If not for their huge leverage, LTCM could have survived these mistakes, or at least survived without such breathtaking losses. The most articulate expression of this arguments can be found in Professor Burton Malkiel's book A Random Walk Down Wall Street . If volatility falls in a bell curve, risk can be estimated. The calculation of volatility assumes that the way a given security or set of securities has acted in the past will reflect the way they will act in the future. Since the past is known, the future can be modeled.
Markets are perfectly efficient.
The actions of market traders will price securities correctly. Markets may be out of balance at some point in time, but they will always move back toward balance. In fact, during the first three years of LTCM's history, markets were very placid. Efficient markets show linear behavior that can be described with calculus and statistics. Academics like this because it leads to elegant results which make good journal articles, with nice equations.