In our previous article, How do you define risk?, we put forth our criticism on the way risk is measured by many in the financial service industry. Today, we will look at the underlying theory behind their measurement of risk. The recommended reading for today will be How the Finance Gurus Get Risk All Wrong.

As you may have noticed, ?risk? is often expressed as a nice and simple number in the world of finance. For example, in many stock research publications, the ?risk? of a stock may be defined in terms of a number called the beta. You may see risk jargons like standard deviation, the Sharpe ratio, variance, correlation, alpha, value at risk and so on. All these mathematical definitions of ?risk? give it a scientific feel, which seem to give us the impression that ?risk? can be measured and controlled. Unfortunately, in reality, these definitions and measurements of ?risk? are pseudo-science. The reason is because the underlying theory behind all of them is flawed in the first place.

What are the assumptions behind these conventional measures of ?risk?? They are all based on the assumption that price follows a statistic device known as the normal distribution. If a stock price follows a normal distribution, it means that at any given day, there is a 50% chance that it will go up and a 50% chance that it will go down by the same amount on average. In the long run, the vast majority of stocks? price will hover around its average, with a smaller percentage deviating from it. In other words, the behaviour of stocks? price will follow a bell curve like this (horizontal axis?stock price, vertical axis?probability of the price being at that level):

Is this a valid assumption?We doubt so. As you can see for yourself in the real market, prices often do not follow such behaviour?frequently, they move in trends and at times, exhibit extreme behaviour. As the article in the suggested reading (How the Finance Gurus Get Risk All Wrong) said,

The inapplicability of the bell curve has long been established, yet close to 100,000 MBA students a year in the U.S. alone are taught to use it to understand financial markets.

Thus, as contrarians, this is not the way we define risk.