TY - JOUR

T1 - Desirable properties of an ideal risk measure in portfolio theory

AU - Rachev, Svetlozar

AU - Ortobelli, Sergio

AU - Stoyanov, Stoyan

AU - Fabozzi, Frank J.

AU - Biglova, Almira

N1 - Funding Information:
Ortobelli’s research has been partially supported under MURST 60% 2005, 2006, 2007. Rachev’s research was supported by grants from the Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara and the Deutschen Forschungsgemeinschaft.

PY - 2008/2

Y1 - 2008/2

N2 - This paper examines the properties that a risk measure should satisfy in order to characterize an investor's preferences. In particular, we propose some intuitive and realistic examples that describe several desirable features of an ideal risk measure. This analysis is the first step in understanding how to classify an investor's risk. Risk is an asymmetric, relative, heteroskedastic, multidimensional concept that has to take into account asymptotic behavior of returns, inter-temporal dependence, risk-time aggregation, and the impact of several economic phenomena that could influence an investor's preferences. In order to consider the financial impact of the several aspects of risk, we propose and analyze the relationship between distributional modeling and risk measures. Similar to the notion of ideal probability metric to a given approximation problem, we are in the search for an ideal risk measure or ideal performance ratio for a portfolio selection problem. We then emphasize the parallels between risk measures and probability metrics, underlying the computational advantage and disadvantage of different approaches.

AB - This paper examines the properties that a risk measure should satisfy in order to characterize an investor's preferences. In particular, we propose some intuitive and realistic examples that describe several desirable features of an ideal risk measure. This analysis is the first step in understanding how to classify an investor's risk. Risk is an asymmetric, relative, heteroskedastic, multidimensional concept that has to take into account asymptotic behavior of returns, inter-temporal dependence, risk-time aggregation, and the impact of several economic phenomena that could influence an investor's preferences. In order to consider the financial impact of the several aspects of risk, we propose and analyze the relationship between distributional modeling and risk measures. Similar to the notion of ideal probability metric to a given approximation problem, we are in the search for an ideal risk measure or ideal performance ratio for a portfolio selection problem. We then emphasize the parallels between risk measures and probability metrics, underlying the computational advantage and disadvantage of different approaches.

KW - Diversification

KW - Investment risk

KW - Portfolio choice

KW - Reward measure

KW - Risk aversion

UR - http://www.scopus.com/inward/record.url?scp=43949118449&partnerID=8YFLogxK

U2 - 10.1142/S0219024908004713

DO - 10.1142/S0219024908004713

M3 - Article

AN - SCOPUS:43949118449

VL - 11

SP - 19

EP - 54

JO - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

SN - 0219-0249

IS - 1

ER -