Here is a chart that tells the whole story with enough context to enable some reasonable judgments about the validity of the charges of incompetence based on stock price. It in necessary to remember that Mrs. Fiorina's leadership of HP began very near the end of a multi-year period of irrational exuberance of technology investors in the late 1990's, during which the NASDAQ soared way beyond the S&P 500. The balloon popped in early 2000 and HP along with most of the stocks listed on the NASDAQ plummeted back to earth. The NASDAQ had peaked at 5048.62 in March, 2000, and is still about 4% below that fifteen years later.
Some have argued that HP was bested during the turmoil by primary competitors IBM, Dell, etc., and that may be true depending on the exact time period chosen, but a cursory examination of the chart below will show that HP generally followed the NASDAQ throughout the process. The general opinion of some writers seems to be that it was actually the fairly small dip in 2004 which led to the firing of Mrs. Fiorina in 2005.
Some, including me, like to argue that the performance of a CEO, especially one of fairly short tenure, is best judged by the performance of the stock after he or she leaves because that is a measure of the competitive position in which the company was left. By that standard HP has done fairly well.
Carly Fiorina may or may not have been a terrible CEO, but the performance of the HP stock price during such a five year period of turmoil provides no evidence to support either position. And when somebody tries to use the S&P 500 as a benchmark for HP, please, just laugh.
You have to click on the chart for a high resolution view.