Portfolio Risk Measures
At this point, we’ve discussed risk either as a concept or as it relates to a particular asset class. In upcoming chapters, we will discuss risk models in greater detail. However, it is a good idea to spend some time discussing risk measures themselves as they relate to the total portfolio. This chapter reviews the attributes of any good risk measure and discusses some commonly used risk measures.
Variance, tracking error (TE), and value at risk (VaR) are all commonly used risk measures. Each of these measures answers a specific question regarding the variability of a portfolio, but no measure answers all questions. Depending on the assumptions used, each of these measures can be translated into the others.
A secondary issue relates to the underlying mathematics of risk. Expected return is a linear function, with its associated ease of computation. In the classic Markowitz framework, risk is a quadratic function, based on an individual security’s variance and its covariance with other securities, simply because of the squared term in the definition of variance. There are two important implications of the last sentence. First is the nonlinear nature of a risk calculation. Whether risk is quadratic or some other formula, the calculation of risk is more difficult and requires more complex mathematics than the calculation of return. Additionally, it is the interaction of each security with the ...