Elicitable distortion risk measures: A concise proof

Elicitability has recently been discussed as a desirable property for risk measures. Kou and Peng (2014) showed that an elicitable distortion risk measure is either a Value-at-Risk or the mean. We give a concise alternative proof of this result, and discuss the conflict between comonotonic additivity and elicitability.

Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting

In this note, we comment on the relevance of elicitability for backtesting risk measure estimates. In particular, we propose the use of Diebold-Mariano tests, and show how they can be implemented for Expected Shortfall (ES), based on the recent result of Fissler and Ziegel (2015) that ES is jointly elicitable with Value at Risk.

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor’s problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio return.

Choosing a random distribution with prescribed risks

We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating rather general random probability distributions on the unit interval. A new algorithm based on the simulation of a weighted barycentres array is suggested to generate random probability distributions with a given value of the spectral risk measure.

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor’s problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio return.

Coherence and Elicitability

The risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical decision theory, risk measures for which such verification and comparison is possible, are called elicitable. It is known that quantile-based risk measures such as value at risk are elicitable. In this paper, the existing result of the nonelicitability of expected shortfall is extended to all law-invariant spectral risk measures unless they reduce to minus the expected value. Hence, it is unclear how to perform forecast verification or comparison. However, the class of elicitable law-invariant coherent risk measures does not reduce to minus the expected value. We show that it consists of certain expectiles.

The risk of musculoskeletal disorders for workers due to repetitive movements during tomato harvesting

Tomatoes are the most common crop in Italy. The production cycle requires operations in the field and factory that can cause musculoskeletal disorders due to the repetitive movements of the upper limbs of the workers employed in the sorting phase. This research aims to evaluate these risks using the OCRA (occupational repetitive actions) index method This method is based firstly on the calculation of a maximum number of recommended actions, related to the way the operation is performed, and secondly on a comparison of the number of actions effectively carried out by the upper limb with the recommended calculated value. The results of the risk evaluation for workers who manually sort tomatoes during harvest showed a risk for the workers, with an exposure index greater than 20; the OCRA index defines an index higher than 3.5 as unacceptable. The present trend of replacing manual sorting onboard a vehicle with optical sorters seems to be appropriate to reduce the risk of work-related musculoskeletal disorders (WMSDs) and is supported from both a financial point of view and as a quality control measure.

Risk of sequelae after Chlamydia trachomatis genital infection in women

Chlamydia trachomatis infection, the most common reportable disease in the United States, can lead to pelvic inflammatory disease (PID), infertility, ectopic pregnancy, and chronic pelvic pain. Although C. trachomatis is identified among many women who receive a diagnosis of PID, the incidence and timing of PID and long-term sequelae from an untreated chlamydial infection have not been fully determined. This article examines evidence reviewed as part of the Centers for Disease Control and Prevention Chlamydia Immunology and Control Expert Advisory Meeting; 24 reports were included. We found no prospective studies directly assessing risk of long-term reproductive sequelae, such as infertility, after untreated C. trachomatis infection. Several studies assessed PID diagnosis after untreated chlamydial infection, but rates varied widely, making it difficult to determine an overall estimate. In high-risk settings, 2%-5% of untreated women developed PID within the approximately 2-week period between testing positive for C. trachomatis and returning for treatment. However, the rate of PID progression in the general, asymptomatic population followed up for longer periods appeared to be low. According to the largest studies, after symptomatic PID of any cause has occurred, up to 18% of women may develop infertility. In several studies, repeated chlamydial infection was associated with PID and other reproductive sequelae, although it was difficult to determine whether the risk per infection increased with each recurrent episode. The present review critically evaluates this body of literature and suggests future research directions. Specifically, prospective studies assessing rates of symptomatic PID, subclinical tubal damage, and long-term reproductive sequelae after C. trachomatis infection; better tools to measure PID and tubal damage; and studies on the natural history of repeated chlamydial infections are needed.

Risk factors for geriatric patient falls in rehabilitation hospital settings: a systematic review

Objective: To review the literature to identify and synthesize the evidence on risk factors for patient falls in geriatric rehabilitation hospital settings. Data sources: Eligible studies were systematically searched on 16 databases from inception to December 2010. Review methods: The search strategies used a combination of terms for rehabilitation hospital patients, falls, risk factors and older adults. Cross-sectional, cohort, case-control studies and randomized clinical trials (RCTs) published in English that investigated risks for falls among patients ≥65 years of age in rehabilitation hospital settings were included. Studies that investigated fall risk assessment tools, but did not investigate risk factors themselves or did not report a measure of risk (e.g. odds ratio, relative risk) were excluded. Results: A total of 2,824 references were identified; only eight articles concerning six studies met the inclusion criteria. In these, 1,924 geriatric rehabilitation patients were followed. The average age of the patients ranged from 77 to 83 years, the percentage of women ranged from 56% to 81%, and the percentage of fallers ranged from 15% to 54%. Two were case-control studies, two were RCTs and four were prospective cohort studies. Several intrinsic and extrinsic risk factors for falls were identified. Conclusion: Carpet flooring, vertigo, being an amputee, confusion, cognitive impairment, stroke, sleep disturbance, anticonvulsants, tranquilizers and antihypertensive medications, age between 71 and 80, previous falls, and need for transfer assistance are risk factors for geriatric patient falls in rehabilitation hospital settings.

Health risk appraisal in older people 3: prevalence, impact, and context of pain and their implications for GPs

BACKGROUND: Pain is a common experience in later life. There is conflicting evidence of the prevalence, impact, and context of pain in older people. GPs are criticised for underestimating and under-treating pain. AIM: To assess the extent to which older people experience pain, and to explore relationships between self-reported pain and functional ability and depression. DESIGN OF STUDY: Secondary analysis of baseline data from a randomised controlled trial of health risk appraisal. SETTING: A total of 1090 community-dwelling non-disabled people aged 65 years and over were included in the study from three group practices in suburban London. METHOD: Main outcome measures were pain in the last 4 weeks and the impact of pain, measured using the 24-item Geriatric Pain Measure; depression symptoms captured using the 5-item Mental Health Inventory; social relationships measured using the 6-item Lubben Social Network Scale; Basic and Instrumental Activities of Daily Living and self-reported symptoms. RESULTS: Forty-five per cent of women and 34% of men reported pain in the previous 4 weeks. Pain experience appeared to be less in the 'oldest old': 27.5% of those aged 85 years and over reported pain compared with 38-53% of the 'younger old'. Those with arthritis were four times more likely to report pain. Pain had a profound impact on activities of daily living, but most of those reporting pain described their health as good or excellent. Although there was a significant association between the experience of pain and depressed mood, the majority of those reporting pain did not have depressed mood. CONCLUSION: A multidimensional approach to assessing pain is appropriate. Primary care practitioners should also assess the impact of pain on activities of daily living.

The self-administered 24-item geriatric pain measure (GPM-24-SA): psychometric properties in three European populations of community-dwelling older adults

OBJECTIVE: To explore the feasibility and psychometric properties of a self-administered version of the 24-item Geriatric Pain Measure (GPM-24-SA). DESIGN: Secondary analysis of baseline data from the Prevention in Older People-Assessment in Generalists' practices trial, an international multi-center study of a health-risk appraisal system. PARTICIPANTS: One thousand seventy-two community dwelling nondisabled older adults self-reporting pain from London, UK; Hamburg, Germany; and Solothurn, Switzerland. OUTCOME MEASURES: GPM-24-SA as part of a multidimensional Health Risk Appraisal Questionnaire including self-reported demographic and health-related information. RESULTS: Among the 1,072 subjects, 655 had complete GPM-24-SA data, 404 had 30% missing GPM-24-SA data. In psychometric analyses across the three European populations with complete GPM-24-SA data, the measure exhibited stable internal consistency, good convergent, divergent and discriminant validity, and produced stable pain measurements. However, factor analysis indicated differences in the GPM-24-SA across sites with discrepancies mainly related to items of a single subscale that failed to load appropriately. Analyses including imputation for subjects with

A fuzzy risk attitude classification based on prospect theory

Traditional methods do not actually measure peoples’ risk attitude naturally and precisely. Therefore, a fuzzy risk attitude classification method is developed. Since the prospect theory is usually considered as an effective model of decision making, the personalized parameters in prospect theory are firstly fuzzified to distinguish people with different risk attitudes, and then a fuzzy classification database schema is applied to calculate the exact value of risk value attitude and risk be- havior attitude. Finally, by applying a two-hierarchical clas- sification model, the precise value of synthetical risk attitude can be acquired.

Evaluation of a novel photography-based home assessment protocol for identification of environmental risk factors for falls in elderly persons

PRINCIPLES To evaluate the validity and feasibility of a novel photography-based home assessment (PhoHA) protocol, as a possible substitute for on-site home assessment (OsHA). METHODS A total of 20 patients aged ≥65 years who were hospitalised in a rehabilitation centre for musculoskeletal disorders affecting mobility participated in this prospective validation study. For PhoHA, occupational therapists rated photographs and measurements of patients' homes provided by patients' confidants. For OsHA, occupational therapists conducted a conventional home visit. RESULTS Information obtained by PhoHA was 79.1% complete (1,120 environmental factors identified by PhoHA vs 1416 by OsHA). Of the 1,120 factors, 749 had dichotomous (potential hazards) and 371 continuous scores (measurements with tape measure). Validity of PhoHA to potential hazards was good (sensitivity 78.9%, specificity 84.9%), except for two subdomains (pathways, slippery surfaces). Pearson's correlation coefficient for the validity of measurements was 0.87 (95% confidence interval [CI 0.80-0.92, p <0.001). Agreement between methods was 0.52 (95%CI 0.34-0.67, p <0.001, Cohen's kappa coefficient) for dichotomous and 0.86 (95%CI 0.79-0.91, p <0.001, intraclass correlation coefficient) for continuous scores. Costs of PhoHA were 53.0% lower than those of OsHA (p <0.001). CONCLUSIONS PhoHA has good concurrent validity for environmental assessment if instructions for confidants are improved. PhoHA is potentially a cost-effective method for environmental assessment.

Moving beyond transition outcomes: meta-analysis of remission rates in individuals at high clinical risk for psychosis

Recent evidence suggests that transition risks from initial clinical high risk (CHR) status to psychosis are decreasing. The role played by remission in this context is mostly unknown. The present study addresses this issue by means of a meta-analysis including eight relevant studies published up to January 2012 that reported remission rates from an initial CHR status. The primary effect size measure was the longitudinal proportion of remissions compared to non-remission in subjects with a baseline CHR state. Random effect models were employed to address the high heterogeneity across studies included. To assess the robustness of the results, we performed sensitivity analyses by sequentially removing each study and rerunning the analysis. Of 773 subjects who met initial CHR criteria, 73% did not convert to psychosis along a 2-year follow. Of these, about 46% fully remitted from the baseline attenuated psychotic symptoms, as evaluated on the psychometric measures usually employed by prodromal services. The corresponding clinical remission was estimated as high as 35% of the baseline CHR sample. The CHR state is associated with a significant proportion of remitting subjects that can be accounted by the effective treatments received, a lead time bias, a dilution effect, a comorbid effect of other psychiatric diagnoses.

Can quantitative EEG measures predict clinical outcome in subjects at Clinical High Risk for psychosis? A prospective multicenter study

BACKGROUND Prediction studies in subjects at Clinical High Risk (CHR) for psychosis are hampered by a high proportion of uncertain outcomes. We therefore investigated whether quantitative EEG (QEEG) parameters can contribute to an improved identification of CHR subjects with a later conversion to psychosis. METHODS This investigation was a project within the European Prediction of Psychosis Study (EPOS), a prospective multicenter, naturalistic field study with an 18-month follow-up period. QEEG spectral power and alpha peak frequencies (APF) were determined in 113 CHR subjects. The primary outcome measure was conversion to psychosis. RESULTS Cox regression yielded a model including frontal theta (HR=1.82; [95% CI 1.00-3.32]) and delta (HR=2.60; [95% CI 1.30-5.20]) power, and occipital-parietal APF (HR=.52; [95% CI .35-.80]) as predictors of conversion to psychosis. The resulting equation enabled the development of a prognostic index with three risk classes (hazard rate 0.057 to 0.81). CONCLUSIONS Power in theta and delta ranges and APF contribute to the short-term prediction of psychosis and enable a further stratification of risk in CHR samples. Combined with (other) clinical ratings, EEG parameters may therefore be a useful tool for individualized risk estimation and, consequently, targeted prevention.