attractor value, but then there was a little rally mid-day and it closed above 500 again.
The Random Stock Walker finds the current AAPL "bubble" very interesting for a number of reasons: (1) It should be a fairly clear test of dynamic attractor theory and (2) it might provide some information about why and how a stock runs up to improbable levels above its attractor value (an important unresolved issue from the late-2000s Financial Crisis).

Calculating a stock's attractor path is based on three steps: first, finding out what drives the stock, second, conducting a "free simulation" of the stock price over the entire sample period and, third, calculating the 98% bootstrap prediction intervals for the attractor. The resulting graph for AAPL is displayed above where the solid black line is the stock price, the dashed red line is the attractor value and the other dashed lines are the upper and lower 98% bootstrap prediction intervals. Such an analysis suggests that AAPL stock in the middle of February 2012 should be somewhere between 400 and 450, rather than improbably above 500.

To find out what drives the stock price, I test a number of models using the Reality Check Bootstrap (a procedure developed by Halbert White). The models I check are (1) a random walk, (2) a business-as-usual model predicting the stock price from its lagged values, (3) a model driven by the SP500, (4) a model driven by USL20 model of the US economy and (5) a model drive by the WL20 model of the world economy. In the case of AAPL, the best state-space model is the stock price driven by the world economy. How does this approach differ from conventional stock forecasting?

First, stock prices are typically forecast from last period's (or at most a 12 period lag) stock price. The Random Stock Walker models ignore last periods stock price but pay more attention to the prior period values of the driver variables. Second, academic theory looks almost exclusively at stock price as a function of earnings. These two decisions, focusing on last period's price and last periods earnings, insures that forecasting program cannot see stock market bubbles. Since there is no attractor value, at best the stock can revert to some moving average but the moving average is not really part of the model. And, since we are focused on earnings we miss the real drivers for stock price. In the case of AAPL and in the case of all strong global companies, the stock price has to be driven by the world economy. Earnings are far too narrow.

Obviously, in the case of AAPL, the attractor does not drive the stock price in the short run or AAPL wouldn't have had its recent run up. The Random Stock Walker models have no idea what drives today's stock price. In the case of AAPL, it's probably speculation. If I actually had the courage of my convictions in all this, I would have shorted AAPL last Wednesday. Another approach would have been to take some money off the table by selling AAPL on Wednesday. Option trading has advantage of not requiring initial buying and selling but it is more risky. Any of these approaches, to include stock investing, could be based on attractor theory. Evaluating attractor theory is the purpose of the Random Stock Walker blog.