Optimal investment strategies and risk measures in defined contribution pension schemes

In this paper, we derive a formula for the optimal investment allocation (derived from a dynamic programming approach) in a defined contribution (DC) pension scheme whose fund is invested in n assets. We then analyse the particular case of n=2 (where we consider the presence in the market of a high-risk and a low-risk asset whose returns are correlated) and study the investment allocation and the downside risk faced by the retiring member of the DC scheme, where optimal investment strategies have been adopted. The behaviour of the optimal investment strategy is analysed when changing the disutility function and the correlation between the assets. Three different risk measures are considered in analysing the final net replacement ratios achieved by the member: the probability of failing the target, the mean shortfall and a value at risk (VaR) measure. The replacement ratios encompass the financial and annuitisation risks faced by the retiree. We consider the relationship between the risk aversion of the member and these different risk measures in order to understand better the choices confronting different categories of scheme member. We also consider the sensitivity of the results to the level of the correlation coefficient

Valuations and dynamic convex risk measures

This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a finite time set and finite sample space, we find natural risk-transfer and time-consistency properties for a firm seeking to spread its risk across a group of subsidiaries.Comment: 26 page

Policy Gradients for CVaR-Constrained MDPs

We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four tools: stochastic approximation, mini batches, policy gradients and importance sampling. Both the algorithms incorporate a CVaR estimation procedure, along the lines of Bardou et al. [2009], which in turn is based on Rockafellar-Uryasev's representation for CVaR and utilize the likelihood ratio principle for estimating the gradient of the sum of one cost function (objective of the SSP) and the gradient of the CVaR of the sum of another cost function (in the constraint of SSP). The algorithms differ in the manner in which they approximate the CVaR estimates/necessary gradients - the first algorithm uses stochastic approximation, while the second employ mini-batches in the spirit of Monte Carlo methods. We establish asymptotic convergence of both the algorithms. Further, since estimating CVaR is related to rare-event simulation, we incorporate an importance sampling based variance reduction scheme into our proposed algorithms

A multi-spacecraft view of a giant filament eruption during 26/27 September 2009

We analyze multi-spacecraft observations of a giant filament eruption that occurred during 26 and 27 September 2009. The filament eruption was associated with a relatively slow coronal mass ejection (CME). The filament consisted of a large and a small part, both parts erupted nearly simultaneously. Here we focus on the eruption associated with the larger part of the filament. The STEREO satellites were separated by about 117 degree during this event, so we additionally used SoHO/EIT and CORONAS/TESIS observations as a third eye (Earth view) to aid our measurements. We measure the plane-of-sky trajectory of the filament as seen from STEREO-A and TESIS view-points. Using a simple trigonometric relation, we then use these measurements to estimate the true direction of propagation of the filament which allows us to derive the true R=R_sun v/s time profile of the filament apex. Furthermore, we develop a new tomographic method that can potentially provide a more robust three-dimensional reconstruction by exploiting multiple simultaneous views. We apply this method also to investigate the 3D evolution of the top part of filament. We expect this method to be useful when SDO and STEREO observations are combined. We then analyze the kinematics of the eruptive filament during its rapid acceleration phase by fitting different functional forms to the height-time data derived from the two methods. We find that, for both methods, an exponential function fits the rise profile of the filament slightly better than parabolic or cubic functions. Finally, we confront these results with the predictions of theoretical eruption models.Comment: 16 pages, 9 figures, to appear in Astrophysical Journa

Description Of Procedures In Automotive Engine Plants (ABSTRACT)

ABSTRACT 1. Human resources - For automakers, the total cost of paying average workers is around $40000 per year (mean value); the numbers range from$30000 to $60000 (except for a Central European facility where it is much lower). On average, direct pay is three times the amount of benefits. In general, worker qualification does not affect the benefits policy within an automobile engine plant. - Overall, the average age of workers in engine plants is slightly above 40 years old. There is no difference by geographic region. In older engine plants, workers do tend to be older. Annual turnover rates are around 5%. Mean values for unionization levels are 7990 for hourly workers, 45% for salaried workers. It is common for production workers to be assigned different tasks; the engine plants where the union contract restricts the kind of activities are located in North America. - A majority of engine plants surveyed have work teams, and they are deployed in all departments. In most cases, work teams were introduced about five years ago. Sometimes, work team leaders are not elected. The average training received is 41 hours per employee per year. Fluctuations in the values are large. European facilities tend to have more training. Respondents felt that inspecting one's work, being well trained, designing one?s workplace and having suggestions accepted are factors which can help workers make high quality engines. Workers and management interact via meetings and surveys. There are usually fewer than 2 suggestions per worker per year. The more training people get, the more likely they are to make suggestions. 2. Logistics - Delivery of parts to the assembly department of engine plants: the Japanese-owned facilities get a much higher fraction of these components delivered more than once per shift, compared to other plants. There are more instances of "just-in-time" practice for castings and parts delivered to the machining departments. - Engine and vehicle assembly plants: for half of our sample, the average delivery pace of finished engines to the car assembly plant is once per shift or more frequently. Engine plants which deliver engines very frequently no matter how far their customer vehicle assembly plants are located. The average value of the average delivery size of finished engines is 273 units (the results are very variable, but in general, the more engines are produced per unit time, the larger the batch size). For one out of two engine plants, the average transit time to the customer vehicle assembly plant is less than half a day; however, there are many cases where finished engines are delivered to vehicle assembly plants located very far away. 3. Maintenance policies - Total Productive Maintenance (TPM) is in place in all of the plants surveyed, but this is quite recent (implementation started between 1990 and 1994). In two out of three cases, it is based on a centralized planning and information system. All of the key maintenance items mentioned in the questionnaire are taken care of by all engine plants; however, the frequency at which maintenance is done varies a lot from plant to plant (average: one and a half times per week). ProceduresinEnginePlants(ABSTRACT) MIT /IMVP --Oct.1997 Page2 - Throughout all departments of engine plants, breakdowns are caused on average mostly by mechanical problems and then by electrical problems although there is a lot of variation between plants. For those types of failures, there is no link with any downtime statistics. Hydraulic failures occur more frequently in those plants which are older. 4. Production technologies - Several of the engine plants surveyed are currently undergoing major changes. For a new engine variant, most engine plants can deal with the adaptation by using much more than half of the existing machines. In engine plants, a ?minor upgrade? can stop lines anywhere between less than 24 hours to more than a week. Currently, assembly lines in engine plants can handle more flexibility than machining lines. When different engines are built in sequence, the pattern used most often is 1-1- 1-2-2-2 (batch sizes range from 6 to 100?s of engines). - Current and future design and acquisition processes for equipment do not differ. There is one policy for the whole plant. For a majority of engine plants, the methodology is as follows: the automobile company takes care of defining the requirements, it has a large influence (along with an affiliate or sister company sometimes) for the planning process, but the design and building of equipment is done by an outside equipment or system supplier. Two areas where answers differ a lot concern the system integration and the actual installation of equipment in engine plants: in some cases, the automobile company is in charge, while in other cases, an outside firm does the job. 5. Quality - Engines made in European plants have more complaints per 1000 than the North American or Japanese ones (caution: we have rather few of these data points from non-European plants). Engine quality as measured by complaints per 1000 units after engines are delivered: 3-month quality data are quite good predictors of 12-month data. - In almost all engine plants, Statistical Process Control (SPC) data are collected and displayed at the line or work station. Engine plants also get back some engine performance and warranty data. - In most instances, communication of engine design information is done via fax or hardcopy. Sometimes, CAD systems (mostly 2-D) are used to exchange design dat~ however, whether CAD systems are used or not, is not a function of the age of the engine plant or of the lines. In a majority of cases, the exchange of information between the plant and the engine design department take place weekly, with actual design changes happening monthly. On average, half of the design changes are due to the engine engineering department, in order to improve the engine and to fix design or performance problems. Other causes for design changes are the meeting market needs, fixing production problems, and responding to the evolution of regulations. - All plants conduct hot testing of engines; in two facilities, only some of the engines are hottested. The test can last from 45 seconds to 18 minutes. The (few) all-aluminum engines of our survey are among those which undergo longer periods of hot testing. Less than 7% of the engines fail the hot test the first time. By looking simultaneously at the engine quality data and at the hot testing results, we did not find any correlation: hot test duration does not uncover problems which cause quality complaints 3 or 12 months after the engines are delivered to customers. Proceduresin EnginePlants(ABSTRACT) MIT /IMVP --Oct.1997 Page 3 - According toourrespondents, production technologies thatcan becritical formanufacturing high quality automotive engines concern machining operations more than the sub-assembly and final dressing ofengines; interestingly, these technologies are most often supplied by outside vendors. In addition, organizational factors are seen as much more effective than automatization, in order to produce high-quality engines. 6. Information systems - Information systems are in place in engine plants, and they are used quite extensively. - While centralized systems tend to be used mainly for planning purposes, non-centralized computer systems can help compile some statistical data and tell about equipment problems. Rarely are information systems actually used to give work assignments to employees. 7. Accounting procedures and investment decisions - For a series of recent major installations of equipment in engine plants, it took around two years between the approval of the plan and the moment when the first part was produced, and from there on, an extra three to six months for full production levels to be reached. - The top financial indicator used by car firms for measuring the "performance" of engine plants is clearly variance from budget. Some financial ratios like return on equity or return on assets are not used at all. For non-financial indicators, the quality of engines is most important, followed by safety and environment concerns, logistical issues, and labor productivity. - Product quality and internal rate of return are the two most important factors involved in engine plant investment decisions. - Most common practice is that indirect cost allocation uses standard or actual labor hours. - Activity-based costing systems were in place in 30% of the engine plants surveyed ( 1995 data). 8. Plant improvement efforts - The persons surveyed do not think that more automation will be the key for progress in engine manufacturing. For the future, a strong desire is the ability to improve the flexibility of the factory, of the machines, and of the material flow. Interestingly, the respondents most interested by flexibility improvements are based in engine plants which currently deal with rather low levels of engine variety. - On the list of factors which can help improve operations in engine plants, is the need to establish better contacts with people in the engine design department and with the suppliers of machinery. Also, being able to build more engines in less space is an important goal for several respondents; actually, those most interested by this issue are from engine plants where the utilization of space is already more efficient than on average.IMV

Description Of Procedures In Automotive Engine Plants

1. Human resources - For automakers, the total cost of paying average workers is around $40000 per year (mean value); the numbers range from$30000 to $60000 (except for a Central European facility where it is much lower). On average, direct pay is three times the amount of benefits. In general, worker qualification does not affect the benefits policy within an automobile engine plant. - Overall, the average age of workers in engine plants is slightly above 40 years old. There is no difference by geographic region. In older engine plants, workers do tend to be older. Annual turnover rates are around 5%. Mean values for unionization levels are 7990 for hourly workers, 45% for salaried workers. It is common for production workers to be assigned different tasks; the engine plants where the union contract restricts the kind of activities are located in North America. - A majority of engine plants surveyed have work teams, and they are deployed in all departments. In most cases, work teams were introduced about five years ago. Sometimes, work team leaders are not elected. The average training received is 41 hours per employee per year. Fluctuations in the values are large. European facilities tend to have more training. Respondents felt that inspecting one?s work, being well trained, designing one?s workplace and having suggestions accepted are factors which can help workers make high quality engines. Workers and management interact via meetings and surveys. There are usually fewer than 2 suggestions per worker per year. The more training people get, the more likely they are to make suggestions. 2. Logistics - Delivery of parts to the assembly department of engine plants: the Japanese-owned facilities get a much higher fraction of these components delivered more than once per shift, compared to other plants. There are more instances of ?just-in-time? practice for castings and parts delivered to the machining departments. - Engine and vehicle assembly plants: for half of our sample, the average delivery pace of finished engines to the car assembly plant is once per shift or more frequently. Engine plants which deliver engines very frequently no matter how far their customer vehicle assembly plants are located. The average value of the average delivery size of finished engines is 273 units (the results are very variable, but in general, the more engines are produced per unit time, the larger the batch size). For one out of two engine plants, the average transit time to the customer vehicle assembly plant is less than half a day; however, there are many cases where finished engines are delivered to vehicle assembly plants located very far away. 3. Maintenance policies - Total Productive Maintenance (TPM) is in place in all of the plants surveyed, but this is quite recent (implementation started between 1990 and 1994). In two out of three cases, it is based on a centralized planning and information system. All of the key maintenance items mentioned in the questionnaire are taken care of by all engine plants; however, the frequency at which maintenance is done varies a lot from plant to plant (average: one and a half times per week). ProceduresinEnginePlants(ABSTRACT) MIT /IMVP --Oct.1997 Page2 - Throughout all departments of engine plants, breakdowns are caused on average mostly by mechanical problems and then by electrical problems although there is a lot of variation between plants. For those types of failures, there is no link with any downtime statistics. Hydraulic failures occur more frequently in those plants which are older. 4. Production technologies - Several of the engine plants surveyed are currently undergoing major changes. For a new engine variant, most engine plants can deal with the adaptation by using much more than half of the existing machines. In engine plants, a ?minor upgrade? can stop lines anywhere between less than 24 hours to more than a week. Currently, assembly lines in engine plants can handle more flexibility than machining lines. When different engines are built in sequence, the pattern used most often is 1-1- 1-2-2-2 (batch sizes range from 6 to 100?s of engines). - Current and future design and acquisition processes for equipment do not differ. There is one policy for the whole plant. For a majority of engine plants, the methodology is as follows: the automobile company takes care of defining the requirements, it has a large influence (along with an affiliate or sister company sometimes) for the planning process, but the design and building of equipment is done by an outside equipment or system supplier. Two areas where answers differ a lot concern the system integration and the actual installation of equipment in engine plants: in some cases, the automobile company is in charge, while in other cases, an outside firm does the job. 5. Quality - Engines made in European plants have more complaints per 1000 than the North American or Japanese ones (caution: we have rather few of these data points from non-European plants). Engine quality as measured by complaints per 1000 units after engines are delivered: 3-month quality data are quite good predictors of 12-month data. - In almost all engine plants, Statistical Process Control (SPC) data are collected and displayed at the line or work station. Engine plants also get back some engine performance and warranty data. - In most instances, communication of engine design information is done via fax or hardcopy. Sometimes, CAD systems (mostly 2-D) are used to exchange design dat~ however, whether CAD systems are used or not, is not a function of the age of the engine plant or of the lines. In a majority of cases, the exchange of information between the plant and the engine design department take place weekly, with actual design changes happening monthly. On average, half of the design changes are due to the engine engineering department, in order to improve the engine and to fix design or performance problems. Other causes for design changes are the meeting market needs, fixing production problems, and responding to the evolution of regulations. - All plants conduct hot testing of engines; in two facilities, only some of the engines are hottested. The test can last from 45 seconds to 18 minutes. The (few) all-aluminum engines of our survey are among those which undergo longer periods of hot testing. Less than 7% of the engines fail the hot test the first time. By looking simultaneously at the engine quality data and at the hot testing results, we did not find any correlation: hot test duration does not uncover problems which cause quality complaints 3 or 12 months after the engines are delivered to customers. Proceduresin EnginePlants(ABSTRACT) MIT /IMVP --Oct.1997 Page 3 - According toourrespondents, production technologies thatcan becritical formanufacturing high quality automotive engines concern machining operations more than the sub-assembly and final dressing ofengines; interestingly, these technologies are most often supplied by outside vendors. In addition, organizational factors are seen as much more effective than automatization, in order to produce high-quality engines. 6. Information systems - Information systems are in place in engine plants, and they are used quite extensively. - While centralized systems tend to be used mainly for planning purposes, non-centralized computer systems can help compile some statistical data and tell about equipment problems. Rarely are information systems actually used to give work assignments to employees. 7. Accounting procedures and investment decisions - For a series of recent major installations of equipment in engine plants, it took around two years between the approval of the plan and the moment when the first part was produced, and from there on, an extra three to six months for full production levels to be reached. - The top financial indicator used by car firms for measuring the ?performance? of engine plants is clearly variance from budget. Some financial ratios like return on equity or return on assets are not used at all. For non-financial indicators, the quality of engines is most important, followed by safety and environment concerns, logistical issues, and labor productivity. - Product quality and internal rate of return are the two most important factors involved in engine plant investment decisions. - Most common practice is that indirect cost allocation uses standard or actual labor hours. - Activity-based costing systems were in place in 30% of the engine plants surveyed ( 1995 data). 8. Plant improvement efforts - The persons surveyed do not think that more automation will be the key for progress in engine manufacturing. For the future, a strong desire is the ability to improve the flexibility of the factory, of the machines, and of the material flow. Interestingly, the respondents most interested by flexibility improvements are based in engine plants which currently deal with rather low levels of engine variety. - On the list of factors which can help improve operations in engine plants, is the need to establish better contacts with people in the engine design department and with the suppliers of machinery. Also, being able to build more engines in less space is an important goal for several respondents; actually, those most interested by this issue are from engine plants where the utilization of space is already more efficient than on average. This study was sponsored by the International Motor Vehicie Program. The authors gratejidly acknowledge its support

Risk Minimization through Portfolio Replication

We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short with respect to the size of the portfolio. We also study the noise sensitivity of portfolio allocation when this transition is approached. We consider explicitely the cases where the absolute deviation and the conditional value-at-risk are chosen as a risk measure. We show how the replica method can study a wide range of risk measures, and deal with various types of time series correlations, including realistic ones with volatility clustering.Comment: 12 pages, APFA5 conferenc

Lambda value at risk and regulatory capital: a dynamic approach to tail risk

This paper presents the first methodological proposal of estimation of the ΛVaR . Our approach is dynamic and calibrated to market extreme scenarios, incorporating the need of regulators and financial institutions in more sensitive risk measures. We also propose a simple backtesting methodology by extending the VaR hypothesis-testing framework. Hence, we test our ΛVaR proposals under extreme downward scenarios of the financial crisis and different assumptions on the profit and loss distribution. The findings show that our ΛVaR estimations are able to capture the tail risk and react to market fluctuations significantly faster than the VaR and expected shortfall. The backtesting exercise displays a higher level of accuracy for our ΛVaR estimations