Financial Risk Modelling and Portfolio Optimization with R

4

Measuring risks

4.1 Introduction

Toward the end of the first decade of this century, the focus of investors shifted, not least because of the financial crisis, to the need to adequately measure risks. But it is also worth being able to capture potential losses correctly during market episodes that are more tranquil. If an investor were too conservative with respect to risk during such phases, he would jeopardize potential investment opportunities. Furthermore, there are regulatory reasons and economic arguments which necessitate a proper risk assessment. With respect to the former the stricter requirements imposed by the Basel Accords are worthy of mention, and for the latter the normative presumption of an efficient resource allocation between risky assets. If the riskiness of a financial instrument is not captured correctly, its price would in general be misleading and would therefore cause an inefficient allocation of funds. Finally, a proper assessment of market risks by its participants helps to ensure a smooth functioning of the financial system. For example, if market participants have to revise their risk estimates on a larger scale, as was the case during the sub-prime mortgage crisis, and hence want or have to rebalance their funds, a stampede-like reaction will quickly dry-up market liquidity and aggravate the potential losses, due to the lack of counter-parties.

4.2 Synopsis of risk measures

The risk measures introduced in this section are based upon a probability ...