What does a stock's price depend on?

I would venture to state:

P = f (HS)                                 (1)

Where P is the stock price,
and HS (Happy/Sad) represent the prevailing sentiment towards the stock like the faces on the right.

HS (sentiment) in turn depends on, at least, the following three variables:

• Market Sentiment - When Mr. Market feels good, everything under the Sun flourishes. However, when he is in a foul mood, it is as if the world is experiencing a nuclear winter when everything perishes. For instance, all Dot Com stocks took off in the 90s and almost all stocks crashed in late 2008! Possible causes for the mood swings:
• Collective mood swings of the market crowd. There are natural cycles in the collective mood changes of the crowd who can get extremely euphoric and depressive by itself, causing bubbles and crashes.
• External forces
• Industry Events: Emergence of new industries: Semiconductors, PCs, Wireless, Internet, Sub-prime lending, Social Media
• Man-Made events: Authorities' Decisions: Interest rate policy changes, Money Printing/QE, Bailing out or Abandoning certain companies (Bear or Lehman, Greece or no Greece). 
• Conflicts: Wars, Trade Barriers
• Natural Disasters: Volcano, Earthquake, Tsunami, Nuclear Accident, Hurricanes, etc.
• Sector Sentiment - Sentiment changes wildly from sector to sector and from time to time. When the Dot Coms were hot in the late 90s, everything goes up. On the other hand, the traditional industries such as insurance companies hardly took notice.
• Trends: Emergence of new industries: Semiconductors, PCs, Wireless, Internet, Sub-prime lending, Social Media, Secular demand growth.
• Sector Challenges: 
• Hawkish policy: FDA, Regulation of the banks, Nuclear industry
• Slowing growth: PC, Drug, Brick and Mortar retail industries
• Company Specific Sentiment - Every company goes thru its love affair with Mr. Market who have many concubines, he does not stay with the same one all the time.
• Earnings
• New Products/Inventions
• Product obsolescence
• Fraud
• Competition
• Interactions with external forces
• Authorities' handouts or panelties
• Lawsuits

The next question is how much does P change when sentiment HS changes:

dP = f'(HS) dHS                                                                      (2)

f'(HS) is the first derivative, it is kindly of like beta, which depends on the market cap, industry, stock price, domicile, short interest, etc.

Equation (1) and (2) should not be treated as precise mathematical formulas as in physics, but it is rather an attempt to draw a stock's dependence tree, which hopefully can help to better understand the movements of stocks. In general, dominant variables change over time. Yet too often, market participants are trying to look for one smoking gun (one variable) for explanation. The end result is that it only leads confusion and poor decision making.