44:
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risky-asset portfolio, and therefore there is nothing to prevent it from being a portfolio that invests solely in a single asset. Managing concentration risk should be part of a comprehensive risk management framework and to achieve a reduction in such a risk it is possible to add constraints that force upper bound limits to the weight that can be attributed to any single component of the optimal portfolio.
940:) in investment portfolios are popular among risk averse investors. To minimize exposure to tail risk, forecasts of asset returns using Monte-Carlo simulation with vine copulas to allow for lower (left) tail dependence (e.g., Clayton, Rotated Gumbel) across large portfolios of assets are most suitable.
853:
refers to the risk caused by holding an exposure to a single position or sector that is large enough to cause material losses to the overall portfolio when adverse events occur. If the portfolio is optimized without any constraints with regards to concentration risk, the optimal portfolio can be any
837:
are the costs of trading to change the portfolio weights. Since the optimal portfolio changes with time, there is an incentive to re-optimize frequently. However, too frequent trading would incur too-frequent transactions costs; so the optimal strategy is to find the frequency of re-optimization and
812:
Portfolio optimization is usually done subject to constraints, such as regulatory constraints, or illiquidity. These constraints can lead to portfolio weights that focus on a small sub-sample of assets within the portfolio. When the portfolio optimization process is subject to other constraints such
642:
was first defined. The model assumes that an investor aims to maximize a portfolio's expected return contingent on a prescribed amount of risk. Portfolios that meet this criterion, i.e., maximize the expected return given a prescribed amount of risk, are known as efficient portfolios. By definition,
701:
and hence can be viewed as separate asset classes; holding some of the portfolio in each class provides some diversification, and holding various specific assets within each class affords further diversification. By using such a two-step procedure one eliminates non-systematic risks both on the
696:
Portfolio optimization often takes place in two stages: optimizing weights of asset classes to hold, and optimizing weights of assets within the same asset class. An example of the former would be choosing the proportions placed in equities versus bonds, while an example of the latter would be
643:
any other portfolio yielding a higher amount of expected return must also have excessive risk. This results in a trade-off between the desired expected return and allowable risk. This risk-expected return relationship of efficient portfolios is graphically represented by a curve known as the
950:
More recently, hedge fund managers have been applying "full-scale optimization" whereby any investor utility function can be used to optimize a portfolio. It is purported that such a methodology is more practical and suitable for modern investors whose risk preferences involve reducing
905:
and the stock prices may exhibit significant differences between their historical or forecast values and what is experienced. In particular, financial crises are characterized by a significant increase in correlation of stock price movements which may seriously degrade the benefits of
731:
that can handle additional linear constraints and upper and lower bounds on holdings. Moreover, in this context, the approach provides a method for determining the entire set of efficient portfolios. Its application here was later explicated by
981:/risk preferences. It turns out that, at least in the expected utility model, and mean-deviation model, each investor can usually get a share which he/she values strictly more than his/her optimal portfolio from the individual investment.
825:
of some assets. However short-selling can be forbidden. Sometimes it is impractical to hold an asset because the associated tax cost is too high. In such cases appropriate constraints must be imposed on the optimization process.
976:
A group of investors, instead of investing individually, may choose to invest their total capital into the joint portfolio, and then divide the (uncertain) investment profit in a way which suits best their
959:
in the returns distribution of the investment portfolio. Where such methodologies involve the use of higher-moment utility functions, it is necessary to use a methodology that allows for forecasting of a
675:
functions define it as the expected portfolio return (net of transaction and financing costs) minus a cost of risk. The latter component, the cost of risk, is defined as the portfolio risk multiplied by a
929:
is important. Not accounting for these attributes can lead to severe estimation error in the correlations, variances and covariances that have negative biases (as much as 70% of the true values).
1381:
Talebi, Arash; Molaei, Sheikh (17 September 2010). "Performance investigation and comparison of two evolutionary algorithms in portfolio optimization: Genetic and particle swarm optimization".
838:
trading that appropriately trades off the avoidance of transaction costs with the avoidance of sticking with an out-of-date set of portfolio proportions. This is related to the topic of
651:. While ignoring higher moments of the return can lead to significant over-investment in risky securities, especially when volatility is high, the optimization of portfolios when return
964:
that accounts for asymmetric dependence. A suitable methodology that allows for the joint distribution to incorporate asymmetric dependence is the
Clayton Canonical Vine Copula. See
917:
with the
Gaussian copula and well-specified marginal distributions are effective. Allowing the modeling process to allow for empirical characteristics in stock returns such as
713:
defined over final portfolio wealth; the expected value of utility is to be maximized. To reflect a preference for higher rather than lower returns, this objective function is
697:
choosing the proportions of the stock sub-portfolio placed in stocks X, Y, and Z. Equities and bonds have fundamentally different financial characteristics and have different
744:
The complexity and scale of optimizing portfolios over many assets means that the work is generally done by computer. Central to this optimization is the construction of the
721:. For realistic utility functions in the presence of many assets that can be held, this approach, while theoretically the most defensible, can be computationally intensive.
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1439:. MPS/SIAM Series on Optimization. Vol. 9. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). pp. xvi+436.
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to improve diversification and further limit risk. Examples of such constraints are asset, sector, and region portfolio weight limits.
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of the return, where the corresponding probability is dictated by the risk aversion parameter. Practitioners often add additional
1685:
Fantazzinni, D. (2009). "The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study".
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1535:
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Cvitanić, Jakša; Polimenis, Vassilis; Zapatero, Fernando (1 January 2008). "Optimal portfolio allocation with higher moments".
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parameter (or unit price of risk). For return distributions that are
Gaussian, this is equivalent to maximizing a certain
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Investors may be forbidden by law to hold some assets. In some cases, unconstrained portfolio optimization would lead to
813:
as taxes, transaction costs, and management fees, the optimization process may result in an under-diversified portfolio.
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Kim, Young Shin; Giacometti, Rosella; Rachev, Svetlozar; Fabozzi, Frank J.; Mignacca, Domenico (21 November 2012).
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Different approaches to portfolio optimization measure risk differently. In addition to the traditional measure,
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Adler, Tim; Kritzman, Mark (2007). "Mean-Variance versus Full-Scale
Optimization: In and Out of Sample".
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Active
Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk
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individual asset and the asset class level. For the specific formulas for efficient portfolios, see
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842:, by which stock proportions deviate over time from some benchmark in the absence of re-balancing.
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1491:"Robust dependence modeling for high-dimensional covariance matrices with financial applications"
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Merton, Robert. September 1972. "An analytic derivation of the efficient portfolio frontier,"
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1201:"Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model"
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1714:"Canonical vine copulas in the context of modern portfolio management: Are they worth it?"
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647:. All efficient portfolios, each represented by a point on the efficient frontier, are
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Chua, David; Kritzman, Mark; Page, Sebastien (2009). "The Myth of
Diversification".
1653:"Enhancing mean–variance portfolio selection by modeling distributional asymmetries"
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1256:(1956). "The optimization of a quadratic function subject to linear constraints".
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Maginn, John L.; Tuttle, Donald L.; Pinto, Jerald E.; McLeavey,Dennis W. (2007).
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2010 2nd IEEE International
Conference on Information and Financial Engineering
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Quantitative
Portfolio Optimisation, Asset Allocation and Risk Management
956:
926:
922:
872:
612:
72:
1990:
Advanced
Portfolio Management: A Quant's Guide for Fundamental Investors
1507:
1490:
932:
Other optimization strategies that focus on minimizing tail-risk (e.g.,
587:
distribution), out of a set of considered portfolios, according to some
2892:
2751:
2528:
1108:
978:
672:
487:
312:
194:
1816:
Xia, Jianming (2004). "Multi-agent investment in incomplete markets".
909:
In a mean-variance optimization framework, accurate estimation of the
2595:
155:
1911:; Petter N. Kolm; Dessislava Pachamanova; Sergio M. Focardi (2007).
1100:
2026:
Schulmerich, Marcus; Leporcher, Yves-Michel; Eu, Ching-Hwa (2015).
1888:
Financial
Modeling of the Equity Market: From CAPM to Cointegration
1017:
List of genetic algorithm applications § Finance and Economics
603:
problem. Factors being considered may range from tangible (such as
3160:
947:
focuses on allocation of risk, rather than allocation of capital.
604:
584:
414:
255:
1952:
Strategic Risk Management: Designing Portfolios and Managing Risk
2610:
447:
282:
160:
58:
2723:
2048:
671:
utility-maximization problem. Common formulations of portfolio
727:
developed the "critical line method", a general procedure for
1886:
Fabozzi, Frank J.; Sergio M. Focardi; Petter N. Kolm (2004).
1125:
Portfolio Selection: Efficient Diversification of Investments
1712:
Low, R.K.Y.; Alcock, J.; Faff, R.; Brailsford, T. (2013).
901:
Portfolio optimization assumes the investor may have some
1552:
Humphrey, J.; Benson, K.; Low, R.K.Y.; Lee, W.L. (2015).
1040:, giving a property of mean-variance efficient portfolios
748:
for the rates of return on the assets in the portfolio.
1433:
Lectures on stochastic programming: Modeling and theory
1066:, giving the first online portfolio selection algorithm
966:
Copula (probability theory) § Quantitative finance
894:
Investment is a forward-looking activity, and thus the
709:
One approach to portfolio optimization is to specify a
1012:
Financial risk management § Investment management
1349:"Optimizing the Omega Ratio using Linear Programming"
667:
The portfolio optimization problem is specified as a
1301:
Rockafellar, R. Tyrrell; Uryasev, Stanislav (2000).
1029:, a way of showing that a portfolio is not efficient
591:. The objective typically maximizes factors such as
2451:
2312:
2277:
2229:
2141:
2093:
2086:
1852:"Cooperative games with general deviation measures"
1850:Grechuk, B., Molyboha, A., Zabarankin, M. (2013).
1529:Sefiane, Slimane and Benbouziane, Mohamed (2012).
898:of returns must be forecast rather than observed.
1971:Managing Investment Portfolios: A Dynamic Process
913:is paramount. Quantitative techniques that use
1587:"Concentrate on Concentration Risk | FINRA.org"
1917:. Hoboken, New Jersey: John Wiley & Sons.
1240:Journal of Financial and Quantitative Analysis
717:in wealth, and to reflect risk aversion it is
704:Portfolio separation in mean-variance analysis
2735:
2060:
557:
8:
1914:Robust Portfolio Optimization and Management
1687:Computational Statistics & Data Analysis
634:was introduced in a 1952 doctoral thesis by
1532:Portfolio Selection Using Genetic Algorithm
1303:"Optimization of conditional value-at-risk"
1130:(reprinted by Yale University Press, 1970,
2742:
2728:
2720:
2090:
2067:
2053:
2045:
1950:; Rattray, Sandy; Van Hemert,Otto (2021).
991:Outline of finance § Portfolio theory
879:risk measures, other measures include the
564:
550:
31:
1506:
1027:Marginal conditional stochastic dominance
1612:Chua, D.; Krizman, M.; Page, S. (2009).
711:von Neumann–Morgenstern utility function
1928:Grinold, Richard; Kahn, Ronald (1999).
1854:, Mathematical Finance, 23(2), 339–365.
1651:Low, R.K.Y.; Faff, R.; Aas, K. (2016).
1075:
579:is the process of selecting an optimal
432:
231:
183:
145:
50:
34:
1867:Baker, H. Kent; Filbeck, Greg (2015).
1471:
1460:
1002:Chance-constrained portfolio selection
3211:Valuation using discounted cash flows
972:Cooperation in portfolio optimization
783:for multistage portfolio optimization
7:
1554:"Is diversification always optimal?"
1022:Machine learning § Applications
955:, minimizing negative skewness and
619:) to intangible (such as selective
1259:Naval Research Logistics Quarterly
1128:. New York: John Wiley & Sons.
25:
2028:Applied Asset and Risk Management
1660:Journal of Economics and Business
1489:Zhu, Zhe; Welsch, Roy E. (2018).
1343:Kapsos, Michalis; Zymler, Steve;
1138:; 2nd ed. Basil Blackwell, 1991,
797:Deterministic global optimization
792:Principal component-based methods
2342:Conditional Value-at-Risk (CVaR)
1721:Journal of Banking & Finance
1356:Journal of Computational Finance
885:CVaR (Conditional Value at Risk)
863:Correlations and risk evaluation
858:Improving portfolio optimization
42:
27:Process of selecting a portfolio
3111:Quantitative behavioral finance
1988:Paleologo, Giuseppe A. (2021).
1756:Journal of Portfolio Management
1618:Journal of Portfolio Management
659:is mathematically challenging.
3151:Strategic financial management
2798:Bull (stock market speculator)
2661:Strategic financial management
2464:Asset and liability management
1733:10.1016/j.jbankfin.2013.02.036
1672:10.1016/j.jeconbus.2016.01.003
1347:; Rustem, Berç (Summer 2014).
1083:Markowitz, H.M. (March 1952).
1038:Mutual fund separation theorem
1007:Intertemporal portfolio choice
1:
3181:Sustainable Development Goals
1932:(2nd ed.). McGraw Hill.
1614:"The Myth of Diversification"
1561:Pacific Basin Finance Journal
1205:Annals of Operations Research
1064:Universal portfolio algorithm
1573:10.1016/j.pacfin.2015.09.003
601:multi-objective optimization
2239:Operational risk management
1791:Journal of Asset Management
1059:Stochastic portfolio theory
595:, and minimizes costs like
3258:
2863:Enterprise risk management
2411:Proportional hazards model
2362:Interest rate immunization
1973:(3rd ed.). Springer.
1869:Investment Risk Management
1699:10.1016/j.csda.2008.02.002
1391:10.1109/icife.2010.5609394
1033:Merton's portfolio problem
911:variance-covariance matrix
2848:Diversification (finance)
2758:
2694:
2080:financial risk management
1830:10.1007/s00780-003-0115-2
1768:10.3905/JPM.2009.36.1.026
1630:10.3905/JPM.2009.36.1.026
1289:Macro-Investment Analysis
1217:10.1007/s10479-012-1229-8
1170:10.1007/s10436-007-0071-5
938:conditional value at risk
921:, asymmetric volatility,
771:Mixed integer programming
493:Guaranteed minimum income
288:Diversification (finance)
2357:First-hitting-time model
2322:Arbitrage pricing theory
1285:The Critical Line Method
1122:Markowitz, H.M. (1959).
808:Optimization constraints
171:Employee stock ownership
118:Refund anticipation loan
2666:Stress test (financial)
2372:Modern portfolio theory
1992:(1st ed.). Wiley.
1818:Finance and Stochastics
1803:10.2469/dig.v37.n3.4799
632:Modern portfolio theory
627:Modern portfolio theory
88:Unsecured personal loan
3061:Investment performance
2763:Alternative investment
2011:. Palgrave Macmillan.
2007:Rasmussen, M. (2003).
1272:10.1002/nav.3800030110
1089:The Journal of Finance
915:Monte-Carlo simulation
889:statistical dispersion
781:Stochastic programming
776:Meta-heuristic methods
577:Portfolio optimization
528:Universal basic income
405:Portfolio optimization
380:Investment performance
251:Alternative investment
3056:Investment management
3041:International finance
2868:Environmental finance
2828:Computational finance
2704:Investment management
2606:Investment management
2332:Replicating portfolio
2108:Sovereign credit risk
1538:29 April 2016 at the
1368:10.21314/JCF.2014.283
1322:10.21314/JOR.2000.038
1085:"Portfolio Selection"
766:Nonlinear programming
761:Quadratic programming
729:quadratic programming
3121:Risk-return spectrum
3076:Mathematical finance
2996:Fundamental analysis
2990:Financial technology
2888:Experimental finance
2883:Exchange traded fund
2709:Mathematical finance
2641:Risk-return spectrum
2631:Mathematical finance
2586:Fundamental analysis
2519:Exchange traded fund
2103:Consumer credit risk
1428:Ruszczyński, Andrzej
1422:Shapiro, Alexander;
1385:. pp. 430–437.
993:for related articles
817:Regulation and taxes
787:Copula based methods
751:Techniques include:
663:Optimization methods
533:Volatility (finance)
503:Risk-return spectrum
345:Fundamental analysis
211:Defined contribution
18:Critical line method
3237:Financial economics
3186:Sustainable finance
3156:Statistical finance
3136:Statistical finance
3046:Investment advisory
3006:Greater fool theory
2699:Financial economics
2656:Statistical finance
2422:Value-at-Risk (VaR)
2327:Black–Scholes model
2167:Holding period risk
1871:. Oxford Academic.
1508:10.1214/17-AOAS1087
1345:Christofides, Nicos
1287:in William Sharpe,
692:Specific approaches
478:Financial inclusion
473:Financial deepening
375:Investment advisory
147:Employment contract
3242:Portfolio theories
3171:Structured product
3166:Structured finance
3051:Investment banking
3026:History of banking
2813:Capital management
2676:Structured product
2671:Structured finance
2651:Speculative attack
2337:Cash flow matching
2300:Non-financial risk
2197:Interest rate risk
2123:Concentration risk
1470:Unknown parameter
1424:Dentcheva, Darinka
1046:, for the formulas
962:joint distribution
869:standard deviation
851:Concentration risk
846:Concentration risk
756:Linear programming
740:Mathematical tools
645:efficient frontier
513:Structured product
453:Citizen's dividend
400:Passive management
128:Debt consolidation
3224:
3223:
3101:Position of trust
2833:Corporate finance
2818:Capital structure
2778:Asset (economics)
2750:General areas of
2717:
2716:
2489:Corporate finance
2484:Capital structure
2438:Cash flow at risk
2434:Liquidity at risk
2407:Survival analysis
2308:
2307:
2254:Reputational risk
2128:Credit derivative
1954:. Wiley Finance.
1923:978-0-471-92122-6
1909:Fabozzi, Frank J.
1446:978-0-89871-687-0
1400:978-1-4244-6927-7
1158:Annals of Finance
1144:978-1-55786-108-5
1136:978-0-300-01372-6
906:diversification.
875:), which are not
871:, or its square (
835:Transaction costs
830:Transaction costs
802:Genetic algorithm
746:covariance matrix
599:, resulting in a
574:
573:
246:Active management
176:Employee benefits
133:Debt rescheduling
16:(Redirected from
3249:
3096:Personal finance
3086:Over-the-counter
3066:Investor profile
3036:Impact investing
3031:History of money
3011:Growth investing
2873:Equity (finance)
2783:Asset allocation
2744:
2737:
2730:
2721:
2591:Growth investing
2509:Enterprise value
2459:Asset allocation
2442:Earnings at risk
2424:and extensions (
2367:Market portfolio
2231:Operational risk
2216:Refinancing risk
2091:
2069:
2062:
2055:
2046:
2041:
2022:
2003:
1984:
1965:
1948:Harvey, Campbell
1943:
1905:
1882:
1855:
1848:
1842:
1841:
1813:
1807:
1806:
1786:
1780:
1779:
1751:
1745:
1744:
1718:
1709:
1703:
1702:
1693:(6): 2168–2188.
1682:
1676:
1675:
1657:
1648:
1642:
1641:
1609:
1603:
1602:
1600:
1598:
1583:
1577:
1576:
1558:
1549:
1543:
1527:
1521:
1520:
1510:
1501:(2): 1228–1249.
1486:
1480:
1479:
1473:
1468:
1466:
1458:
1438:
1419:
1413:
1412:
1378:
1372:
1371:
1353:
1340:
1334:
1333:
1307:
1298:
1292:
1282:
1276:
1275:
1266:(1–2): 111–133.
1254:Markowitz, Harry
1250:
1244:
1235:
1229:
1228:
1196:
1190:
1189:
1153:
1147:
1129:
1119:
1113:
1112:
1080:
1054:Tail risk parity
1044:Portfolio theory
997:Asset allocation
649:well-diversified
566:
559:
552:
435:
425:Target date fund
390:Investor profile
385:Investment style
370:Impact investing
355:Growth investing
293:Equity (finance)
166:Salary packaging
46:
36:Personal finance
32:
21:
3257:
3256:
3252:
3251:
3250:
3248:
3247:
3246:
3227:
3226:
3225:
3220:
3201:Too big to fail
3196:Systematic risk
3116:Quantum finance
3021:Hedge (finance)
3001:Government bond
2838:Cost of capital
2823:Climate finance
2754:
2748:
2718:
2713:
2690:
2626:Systematic risk
2524:Expected return
2504:Economic bubble
2499:Diversification
2494:Cost of capital
2447:
2304:
2273:
2225:
2207:Volatility risk
2171:Price area risk
2137:
2113:Settlement risk
2082:
2073:
2038:
2025:
2019:
2006:
2000:
1987:
1981:
1968:
1962:
1946:
1940:
1927:
1902:
1890:. Hoboken, NJ:
1885:
1879:
1866:
1863:
1858:
1849:
1845:
1815:
1814:
1810:
1788:
1787:
1783:
1753:
1752:
1748:
1716:
1711:
1710:
1706:
1684:
1683:
1679:
1655:
1650:
1649:
1645:
1611:
1610:
1606:
1596:
1594:
1585:
1584:
1580:
1556:
1551:
1550:
1546:
1540:Wayback Machine
1528:
1524:
1495:Ann. Appl. Stat
1488:
1487:
1483:
1469:
1459:
1447:
1436:
1421:
1420:
1416:
1401:
1380:
1379:
1375:
1351:
1342:
1341:
1337:
1310:Journal of Risk
1305:
1300:
1299:
1295:
1283:
1279:
1252:
1251:
1247:
1236:
1232:
1198:
1197:
1193:
1155:
1154:
1150:
1121:
1120:
1116:
1101:10.2307/2975974
1082:
1081:
1077:
1073:
987:
974:
865:
860:
848:
832:
819:
810:
742:
725:Harry Markowitz
699:systematic risk
694:
665:
640:Markowitz model
636:Harry Markowitz
629:
593:expected return
570:
523:Systematic risk
508:Social dividend
468:Economic bubble
433:
365:Hedge (finance)
350:Government bond
303:Estate planning
233:Personal budget
227:
223:Social security
206:Defined benefit
199:
28:
23:
22:
15:
12:
11:
5:
3255:
3253:
3245:
3244:
3239:
3229:
3228:
3222:
3221:
3219:
3218:
3213:
3208:
3203:
3198:
3193:
3191:Swap (finance)
3188:
3183:
3178:
3176:Sustainability
3173:
3168:
3163:
3158:
3153:
3148:
3143:
3141:Stock exchange
3138:
3133:
3128:
3126:Social finance
3123:
3118:
3113:
3108:
3106:Public finance
3103:
3098:
3093:
3088:
3083:
3078:
3073:
3068:
3063:
3058:
3053:
3048:
3043:
3038:
3033:
3028:
3023:
3018:
3013:
3008:
3003:
2998:
2993:
2987:
2986:
2985:
2980:
2975:
2970:
2965:
2960:
2955:
2950:
2945:
2940:
2935:
2930:
2925:
2920:
2915:
2910:
2905:
2900:
2890:
2885:
2880:
2875:
2870:
2865:
2860:
2855:
2850:
2845:
2840:
2835:
2830:
2825:
2820:
2815:
2810:
2805:
2800:
2795:
2793:Bond (finance)
2790:
2785:
2780:
2775:
2770:
2768:Angel investor
2765:
2759:
2756:
2755:
2749:
2747:
2746:
2739:
2732:
2724:
2715:
2714:
2712:
2711:
2706:
2701:
2695:
2692:
2691:
2689:
2688:
2683:
2678:
2673:
2668:
2663:
2658:
2653:
2648:
2643:
2638:
2633:
2628:
2623:
2618:
2613:
2608:
2603:
2598:
2593:
2588:
2583:
2582:
2581:
2576:
2571:
2566:
2561:
2556:
2551:
2546:
2541:
2536:
2526:
2521:
2516:
2511:
2506:
2501:
2496:
2491:
2486:
2481:
2476:
2471:
2466:
2461:
2455:
2453:
2452:Basic concepts
2449:
2448:
2446:
2445:
2430:Margin at risk
2426:Profit at risk
2419:
2417:Tracking error
2414:
2404:
2399:
2394:
2389:
2387:Risk-free rate
2384:
2379:
2374:
2369:
2364:
2359:
2354:
2349:
2344:
2339:
2334:
2329:
2324:
2318:
2316:
2310:
2309:
2306:
2305:
2303:
2302:
2297:
2292:
2287:
2285:Execution risk
2281:
2279:
2275:
2274:
2272:
2271:
2266:
2264:Political risk
2261:
2256:
2251:
2246:
2241:
2235:
2233:
2227:
2226:
2224:
2223:
2212:Liquidity risk
2209:
2204:
2202:Inflation risk
2199:
2194:
2192:Margining risk
2189:
2184:
2182:Valuation risk
2179:
2174:
2151:Commodity risk
2147:
2145:
2139:
2138:
2136:
2135:
2133:Securitization
2130:
2125:
2120:
2115:
2110:
2105:
2099:
2097:
2088:
2084:
2083:
2076:Financial risk
2074:
2072:
2071:
2064:
2057:
2049:
2043:
2042:
2037:978-3642554438
2036:
2023:
2018:978-1403904584
2017:
2004:
1999:978-1119789796
1998:
1985:
1980:978-0470080146
1979:
1966:
1961:978-1119773917
1960:
1944:
1939:978-0070248823
1938:
1925:
1906:
1900:
1883:
1878:978-0199331963
1877:
1862:
1859:
1857:
1856:
1843:
1824:(2): 241–259.
1808:
1781:
1746:
1704:
1677:
1643:
1604:
1593:. 15 June 2022
1578:
1544:
1522:
1481:
1445:
1414:
1399:
1373:
1335:
1293:
1277:
1245:
1230:
1211:(1): 325–343.
1191:
1148:
1114:
1074:
1072:
1069:
1068:
1067:
1061:
1056:
1047:
1041:
1035:
1030:
1024:
1019:
1014:
1009:
1004:
999:
994:
986:
983:
973:
970:
919:autoregression
864:
861:
859:
856:
847:
844:
840:tracking error
831:
828:
818:
815:
809:
806:
805:
804:
799:
794:
789:
784:
778:
773:
768:
763:
758:
741:
738:
734:William Sharpe
693:
690:
664:
661:
628:
625:
597:financial risk
572:
571:
569:
568:
561:
554:
546:
543:
542:
541:
540:
535:
530:
525:
520:
518:Sustainability
515:
510:
505:
500:
495:
490:
485:
483:Financial risk
480:
475:
470:
465:
460:
455:
450:
445:
437:
436:
430:
429:
428:
427:
422:
417:
412:
407:
402:
397:
392:
387:
382:
377:
372:
367:
362:
357:
352:
347:
342:
341:
340:
335:
330:
325:
320:
310:
305:
300:
295:
290:
285:
280:
278:Bond (finance)
275:
274:
273:
268:
263:
253:
248:
240:
239:
229:
228:
226:
225:
220:
219:
218:
216:Social pension
213:
208:
200:
198:
197:
191:
188:
187:
181:
180:
179:
178:
173:
168:
163:
158:
150:
149:
143:
142:
141:
140:
135:
130:
125:
120:
115:
110:
105:
100:
95:
90:
85:
80:
75:
70:
62:
61:
48:
47:
39:
38:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3254:
3243:
3240:
3238:
3235:
3234:
3232:
3217:
3216:Watered stock
3214:
3212:
3209:
3207:
3204:
3202:
3199:
3197:
3194:
3192:
3189:
3187:
3184:
3182:
3179:
3177:
3174:
3172:
3169:
3167:
3164:
3162:
3159:
3157:
3154:
3152:
3149:
3147:
3144:
3142:
3139:
3137:
3134:
3132:
3129:
3127:
3124:
3122:
3119:
3117:
3114:
3112:
3109:
3107:
3104:
3102:
3099:
3097:
3094:
3092:
3089:
3087:
3084:
3082:
3079:
3077:
3074:
3072:
3069:
3067:
3064:
3062:
3059:
3057:
3054:
3052:
3049:
3047:
3044:
3042:
3039:
3037:
3034:
3032:
3029:
3027:
3024:
3022:
3019:
3017:
3014:
3012:
3009:
3007:
3004:
3002:
2999:
2997:
2994:
2991:
2988:
2984:
2981:
2979:
2976:
2974:
2971:
2969:
2966:
2964:
2961:
2959:
2956:
2954:
2951:
2949:
2946:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2924:
2921:
2919:
2916:
2914:
2911:
2909:
2906:
2904:
2901:
2899:
2896:
2895:
2894:
2891:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2858:Eco-investing
2856:
2854:
2851:
2849:
2846:
2844:
2843:Disinvestment
2841:
2839:
2836:
2834:
2831:
2829:
2826:
2824:
2821:
2819:
2816:
2814:
2811:
2809:
2808:Capital asset
2806:
2804:
2801:
2799:
2796:
2794:
2791:
2789:
2786:
2784:
2781:
2779:
2776:
2774:
2771:
2769:
2766:
2764:
2761:
2760:
2757:
2753:
2745:
2740:
2738:
2733:
2731:
2726:
2725:
2722:
2710:
2707:
2705:
2702:
2700:
2697:
2696:
2693:
2687:
2684:
2682:
2681:Systemic risk
2679:
2677:
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2657:
2654:
2652:
2649:
2647:
2644:
2642:
2639:
2637:
2634:
2632:
2629:
2627:
2624:
2622:
2619:
2617:
2614:
2612:
2609:
2607:
2604:
2602:
2599:
2597:
2594:
2592:
2589:
2587:
2584:
2580:
2577:
2575:
2572:
2570:
2567:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2545:
2542:
2540:
2537:
2535:
2532:
2531:
2530:
2527:
2525:
2522:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2492:
2490:
2487:
2485:
2482:
2480:
2479:Capital asset
2477:
2475:
2472:
2470:
2469:Asset pricing
2467:
2465:
2462:
2460:
2457:
2456:
2454:
2450:
2443:
2439:
2435:
2431:
2427:
2423:
2420:
2418:
2415:
2412:
2408:
2405:
2403:
2402:Sortino ratio
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2325:
2323:
2320:
2319:
2317:
2315:
2311:
2301:
2298:
2296:
2295:Systemic risk
2293:
2291:
2288:
2286:
2283:
2282:
2280:
2276:
2270:
2267:
2265:
2262:
2260:
2257:
2255:
2252:
2250:
2247:
2245:
2244:Business risk
2242:
2240:
2237:
2236:
2234:
2232:
2228:
2221:
2217:
2213:
2210:
2208:
2205:
2203:
2200:
2198:
2195:
2193:
2190:
2188:
2185:
2183:
2180:
2178:
2175:
2172:
2168:
2164:
2160:
2156:
2152:
2149:
2148:
2146:
2144:
2140:
2134:
2131:
2129:
2126:
2124:
2121:
2119:
2116:
2114:
2111:
2109:
2106:
2104:
2101:
2100:
2098:
2096:
2092:
2089:
2085:
2081:
2077:
2070:
2065:
2063:
2058:
2056:
2051:
2050:
2047:
2039:
2033:
2029:
2024:
2020:
2014:
2010:
2005:
2001:
1995:
1991:
1986:
1982:
1976:
1972:
1967:
1963:
1957:
1953:
1949:
1945:
1941:
1935:
1931:
1926:
1924:
1920:
1916:
1915:
1910:
1907:
1903:
1901:0-471-69900-4
1897:
1893:
1889:
1884:
1880:
1874:
1870:
1865:
1864:
1860:
1853:
1847:
1844:
1839:
1835:
1831:
1827:
1823:
1819:
1812:
1809:
1804:
1800:
1796:
1792:
1785:
1782:
1777:
1773:
1769:
1765:
1761:
1757:
1750:
1747:
1742:
1738:
1734:
1730:
1726:
1722:
1715:
1708:
1705:
1700:
1696:
1692:
1688:
1681:
1678:
1673:
1669:
1665:
1661:
1654:
1647:
1644:
1639:
1635:
1631:
1627:
1623:
1619:
1615:
1608:
1605:
1592:
1591:www.finra.org
1588:
1582:
1579:
1574:
1570:
1566:
1562:
1555:
1548:
1545:
1541:
1537:
1534:
1533:
1526:
1523:
1518:
1514:
1509:
1504:
1500:
1496:
1492:
1485:
1482:
1477:
1472:|agency=
1464:
1456:
1452:
1448:
1442:
1435:
1434:
1429:
1425:
1418:
1415:
1410:
1406:
1402:
1396:
1392:
1388:
1384:
1377:
1374:
1369:
1365:
1361:
1357:
1350:
1346:
1339:
1336:
1331:
1327:
1323:
1319:
1315:
1311:
1304:
1297:
1294:
1291:(online text)
1290:
1286:
1281:
1278:
1273:
1269:
1265:
1261:
1260:
1255:
1249:
1246:
1243:7, 1851–1872.
1242:
1241:
1234:
1231:
1226:
1222:
1218:
1214:
1210:
1206:
1202:
1195:
1192:
1187:
1183:
1179:
1175:
1171:
1167:
1163:
1159:
1152:
1149:
1145:
1141:
1137:
1133:
1127:
1126:
1118:
1115:
1110:
1106:
1102:
1098:
1094:
1090:
1086:
1079:
1076:
1070:
1065:
1062:
1060:
1057:
1055:
1051:
1048:
1045:
1042:
1039:
1036:
1034:
1031:
1028:
1025:
1023:
1020:
1018:
1015:
1013:
1010:
1008:
1005:
1003:
1000:
998:
995:
992:
989:
988:
984:
982:
980:
971:
969:
967:
963:
958:
954:
948:
946:
943:
939:
935:
934:value at risk
930:
928:
924:
920:
916:
912:
907:
904:
903:risk aversion
899:
897:
892:
890:
886:
882:
881:Sortino ratio
878:
874:
870:
862:
857:
855:
852:
845:
843:
841:
836:
829:
827:
824:
823:short-selling
816:
814:
807:
803:
800:
798:
795:
793:
790:
788:
785:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
753:
752:
749:
747:
739:
737:
735:
730:
726:
722:
720:
716:
712:
707:
705:
700:
691:
689:
687:
683:
679:
678:risk aversion
674:
670:
662:
660:
658:
654:
653:distributions
650:
646:
641:
637:
633:
626:
624:
622:
618:
614:
610:
606:
602:
598:
594:
590:
586:
582:
578:
567:
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2621:Risk of ruin
2397:Sharpe ratio
2259:Country risk
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2118:Default risk
2030:. Springer.
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98:Student loan
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3146:Stockbroker
3131:Speculation
3081:Mutual fund
3071:Market risk
2978:social work
2928:engineering
2773:Super angel
2686:Toxic asset
2646:Speculation
2579:social work
2564:engineering
2392:Risk parity
2377:Omega ratio
2290:Profit risk
2177:Equity risk
2155:Volume risk
2143:Market risk
2095:Credit risk
1727:(8): 3085.
1164:(1): 1–28.
1050:Risk parity
945:risk parity
896:covariances
686:constraints
669:constrained
609:liabilities
458:Cooperative
420:Stockbroker
410:Speculation
395:Market risk
123:Refinancing
113:Payday loan
93:Rent-to-own
83:Credit card
78:Charge card
3231:Categories
2963:regulation
2943:management
2853:Divestment
2269:Legal risk
2249:Model risk
2163:Shape risk
2159:Basis risk
2087:Categories
1071:References
715:increasing
621:divestment
261:allocation
237:investment
185:Retirement
138:Bankruptcy
108:Title loan
2992:(Fintech)
2933:inclusion
2923:economics
2918:deepening
2893:Financial
2616:Risk pool
2529:Financial
1776:154921810
1741:154138333
1666:: 49–72.
1638:154921810
1474:ignored (
1463:cite book
1178:1614-2446
957:fat tails
953:tail risk
615:or other
589:objective
581:portfolio
313:Financial
266:economics
2973:services
2898:analysis
2788:Bad debt
2539:analysis
2474:Bad debt
2352:Drawdown
2314:Modeling
1597:16 March
1567:(B): B.
1536:Archived
1517:23490041
1430:(2009).
1409:17386345
1225:45585936
1186:16514619
985:See also
927:kurtosis
923:skewness
873:variance
682:quantile
657:Gaussian
655:are non-
613:earnings
434:See also
73:Car loan
68:Mortgage
2958:planner
2903:analyst
2752:finance
2554:betting
2544:analyst
2534:adviser
2187:FX risk
1838:7162635
1455:2562798
1109:2975974
979:utility
719:concave
673:utility
488:Fintech
333:planner
318:adviser
195:Pension
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2948:market
2596:Hazard
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887:, and
877:robust
605:assets
271:growth
156:Salary
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3161:Stock
2913:crime
2908:asset
2601:Hedge
2559:crime
2549:asset
2382:RAROC
2278:Other
1892:Wiley
1834:S2CID
1772:S2CID
1737:S2CID
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1105:JSTOR
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415:Stock
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256:Asset
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2013:ISBN
1994:ISBN
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1476:help
1441:ISBN
1395:ISBN
1174:ISSN
1140:ISBN
1132:ISBN
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2878:ESG
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