Variance-covariance assumes volatility only in terms of standard deviation, and volatility doesn’t come in one flavor or standard deviation. Neither does risk.
Value-at-Risk is a calculation that predicts a worst case scenario in which the maximum loss for a specific investment would be realized. Recently the San Francisco Chronicle investment blog Investopedia, ran a short series posts on VAR. One of the more intriguing of these demonstrated three ways of calculating Value-at-Risk for a single stock investment for more than one time period.
The three methods were historical simulation, variance-covariance, and Monte Carlo simulation. What was intriguing about the comparison of methods was the observation that best choice among these methods was the variance-covariance method because it was easy. The downside of using the historical method was the need to crunch data and the downside of getting out your Monte Carlo software–no mention of using historical data to inform your model–was that the Monte Carlo method was "complex."
Does that mean that risk is simple enough to require only simple statistical analysis? And doesn’t this kind of thinking encourage financial planners to take a direct but drastically reduced view of the possible outcomes of an investment? And isn’t this the same turn of mind that led to the collapse of the financial markets only a year or so ago?