Risk measures

Financial risk is a tangible and quantifiable concept, a value that you can lose on a certain financial investment. Note that here, we strictly differentiate between uncertainty and risk, where the latter is measurable with mathematical-statistical methods with exact probabilities of the different outcomes. However, there are various kinds of measures for financial risks. The most common risk measure is the standard deviation of the returns of a certain financial instrument. Although it is very widespread and easy to use, it has some major disadvantages. One of the most important problems of the standard deviation as a risk measurement is that it treats upside potential the same way as downside risk. In other words, it also punishes a financial instrument that might bring huge positive returns and little negative ones than a less volatile asset.

Consider the following extreme example. Let's assume that we have two stocks on the stock market and we can exactly measure the...