CEO resignations often cause share prices to rise. Witness the effect of the latest CEO departure on Yahoo!. This typically happens because CEO replacements are not necessary when companies are successful. In times of crisis, the market sees management change as a hopeful sign. But Apple is doing well. So it was commonly believed that if Steve Jobs were to leave the helm at Apple the stock would fall. However, as the chart below shows, the stock price has since risen. 
Apple’s share price rise of 3% even out-performed the Dow Jones index, and this phenomenon is not for the short term only. The Jobs resignation sent Apple puts to one-year lows.
So how do we reconcile this? How can such a valuable person be priced as a liability?
First, I should mention that not everyone shared the opinion that the departure of Steve Jobs would cause a decline in the price. Over a year ago, in August 2010 Horace wrote in a comment:
Since I’ve shown repeatedly that Apple is trading at a discount to its growth and to its historic value and to its peer group, and since the health of their CEO is an uncertainty which must be discounted, the possibility exists that the depressed value assigned to Apple is due to Steve Jobs’s continuing presence in the company. If that is true then his departure should increase the stock price.
His argument of why the departure of Steve Jobs would cause an increase in the stock price was based on the fact that the market would have discounted it and the only question would be when it would happen. Since that uncertainty of when was unresolved, it would weigh on the shares until the uncertainty would be lifted and the price would resume its value based on other factors.
To demonstrate that effect, we can turn to data. The discounting was visible in the reactions of the stock in previous events when the tenure of the CEO came into question. Those reactions are shown in the following chart:
Each of the bars above shows the cumulative abnormal returns after all the events when tenure issues cropped up in the news.
If we excluded the first time we learned about Steve Jobs’ health issues, we can see that the stock market likes certainty (January 5th, 2009: health issue but remains CEO; August 24th, 2011: definite resignation as CEO) and rejects uncertainty manifested in medical leave announcements on January 14th, 2009 and on January 17th, 2011 leaving the top organization in a temporary form. We can also see that Apple investors are becoming more comfortable with Tim Cook running the company as the negative cumulative abnormal returns diminish and turn into positives ones when he is appointed CEO.
We can conclude that Steve Jobs’ resignation as CEO, as sad as it may be, has reduced unsystematic risk from the stock and therefore “boosted” the share price performance.