I was just reading a document produced by the Society of Actuaries in Ireland regarding the above and would like to make some important points that are not addressed in this or any other document dealing with this issue.
I have meant for some time to pen some further thoughts,held for a long time, on the modern portfolio theory paradigm. My reply to a recent e-mail provoked a brief encapsulation of these thoughts. My brief e-mail reply is noted below, and below this a more detailed description of the position.
If markets are efficient, and in a general equilibrium, then historical standard deviation will provide you with an “average” sensitivity of price movements to an average set of new information/events/shocks.
The actual price movement at a point in time should have a direct relationship to the news event/shock, and the price movement should therefore be predictable for a given shock. What the average standard deviation does not do is provide you with, in your face as it were, the price movement for all events, both big and small. This is found in the distribution, and for a given equilibrium, the distribution of returns only represents the dataset for one run, or one string of outcomes, for that equilibrium. It tells you nothing about the future shocks, just how price reacts to a shock.
In other words, the standard deviation does not provide the investor, unless they are mathematically inclined, with a full distribution of the price movements of their investment, nor does an historical analysis of price movements provide you with the future profile of price movements. As stated, it only tells you the qualities of the elastic band, nothing about the forces that will attempt to shape it.
But, once we are out of equilibrium then all the physical qualities (normal distribution) of a risk measurement based on standard deviation go out of the window. Way out of equilibrium you only need a small shock to cause a large price movement, so the relationship between risk and change is lost. Standard deviation becomes meaningless. An analogy, is that an elastic band that is fatigued has different physical properties to a new elastic band: we have a fatigued elastic band and standard deviation only applies to new ones.
I think it worth revisiting some of the dogmas that gave the green light to mankind to
go forth and multiply to go forth and leverage him/herself to death, spreading his/her seed risk amongst those whose collapse would strike at the heart of our universe who could best bear it. The world was not becoming a safer place at all, but a riskier, far more dangerous and leveraged place.
In the midst of a sustained market downturn, one that has its roots in the late 1990s, I thought it would be interesting to touch base with modern portfolio theory’s Monte Carlo risk simulations.