TY - JOUR
T1 - Benchmark-based deviation and drawdown measures in portfolio optimization
AU - Zabarankin, Michael
AU - Grechuk, Bogdan
AU - Hao, Dawei
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/9
Y1 - 2024/9
N2 - Understanding and modeling of agent’s risk/reward preferences is a central problem in various applications of risk management including investment science and portfolio theory in particular. One of the approaches is to axiomatically define a set of performance measures and to use a benchmark to identify a particular measure from that set by either inverse optimization or functional dominance. For example, such a benchmark could be the rate of return of an existing attractive financial instrument. This work introduces deviation and drawdown measures that incorporate rates of return of indicated financial instruments (benchmarks). For discrete distributions and discrete sample paths, portfolio problems with such measures are reduced to linear programs and solved based on historical data in cases of a single benchmark and three benchmarks used simultaneously. The optimal portfolios and corresponding benchmarks have similar expected/cumulative rates of return in sample and out of sample, but the former are considerably less volatile.
AB - Understanding and modeling of agent’s risk/reward preferences is a central problem in various applications of risk management including investment science and portfolio theory in particular. One of the approaches is to axiomatically define a set of performance measures and to use a benchmark to identify a particular measure from that set by either inverse optimization or functional dominance. For example, such a benchmark could be the rate of return of an existing attractive financial instrument. This work introduces deviation and drawdown measures that incorporate rates of return of indicated financial instruments (benchmarks). For discrete distributions and discrete sample paths, portfolio problems with such measures are reduced to linear programs and solved based on historical data in cases of a single benchmark and three benchmarks used simultaneously. The optimal portfolios and corresponding benchmarks have similar expected/cumulative rates of return in sample and out of sample, but the former are considerably less volatile.
KW - Benchmark
KW - Deviation measure
KW - Drawdown measure
KW - Portfolio optimization
UR - http://www.scopus.com/inward/record.url?scp=85196800818&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85196800818&partnerID=8YFLogxK
U2 - 10.1007/s11590-024-02124-x
DO - 10.1007/s11590-024-02124-x
M3 - Article
AN - SCOPUS:85196800818
SN - 1862-4472
VL - 18
SP - 1561
EP - 1578
JO - Optimization Letters
JF - Optimization Letters
IS - 7
ER -