On the Use and Misuse of Downside Risk

Sortino, Frank A.; Forsey, Hal J.

doi:10.3905/jpm.1996.35

Cited by 113 publications

(57 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For normal and Student-t-distributions of returns the LPM based model reduces to the conventional CAPM. Empirical and simulation studies show the superiority of mean-LPM based portfolio selection criteria towards the traditional mean-variance based approach under the assumption of shortfall-risk oriented investors (Porter/Gaumnitz 1972;Russell/Seo 1980;Leibowitz/Langetieg 1989;Nawrocki/Staples 1989;Sortino/van der Meer 1991;Sortino/Forsey 1996;Harlow 1991). An empirical study using data from the German stock market shows that regressions with LPM-betas explain stock returns better than regressions with traditional betas.…”

Section: Lower Partial Moments In Finance Theorymentioning

confidence: 99%

Lower partial moments as measures of perceived risk: An experimental study

Unser¹

2000

Journal of Economic Psychology

121

View full text Add to dashboard Cite

Abstract:The paper reports the results of an experiment on individual investors' risk perception in a stock market context under two different modes of information presentation (framings). While the concentration on two moments of a return distribution has been a cornerstone of neo-classic finance theory from the start (Markowitz 1952) an alternative's mean and variance have been selected more by convenience and ease of computation than by theoretical or empirical justification. Even though the most influential models are based on variance as risk measure there has always been much discontent with this proposal. The symmetrical nature of variance does not capture the common notion of risk as something undesired, e. g. negative deviations from a reference point. Instead, lower partial moments (LPM) seem to be more appropriate for measuring risk. The purpose of this paper is to examine experimentally private investors' risk perception in a financial context. The focus is on the correspondence of people's risk perceptions with specific LPMs. The main findings can be summarized as follows. First, symmetrical risk measures like variance can be clearly dismissed in favor of shortfall measures like LPMs. Second, the reference point (target) of individuals for defining losses is not a distribution's mean but the initial price in a time series of stock prices. Third, the LPM which explains risk perception best is the LPM 0 , i. e. the probability of loss. Fourth, the framing of price distributions (histograms versus charts) exerts a significance influence on average risk ratings, the latter being higher for the histogram framing. Fifth, positive deviations from an individual reference point tend to decrease perceived risk.

show abstract

Section: Lower Partial Moments In Finance Theorymentioning

confidence: 99%

Lower partial moments as measures of perceived risk: An experimental study

Unser¹

2000

Journal of Economic Psychology

121

View full text Add to dashboard Cite

show abstract

“…Moreover, there remains an important issue: how does one actually go about calculating these higher moments? To quote Sortino and Forsey [36] who state a popular belief: "Others might say it is difficult enough to estimate the mean and variance; attempting to estimate higher moments is pretentious or superfluous." More importantly, skewness and kurtosis are not so intuitive for many industry practitioners, so advocating a model based on these might prove to be difficult.…”

Section: Introductionmentioning

confidence: 99%

“…However, these techniques usually result in large forecast errors since the data is sporadic (Fildes and Beard [16]). In finance literature, Sortino and Forsey [36] suggest fitting the data to a three-parameter lognormal distribution. Another model proposed by Knight, Satchell and Tran [25] involves partitioning the distribution into the upper and lower partial distributions with respect to some benchmark.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymmetry and Ambiguity in Newsvendor Models

2018

View full text Add to dashboard Cite

The traditional decision-making framework for newsvendor models is to assume a distribution of the underlying demand. However, the resulting optimal policy is typically sensitive to the choice of the distribution. A more conservative approach is to assume that the distribution belongs to a set parameterized by a few known moments. An ambiguity-averse newsvendor would choose to maximize the worst-case profit. Most models of this type assume that only the mean and the variance are known, but do not attempt to include asymmetry properties of the distribution. Other recent models address asymmetry by including skewness and kurtosis. However, closed-form expressions on the optimal bounds are difficult to find for such models. In this paper, we propose a framework under which the expectation of a piecewise linear objective function is optimized over a set of distributions with known asymmetry properties. This asymmetry is represented by the first two moments of multiple random variables that result from partitioning the original distribution. In the simplest case, this reduces to semivariance. The optimal bounds can be solved through a second-order cone programming (SOCP) problem. This framework can be applied to the risk-averse and risk-neutral newsvendor problems and option pricing. We provide a closed-form expression for the worst-case newsvendor profit with only mean, variance and semivariance information.

show abstract

“…This led Markowitz (1959) to propose downside risk measures such as downside standard deviation and semivarianceσ 2 (x) = T t=1 (max{0, μ(x) − n j=1 r jt x j }) 2 p t to replace variance as the risk measure. Consequently, one observes growing popularity of downside risk models for portfolio selection Sortino and Forsey (1996). Several other risk measures (x) have been later considered thus creating the entire family of mean-risk models (cf., Mansini et al 2014Mansini et al , 2015.…”

Section: Portfolio Optimization and Risk Measuresmentioning

confidence: 99%

Efficient optimization of the reward-risk ratio with polyhedral risk measures

Ogryczak

Śliwiński

2017

Math Meth Oper Res

View full text Add to dashboard Cite

In problems of portfolio selection the reward-risk ratio criterion is optimized to search for a risky portfolio offering the maximum increase of the mean return, compared to the risk-free investment opportunities. In the classical model, following Markowitz, the risk is measured by the variance thus representing the Sharpe ratio optimization and leading to the quadratic optimization problems. Several polyhedral risk measures, being linear programming (LP) computable in the case of discrete random variables represented by their realizations under specified scenarios, have been introduced and applied in portfolio optimization. The reward-risk ratio optimization with polyhedral risk measures can be transformed into LP formulations. The LP models typically contain the number of constraints proportional to the number of scenarios while the number of variables (matrix columns) proportional to the total of the number of scenarios and the number of instruments. Real-life financial decisions are usually based on more advanced simulation models employed for scenario generation where one may get several thousands scenarios. This may lead to the LP models with huge number of variables and constraints thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by alternative models based on the inverse ratio minimization and taking advantages of the LP duality. In the introduced models the number of structural constraints (matrix rows) is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability.

show abstract

On the Use and Misuse of Downside Risk

Cited by 113 publications

References 0 publications

Lower partial moments as measures of perceived risk: An experimental study

Lower partial moments as measures of perceived risk: An experimental study

Asymmetry and Ambiguity in Newsvendor Models

Efficient optimization of the reward-risk ratio with polyhedral risk measures

Contact Info

Product

Resources

About