When an airplane is statically stable it will fly in smooth air maintaining any attitude for which the pilot has trimmed the airplane.  An airplane is dynamically stable when it will return to its original attitude for which it was trimmed after it has been disturbed either by rough air or by the pilot.  An airplane is said to have satisfactory trim characteristics when the tabs can be set so that it is not necessary for the pilot to exert any force on any of the controls to maintain the airplane in the desired flight attitude.

In order to secure satisfactory static and dynamic stability, it is necessary that the reactions on the airplane be as shown in the illustration above.  This illustration is considerably simplified and aerodynamics experts could pick flaws in the following explanation, which will also be considerably simplified in order to avoid writing a textbook on aerodynamics and dynamic stability.

As the speed of the airplane increases, the center of pressure moves back, which tends to cause the airplane to dive and further increase in speed.  However, the down load on the tail increases faster yet, if the airplane is  properly balanced, and this increase in tail load overcomes the unstable tendency from the aft movement of the center of pressure, the nose of the airplane rises and the speed is reduced.  When an airplane is disturbed in perfectly smooth air it will oscillate several times as the speed goes alternately above and below the speed for which it was originally trimmed; but if it is dynamically stable it will  return to the original speed for which it was trimmed, or very close to it.  When the speed of the airplane is reduced the center of pressure move forward, tending to nose the airplane up still further.  However, here again, the down load on the tail is reduced faster than the center pressure moves forward and this produces a stable tendency, causing the nose to drop and causing the airplane to return to its original trim.

When an adjustable stabilizer is used and no trim tabs are used on the elevator, the elevator, of course, trails at any time that the pilot is not exerting force on it, and the airplane must be trimmed by adjusting the stabilizer angle.  In general, the more stable the airplane is the more negative the stabilizer angle will be at any given speed.  The nose of the stabilizer rises to trim at high speeds and drops to trim at low speeds.  When a fixed stabilizer is used the angle at which it was set may be varied fairly widely, as the airplane is then trimmed by using the tab to control the elevator position and in that way the trim of the airplane.

With a fixed stabilizer there is only one speed at which the elevator will trail with a neutral tab setting for a give amount of power and angle of attack.  At all speeds above this on speed the stabilizer will be exerting too much down load and at all speeds below this speed it will not be exerting enough down load.  If the leading edge of the stabilizer is set fairly high the elevator will trail at a higher speed, but it will be difficult to get the tail down on landing.  Further, the horizontal tail will stall at a higher speed, resulting in higher stalling and landing speeds for the airplane.  If the leading edge of the stabilizer is set too low, a point will be reached where the wings will stall before the tail surfaces do and an unnecessary drag will be incurred at high speed.  It has also been found from experience that dynamic stability at high speeds is improved by carrying the nose of the stabilizer down sufficiently so that it is necessary to have the elevator down in order to counteract the excessive down load on the stabilizer.

From the above it may be seen that the setting of the stabilizer involves a compromise which can only be arrived at after much flight testing.  The illustration above also shows why it is dangerous to load an airplane so that the C.G. falls outside of the specified limit.  If the weight of the airplane is too far forward of the center of pressure the tail surfaces may not be powerful enough to control the airplane at low speeds during take-off and landing.  (Also, of course, there is more chance of nosing the airplane over on soft fields or by violent use of brakes if the center of gravity is too far forward.)  If the airplane is loaded so that the center of gravity is too far back it comes too close to the center of pressure, which reduces that tail load necessary to balance the airplane.  This reduces the effectiveness of the tail in controlling the unstable movement of the center of pressure with variations in speed -- and will result in an unstable airplane.  If the center of gravity is carried too far back it may even result in an uncontrollable airplane.

To sum up:  if the airplane is loaded within the specified limits the attitude that the elevator takes for trim, whether 'Up', 'Down', or 'Level', should be no cause for concern as it is merely behaving the way it is supposed to.  If the stabilizer angle were changed so that the elevator would ride in neutral in level flight, the high speed would be slightly increased, the stalling and landing speeds would be increased by 10 to 15 miles per hour and the dynamic stability would not be as good.