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Parametric

Parametric Portfolio Associates LLC (Parametric) is a global investment management firm headquartered in Seattle, Washington, that develops and implements customized, tax-optimized portfolio strategies for institutional and individual investors.^[1]^[2] Founded in 1987 by Bill Cornelius, Mark England-Markun, and Randy Lert, the firm employs systematic, quantitative approaches grounded in empirical analysis of securities' risk-return profiles to construct portfolios that prioritize after-tax efficiency and client-specific goals.^[3]^[4] As a subsidiary of Morgan Stanley Investment Management, Parametric manages over $608 billion in assets as of June 30, 2025, across direct indexing, completion strategies, and overlay portfolios that integrate automated tax-loss harvesting with market exposure customization.^[2]^[3] The firm distinguishes itself through innovations like its Custom Core® separately managed account, launched in the early 1990s as an early form of direct indexing, which allows investors to own individual securities for precise control over tax implications and personalization beyond traditional index funds.^[2]^[3] Parametric's risk-averse, research-driven philosophy focuses on bottom-up evaluation and technological implementation to mitigate volatility and enhance long-term outcomes, serving clients via partnerships with financial intermediaries and direct institutional mandates.^[4]^[5]

Mathematics and Statistics

Parametric Equations and Representations

Parametric equations express the coordinates of points on a curve or surface as functions of one or more independent parameters, typically denoted as x = f(t), y = g(t) for plane curves, where t varies over an interval.^[6]^[7] This formulation contrasts with Cartesian equations, which relate variables implicitly or explicitly without an auxiliary parameter, allowing parametric representations to describe paths where direct functional relations between coordinates are absent or algebraically intractable.^[8] The development of parametric equations emerged within analytic geometry in the 17th century, building on René Descartes' 1637 coordinate system, though explicit parametric forms gained prominence later.^[9] For instance, Pierre de Fermat examined curves like the witch of Agnesi in 1630, and by 1748, Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, detailed parametric representations in her analytic geometry text, facilitating descriptions of non-algebraic loci.^[10] These methods addressed limitations in implicit equations, such as high-degree polynomials for conics, by leveraging trigonometric or rational functions for parameterization. Classic examples include the ellipse, parameterized as x = a \cos t, y = b \sin t for t \in [0, 2\pi), which traces the curve uniformly and simplifies arc length computations compared to the implicit form \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.^[11] The cycloid, generated by a point on a rolling circle of radius r, follows x = r(t - \sin t), y = r(1 - \cos t), illustrating parametric utility for trajectories involving periodic motion, where Cartesian elimination yields a fourth-degree equation.^[12] Parametric forms excel in representing complex geometries, such as rational Bézier curves used in design, where control points and polynomials enable smooth interpolation without solving high-order implicit equations.^[13] In computational contexts, they reduce algebraic complexity; for instance, rendering parametric curves in graphics software avoids root-finding in Cartesian forms, enabling efficient evaluation at discrete parameter values for interpolation and subdivision algorithms.^[13] This explicit parameterization supports vector-based operations, preserving geometric properties like tangency under affine transformations, as verified in numerical simulations where parametric splines outperform implicit methods in convergence speed for curve fitting.^[14]

Parametric Statistical Models

Parametric statistical models posit that data arise from a probability distribution belonging to a specified family indexed by a finite-dimensional parameter vector θ ∈ Θ, where Θ is a subset of Euclidean space.^[15] This finite parameterization contrasts with nonparametric alternatives by imposing strong distributional assumptions, such as normality for error terms in regression, enabling compact representation but risking invalidity if the true data-generating process deviates.^[16] Common examples include the normal distribution N(μ, σ²), characterized by mean μ and variance σ², or the linear regression model y = Xβ + ε with ε ~ N(0, σ²I), assuming homoscedasticity and independence.^[17] Parameter estimation typically employs maximum likelihood estimation (MLE), which maximizes the likelihood function L(θ; data) = ∏ f(x_i | θ) over observed data x_i, yielding asymptotically efficient estimators under correct specification.^[18] In large samples, the central limit theorem implies that √n (θ̂ - θ₀) converges in distribution to N(0, I(θ₀)^{-1}), where I(θ₀) is the Fisher information matrix, justifying approximate normality for inference and achieving the Cramér-Rao lower bound for variance.^[19] This efficiency manifests in applications like analysis of variance (ANOVA), where normality assumptions facilitate F-tests with controlled Type I error rates near the nominal 5% for balanced designs and n > 30 per group.^[20] Despite these strengths, parametric models exhibit sensitivity to misspecification, such as omitted variables or non-normality, inducing bias in θ̂ and inflated Type I/II errors.^[21] ^[22] For instance, heteroscedasticity in linear regression biases standard errors downward, elevating rejection rates beyond nominal levels, as evidenced by simulations showing up to 20-30% Type I error inflation under moderate violations.^[23] Empirical meta-analyses of mixed-effects models confirm that unaddressed random effects misspecification similarly distorts p-values, with average empirical Type I rates exceeding 10% in violated scenarios across 50+ simulation studies.^[23] Such vulnerabilities underscore the necessity of diagnostic checks, like residual plots or bootstrapping for robustness, particularly in heterogeneous datasets where causal interpretations hinge on verified assumptions rather than untested idealizations.^[24]

Physics and Engineering

Parametric Processes in Optics and Waves

Parametric processes in optics and waves refer to nonlinear interactions in which optical fields couple through the second-order susceptibility \chi^{(2)} of a medium, enabling frequency conversion while preserving the medium's quantum state unchanged, as the nonlinearity excites virtual population only.^[25] These processes, rooted in quantum electrodynamics, involve parametric amplification or down-conversion where energy and momentum are conserved among interacting photons, distinct from absorptive nonlinearities that alter the medium's population.^[26] A canonical example is spontaneous parametric down-conversion (SPDC), in which a high-frequency pump photon spontaneously annihilates in the nonlinear crystal, producing lower-frequency signal and idler photon pairs satisfying \omega_p = \omega_s + \omega_i and \mathbf{k}_p = \mathbf{k}_s + \mathbf{k}_i.^[26] Efficiency in these processes demands phase-matching, where the wavevector mismatch \Delta k = k_p - k_s - k_i = 0 ensures constructive interference over the interaction length.^[27] Traditional birefringent phase-matching exploits ordinary and extraordinary refractive indices in anisotropic crystals like beta-barium borate (BBO), while quasi-phase-matching (QPM) periodically reverses the nonlinearity via ferroelectric domain poling in materials such as lithium niobate, compensating for residual \Delta k with a grating vector.^[27] SPDC was theoretically predicted in the 1960s and first experimentally observed in 1970 using a lithium iodate crystal pumped by a ruby laser, yielding entangled photon pairs tunable across visible and near-infrared wavelengths.^[28] In quantum optics applications, parametric processes generate non-classical states, including polarization- or momentum-entangled photon pairs from type-I or type-II SPDC, enabling Bell inequality violations and quantum key distribution protocols with pair production rates up to 10^6 pairs per second per milliwatt of pump power in periodically poled crystals.^[29] Degenerate parametric down-conversion in sub-threshold optical parametric oscillators produces squeezed vacuum states, reducing quadrature noise below the shot-noise limit by factors exceeding 10 dB, as demonstrated in cavity-enhanced setups for precision interferometry and gravitational wave detection.^[30] These outcomes stem from the Hamiltonian describing the \chi^{(2)} interaction, H = i \hbar \kappa (a_p a_s^\dagger a_i^\dagger + \mathrm{h.c.}), where \kappa is the coupling strength proportional to \chi^{(2)}.^[26] However, real-world implementations reveal limitations beyond ideal lab conditions, including multi-photon pair emissions that introduce heralding noise and reduce single-photon purity to below 90% in high-gain regimes, as quantified in quantum state tomography of pulsed SPDC sources.^[31] Environmental decoherence, such as from atmospheric turbulence in free-space links, further degrades entanglement fidelity, with field experiments showing visibility drops to 70-80% over kilometer distances due to phase fluctuations, underscoring the gap between controlled crystal interactions and propagation losses.^[32] These constraints highlight that while parametric processes excel in generating quantum resources, causal factors like dispersion and scattering impose practical bounds on scalability.^[33]

Parametric Amplification and Oscillation

Parametric amplification arises from the periodic modulation of a reactive system parameter, such as capacitance in a varactor diode, which enables energy transfer from a high-frequency pump signal to lower-frequency signal and idler waves, producing net gain through negative resistance effects without relying on dissipative active elements.^[34] This process leverages the nonlinearity of the varying parameter to couple frequencies, where the pump power excites the system, amplifying the signal while generating an idler to conserve energy and momentum.^[35] The Manley-Rowe relations govern this interaction, stating that the weighted sum of real powers at the involved frequencies—proportional to the inverse of their frequencies—equals zero, ensuring no net power dissipation in the ideal reactive element and quantifying the power flow between pump, signal, and idler.^[34]^[36] The technology emerged practically in the 1950s for microwave applications, with early theoretical foundations in nonlinear reactance studies from the late 19th century but viable implementations via varactor diodes at Bell Laboratories around 1958, achieving 10 dB gain at 400 MHz using four-diode stages.^[37] These devices facilitated low-noise amplification in satellite communications by pumping energy reactively, outperforming transistor-based alternatives in noise performance at the time.^[38] In parametric oscillation, a subset of this phenomenon, the system self-sustains above a threshold pump power, producing coherent output at signal and idler frequencies, as seen in early maser-like setups for quantum-limited detection. Advantages include ultra-low noise figures approaching the quantum limit—often below 1 dB in cryogenic operation—due to the absence of thermal generation in reactive elements, enabling high-efficiency energy transfer in superconducting circuits like Josephson parametric oscillators for quantum information processing and microwave spectroscopy.^[39]^[40] Tunability arises from pump frequency control, allowing adjustable gain and phase in applications such as noise spectroscopy of superconducting resonators.^[41] However, drawbacks encompass narrow bandwidth from stringent phase-matching requirements between frequencies, risking spurious oscillations and instability that demand damping circuits, which in turn reduce overall gain and introduce losses, as evidenced by simulations showing thermal noise degrading ideal Manley-Rowe predictions in non-ideal implementations.^[42]^[43] Real-world amplification thus depends on pump energy input overriding losses, but practical limits from diode parasitics and environmental noise constrain broadband utility compared to solid-state amplifiers.^[35]

Finance and Insurance

Parametric Insurance Products

Parametric insurance products are financial contracts that provide predefined payouts triggered by the occurrence of specific, measurable parameters or indices, such as earthquake magnitude exceeding 7.0 on the Richter scale or wind speeds surpassing 150 km/h during a hurricane, without requiring assessment of actual incurred losses.^[44] ^[45] This structure bypasses traditional indemnity processes involving loss adjusters, enabling rapid disbursements often within days of the event verification.^[46] Originating in the late 1990s as an evolution of catastrophe bonds—securities that transfer peak reinsurance risks to capital markets—parametric insurance emerged to address capacity constraints following major disasters and to offer alternative risk transfer mechanisms for insurers and governments.^[47] ^[48] The appeal of parametric products intensified after events like Hurricane Katrina in 2005, which generated insured losses of $105 billion (in 2024 prices) and exposed prolonged delays in traditional claims processing amid widespread infrastructure damage and disputes over coverage scopes.^[49] Reinsurers such as Swiss Re have since promoted parametric solutions to mitigate such frictions, offering policies triggered by verifiable meteorological data for faster liquidity to policyholders in catastrophe-prone regions.^[50] Market growth has been driven by escalating natural catastrophe frequencies—linked to climate variability—and demand for efficient capital deployment, with global premiums expanding from under $10 billion in the early 2010s to approximately $16.2 billion by 2024, projected to reach $39.3 billion by 2032 at a 12.6% compound annual growth rate.^[51] ^[52] Key adopters include governments in developing nations via programs like the African Risk Capacity, which uses satellite-derived drought indices to trigger aid for agricultural shortfalls.^[53] Despite these advantages, parametric insurance faces inherent limitations, primarily basis risk—the disconnect between index triggers and on-ground losses—leading to over- or under-compensation.^[54] For instance, in the 2017 Hurricane Maria aftermath in Dominica, parametric policies failed to activate sufficiently despite severe damages, as indices based on broad seismic or wind metrics did not capture localized impacts, resulting in inadequate payouts relative to reconstruction needs.^[54] Similar issues arise in drought-prone African contexts, where rainfall or vegetation indices may overlook micro-climatic variations, prompting criticisms that uncalibrated parameters can exacerbate vulnerabilities rather than ensure resilience, particularly without hybrid models blending parametric and indemnity elements.^[48] ^[55] To address transparency and verification challenges, recent innovations incorporate blockchain for automating triggers via smart contracts, which embed policy logic and oracle-fed data to execute payouts verifiably and reduce disputes, as demonstrated in reinsurance platforms handling severe storm events.^[56] ^[57]

Parametric Approaches in Portfolio Management

Parametric approaches in portfolio management utilize mathematical models with specified parameters to estimate risk, optimize asset allocation, and enhance returns through quantitative techniques. These methods rely on assumed probability distributions, such as normal or Student's t-distributions, to parameterize variables like volatility and correlations, enabling efficient computation for large portfolios. Unlike non-parametric methods that depend on historical data without distributional assumptions, parametric models facilitate rapid scenario analysis and optimization under frameworks like mean-variance analysis extended with risk parameters.^[58]^[59] A core application is parametric Value-at-Risk (VaR), which quantifies potential portfolio losses over a time horizon at a given confidence level by leveraging the variance-covariance matrix of asset returns. For instance, under a normal distribution assumption, VaR is calculated as the portfolio's standard deviation multiplied by the z-score corresponding to the confidence level (e.g., 1.65 for 95% VaR over one day), adjusted for expected returns. This approach offers computational speed—often orders of magnitude faster than Monte Carlo simulations—making it suitable for real-time risk management in high-frequency trading and dynamic rebalancing. Firms like Parametric Portfolio Associates, founded in 1987 and specializing in systematic investment strategies, apply parametric overlays to customize portfolios for tax efficiency, such as through direct indexing that tracks benchmarks while harvesting losses, demonstrating empirical outperformance in volatile periods via multifactor models targeting value, momentum, and quality factors.^[60]^[59]^[61]^[62] Despite advantages in efficiency, parametric models face limitations from unrealistic distributional assumptions, particularly underestimating tail risks in fat-tailed real-world returns. During the 2008 financial crisis, Gaussian-based parametric VaR models prevalent in banks failed to capture extreme correlations and leptokurtic losses, leading to systematic underestimation of portfolio drawdowns as high as 20-30% beyond predicted levels, which contributed to inadequate capital buffers. Empirical evaluations post-crisis showed parametric VaR backtests rejecting normality more frequently during turmoil, underscoring the need for robustness checks like stress-testing against historical black swan events or incorporating heavier-tailed distributions such as t-copulas.^[63]^[64]^[65] Recent advancements integrate ESG parameters into parametric frameworks, treating environmental, social, and governance scores as additional factors in portfolio policies without necessarily sacrificing returns, as evidenced by linear deviation models from benchmarks that maintain risk-adjusted performance. For example, rules-based ESG incorporation via quantitative screens or multifactor tilts allows customization while monitoring real-time exposures, though critiques note potential selection bias in backtested results that overlook transaction costs and data quality issues in ESG datasets. Parametric Portfolio Associates employs such techniques, combining ESG integration with tax-managed overlays to align portfolios with client preferences amid growing regulatory emphasis on sustainability reporting since 2020.^[66]^[67]^[68]

Computing and Machine Learning

Parametric Modeling in Software and Design

Parametric modeling in software and design employs constraint-driven techniques in CAD systems, where geometric entities are governed by editable parameters, equations, and relational constraints rather than fixed sketches. Features such as a revolved shaft's diameter in SolidWorks can be tied to a global variable—defined via the Equations manager—enabling automatic regeneration of downstream geometry upon parameter adjustment, thus supporting iterative "what-if" analyses and design variants without manual reconstruction.^[69]^[70] This history-based approach captures design intent through a feature tree, where parent-child dependencies ensure associativity, distinguishing it from earlier wireframe or surface modeling paradigms.^[71] Developed in the 1980s, parametric modeling gained commercial viability with PTC's Pro/ENGINEER release in 1988, introducing rule-based, feature-driven solid modeling that linked parameters to constraints for associative updates—the first such system to achieve widespread adoption in engineering workflows.^[72]^[73] By the early 1990s, successors like SolidWorks (launched 1995) popularized it for mechanical design, while AutoCAD incorporated parametric dimensions and constraints starting in version 2010, extending the method to 2D and 3D variant generation in architectural and drafting contexts.^[74] These tools now underpin simulation-integrated environments, where parameters drive finite element analysis inputs for predictive validation.^[75] In practice, parametric modeling accelerates manufacturing design cycles by propagating changes across assemblies via single-variable edits, as evidenced in aerospace applications where it shortens iteration loops compared to non-associative methods.^[76] Industry reports note substantial time savings in incorporating modifications, with one analysis attributing efficiency gains to semantic embedding of design rules that obviate redundant redraws.^[75] Yet, in large assemblies, escalating interdependencies foster "parameter explosion," where proliferating variables and constraints precipitate regeneration failures, demanding extensive debugging.^[77] Relative to direct modeling—which edits facets or edges sans history—parametric systems amplify risks of error propagation: flawed foundational parameters or conflicting constraints cascade failures through the dependency tree, undermining reliability absent rigorous validation.^[78]

Parametric vs. Non-Parametric Models in AI

Parametric models in artificial intelligence, particularly in machine learning, are characterized by a fixed, finite-dimensional set of parameters that encapsulate the model's knowledge, such as the weights θ in neural networks. These parameters are optimized through methods like gradient descent during training, enabling efficient handling of massive datasets without increasing model complexity proportional to sample size. For instance, transformer architectures underlying GPT models, starting with GPT-1 in 2018, rely on billions of fixed parameters learned from vast corpora, achieving scalability in natural language processing tasks by distributing computation across parallelizable layers. This fixed-parameter structure contrasts with the data-dependent capacity of non-parametric alternatives, allowing parametric models to interpolate effectively within trained distributions but requiring explicit regularization techniques, such as dropout or weight decay, to mitigate overfitting on benchmarks like ImageNet, where convolutional neural networks have consistently topped leaderboards since AlexNet's 2012 introduction. Non-parametric models, by contrast, adapt their effective complexity to the training data volume, eschewing a predetermined parameter count in favor of data-driven representations; Gaussian processes exemplify this by treating functions as draws from a distribution over infinite-dimensional spaces, with predictive uncertainty scaling with observed samples via kernel computations.^[79] While offering greater flexibility for capturing unknown forms without strong distributional assumptions, non-parametric approaches suffer from computational burdens—often O(n³) for inference in Gaussian processes—limiting scalability to smaller datasets and hindering generalization in high-dimensional regimes like image classification or large-scale forecasting. Empirical trade-offs highlight parametric advantages in compute-abundant settings: on ImageNet, parametric models with regularization outperform non-parametric counterparts in accuracy and efficiency, though they risk high variance if priors encoded in the architecture mismatch the data-generating process, as evidenced by variance-bias analyses in kernel methods versus fixed-form regressions. Parametric models demonstrate superior asymptotic performance when specifications align with underlying causal structures, such as linear regressions in stationary econometric data where maximum likelihood yields efficient estimators under correct parameterization.^[80] However, misspecification leads to empirical failures, notably in non-stationary environments; during the COVID-19 pandemic, parametric compartmental models like SIR exhibited systematic over- or under-predictions due to unverified assumptions about transmission dynamics and intervention effects, with root-mean-square errors exceeding 50% in multi-week horizons across global ensembles.^[81] From a causal perspective, parameters implicitly embed inductive biases—e.g., locality in convolutional layers or autoregression in transformers—that enhance interpolation but propagate errors if causal invariances shift, underscoring the need for verification beyond correlative fit. Non-parametric models avoid such rigid priors but falter in extrapolation, reinforcing parametric dominance in regimes with abundant compute and data, per scaling laws observed in language model pretraining where parameter count correlates with emergent capabilities. In the 2020s, hybrid approaches have emerged to blend strengths, such as mixture-of-experts frameworks integrating parametric value functions with non-parametric environment estimators in reinforcement learning, yielding improved off-policy evaluation on benchmarks like Atari suites.^[82] Despite these innovations, empirical evidence from large-scale deployments favors pure parametric models in resource-rich AI systems, where fixed parameters enable predictable scaling and deployment, though ongoing research critiques over-reliance on unverified architectural priors amid distribution shifts.^[83]

Design and Architecture

Parametric Design Principles

Parametric design principles involve algorithmic processes where architectural forms arise from interdependent parameters, such as geometric constraints, material properties, and environmental factors, encoded via scripts to generate and iterate structures dynamically.^[84] These parameters establish relational rules— for instance, adjusting a facade's curvature in response to wind loads or solar angles—enabling designers to explore outcomes beyond manual drafting limitations. Tools like Grasshopper, integrated into Rhinoceros 3D software since March 2008, exemplify this by allowing visual scripting of parameter networks without traditional coding, facilitating generative designs such as tensile membranes that adapt to site-specific loads.^[85] This approach prioritizes causal linkages between inputs and outputs, simulating real-world physics to optimize structural integrity over aesthetic imposition.^[86] Historically, parametric principles mark a departure from modernism's emphasis on rigid, orthogonal geometries and standardized components, which dominated mid-20th-century architecture to enforce functional efficiency and mass production.^[87] Post-2000 computational advancements shifted toward flexible, non-Euclidean morphologies, leveraging increased processing power for complex simulations unattainable in analog eras; early parametric experiments in the 1980s-1990s laid groundwork, but widespread adoption accelerated with accessible software, enabling forms like doubly curved surfaces that modernism rejected as inefficient.^[87] This evolution reflects a causal realism in design, where forms emerge from parameter-driven iterations rather than preconceived ideals, though it demands validation against empirical structural tests to avoid illusory complexity.^[88] Advantages include enhanced material efficiency through iterative simulations that minimize waste; for example, parametric modeling in construction has demonstrated significant reductions in building material wastage by optimizing component geometries prior to fabrication.^[89] Such processes allow rapid prototyping of load-bearing elements, like optimized truss systems, yielding structures with lower embodied energy while maintaining performance under verified loads.^[90] However, drawbacks encompass high computational demands, requiring substantial hardware and time for complex parameter evaluations, and "black box" tendencies where opaque algorithms obscure underlying causal mechanisms, complicating error diagnosis in projects where outputs deviate from physical realities.^[91] Critiques highlight instances of failed implementations, such as overly intricate designs that prove unconstructible without revealing integration gaps in physics-based validations.^[92]

Recent Advances in Parametric Fabrication

In the early 2020s, artificial intelligence techniques, particularly generative adversarial networks (GANs) and diffusion models, have been integrated into parametric fabrication workflows to optimize structural topologies for complex geometries unachievable through traditional methods. For instance, conditional diffusion models applied to topology optimization have demonstrated superior performance over GANs in generating diverse, high-fidelity designs that minimize material use while maximizing load-bearing capacity, as evidenced in engineering simulations published in 2022.^[93] These AI-driven approaches allow parametric models to iteratively refine parameters based on performance criteria, facilitating the fabrication of lightweight components via additive manufacturing processes like 3D printing.^[94] Cloud-based platforms have further advanced parametric fabrication by enabling real-time collaboration across distributed teams, mitigating silos between designers, engineers, and fabricators. Tools such as ShapeDiver convert parametric models into interactive web applications, allowing seamless parameter adjustments and simulation sharing without proprietary software dependencies, which has streamlined workflows in facade and component production since their expanded adoption around 2023.^[95] This shift was accelerated by post-2020 supply chain disruptions from the COVID-19 pandemic, prompting a surge in localized 3D printing of parametric components to bypass global logistics delays, with studies indicating up to 85% reductions in lead times for on-demand production.^[96] Empirical benefits include enhanced sustainability through parametric simulations of adaptive building envelopes, which have shown potential reductions in HVAC energy demands by optimizing shading and ventilation parameters to site-specific conditions, though real-world validations often reveal variances due to material tolerances exceeding simulation assumptions.^[97] However, critics note that the hype surrounding these advances overlooks scalability constraints outside urban settings, where cost overruns in iconic parametric projects—stemming from unconstructable documentation and fabrication errors—have exceeded budgets by 20-50% in documented cases, underscoring the necessity for hybrid empirical testing to bridge computational ideals with physical realities.^[98] Such limitations arise causally from exponential compute growth enabling intricate models, yet persistent manufacturing inconsistencies demand iterative physical prototyping.^[99]

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Please contact your financial advisor to ask about Parametric investment strategies. Office Locations. headquarters. Seattle 800 Fifth Avenue, Suite 2800.
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Parametric Amplifier Types | Narrowband Amplifiers | Noise Cooling
The only real disadvantage is a lower gain than with narrowband amplifiers. In order to obtain useful amplification, the pump, signal and idler frequencies must ...
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What is parametric insurance - Artemis.bm
Parametric insurance is a type of insurance that provides coverage based on a predetermined set of conditions, or “parameters,” rather than the actual value ...Missing: origins | Show results with:origins
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Parametric Risk Transfer – When Does It Make Sense?
Parametric insurance provides cover for predetermined catastrophic natural events such as an earthquake exceeding a certain magnitude, a hurricane producing ...Missing: origins | Show results with:origins
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Parametric Insurance Solutions | Swiss Re
Our innovative parametric insurance can be tailored to your specific risk profile, and once we hit a pre-defined threshold, we pay you – it's as simple as that.
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Insuring for Climate Change: The Role of Parametric Insurance
Jan 25, 2023 · Parametric products have existed in some form or another since the late 1990s and evolved from the practice of issuing catastrophe bonds, which ...
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[PDF] can parametric insurance help bridge NatCat protection gaps?
The origins of parametric insurance date back to the late 1990s. It was ... The most common type is catastrophe bonds (CAT bonds), which provide coupon ...
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Hurricane Katrina: a watershed event for insurance | Swiss Re
Jun 23, 2025 · Total insured losses came to USD 105 billion at 2024 prices and makes Katrina the most expensive natural catastrophe event for the global insurance industry ...Missing: parametric | Show results with:parametric
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STORM | Parametric Storm & Hurricane Insurance | Swiss Re
In a parametric insurance policy, the loss amount is pre-agreed. The policy pays out when an event – in this case, a tropical cyclone related wind speed – meets ...
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Parametric Insurance Market Size & Share, Growth Analysis 2034
The global parametric insurance market was valued at USD 16.2 billion in 2024 and is projected to grow at a CAGR of 12.6% between 2025 and 2034.Missing: 2020s | Show results with:2020s
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Parametric Insurance Market Set for Significant Growth - Captive.com
Aug 2, 2024 · As detailed in the report, the market is expected to reach $39.3 billion by 2032. Key growth drivers include the adoption of advanced technology ...Missing: 2020s | Show results with:2020s
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African Risk Capacity expects parametric drought insurance to ...
Apr 29, 2024 · The ongoing severe drought across the southern African region is expected to trigger its parametric insurance policies for at least four countries.Missing: underpayments | Show results with:underpayments
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[PDF] Basis risk in parametric insurance: challenges and mitigation ...
In 2017, Hurricane Maria caused significant damage in Dominica, but the parametric insurance policies purchased by the country didn't provide adequate coverage ...
[55]
[PDF] Parametric Insurance for Disasters - Wharton Impact
The benefits of parametric insurance come with a couple drawbacks. The first is the possibility that the payout does not fully cover losses. This is known as ...
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Arbol automates parametric reinsurance triggers using a blockchain
Jun 20, 2023 · It's a smart contract-based system offering “efficient and transparent parametric loss calculations for severe storm catastrophe transactions,” the firms note.
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Powering blockchain-enabled insurance - Chainlink
With Chainlink, blockchain-based parametric insurance applications get access to real-world data, allowing them to automate claims processing and lower ...
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Parametric Method in Value at Risk (VaR): Definition and Examples
The parametric method, also known as the variance-covariance method, is a risk management technique for calculating the VaR of a portfolio of assets.Parametric vs Non-Parametric... · Example With Two Securities
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Estimate VaR for Equity Portfolio Using Parametric Methods
Using a parametric model simplifies the problem of VaR calculation to that of estimating the parameters of the distribution. Parametric methods are often ...
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How to Calculate Value at Risk (VaR) for Financial Portfolios
Value at Risk (VaR) quantifies potential financial losses within a firm or portfolio over a specified timeframe, helping risk managers control exposure.Parametric Method · How To Calculate VaR · Historical Returns
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Parametric Portfolio Associates 2025 Company Profile - PitchBook
Corporate Office · 800 Fifth Avenue · Suite 2800 · Seattle, WA 98104 · United States.
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[PDF] Parametric Multifactor Strategies
Feb 12, 2025 · Parametric also offers implementation services, including customized equity, traditional overlay and centralized portfolio management.
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(PDF) Evaluating value-at-risk models before and after the financial ...
Aug 5, 2025 · However, the limitations of traditional VaR models became particularly evident during the 2008 global financial crisis, when many financial ...
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VaR before and after the 2008 crisis - MidhaFin
Nov 16, 2024 · Explore how Value at Risk (VaR) evolved before and after the 2008 financial crisis, highlighting its limitations and regulatory changes.De Facto Reduction in... · Increased Usage of Additional...
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[PDF] Evaluating Value-at-Risk Models before and after the Financial ...
Jul 30, 2017 · The extend of the crisis began with the failure of three large US investment banks, which turned to unstable stock prices and high volatility of ...
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[PDF] Parametric portfolio policies with ESG -There is no cost
Apr 19, 2023 · The parametric portfolio policy chooses asset weights that deviate linearly from its initial benchmark weights using a set of long-short ...
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Responsible Investing Policy - Parametric Portfolio Associates
Through screens, quantitative integration techniques, or both, Parametric takes a rules-based approach to ESG incorporation, and we subscribe to hundreds of ESG ...Missing: models | Show results with:models
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ESG integration in portfolio selection: A robust preference-based ...
By integrating ESG risk scores into the mean–variance analysis, investors can make more informed decisions that not only optimize financial returns, but also ...
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Defining Parameters for Parametric Design Studies - 2021
To define parameters, right-click Equations, add/edit parameters, name it, and optionally select a dimension or global variable.
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Improve Your Solidworks Models With Parametric Modeling : 6 Steps
Parametric modeling in Solidworks involves adding variables via Tools->Equations, applying them, and extruding the model. This improves efficiency.
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[PDF] Using Parametric Equations in SolidWorks, Example 1
Oct 25, 2006 · To use parametric equations in SolidWorks, open the Equations panel, add an equation, and type the equation format. You can add equations ...
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A Quick History of PTC and PTC Creo
Aug 14, 2014 · With Pro/ENGINEER, PTC was the first to market with parametric, associative feature-based, solid modeling software. During that same year, ...
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Parametric Technology Corporation - History of CAD - Shapr3D
Beta testing of Pro/ENGINEER began in September 1987 with the first public demonstrations taking place at AUTOFACT in Detroit, Michigan in November 1987.
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[PDF] WHY ENGINEERS DESIGN WITH PARAMETRIC 3D
Adding parametric modeling to your engineering process leads to a significant reduction in time spent incorporating design changes, as a single parameter can.
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Parametric CAD modeling: An analysis of strategies for design ...
If properly used, parametric CAD enables the addition of design semantics to the model, which translates into the rapid alteration of existing models by simply ...
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Parametric modelling is hard - Daniel Davis
Dec 13, 2011 · In cracks between the evangelical facade that cocoons parametric modelling with a blanket of positive writing, you catch glimpses of dissent.
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What is Parametric Modeling and How Does it Compare to Direct ...
Mar 16, 2023 · PTC Creo was the first to market with parametric modeling capabilities when it launched as Pro/Engineer back in 1988. In 2011, PTC Inc. renamed ...
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1.7. Gaussian Processes - Scikit-learn
Gaussian Processes (GP) are a nonparametric supervised learning method used to solve regression and probabilistic classification problems.Gaussian Processes · GaussianProcessRegressor · 1.8. Cross decomposition · RBF
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Efficient shrinkage in parametric models - ScienceDirect.com
We show that if the shrinkage dimension exceeds two, the asymptotic risk of the shrinkage estimator is strictly less than that of the maximum likelihood ...
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Inefficiency of SIR models in forecasting COVID-19 epidemic - Nature
Feb 25, 2021 · The failure of SIR-based models to forecast the COVID-19 pandemic can be described by a variety of reasons. These over-simplified models ...
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Combining Parametric and Nonparametric Models for Off-Policy ...
May 14, 2019 · Our method takes a mixture-of-experts approach to combine parametric and non-parametric models of the environment such that the final value estimate has the ...
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[PDF] When to use parametric models in reinforcement learning?
We examine the question of when and how parametric models are most useful in reinforcement learning. In particular, we look at commonalities and differences.
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An Introduction to Parametric Design in Architecture - Vectorworks
Mar 11, 2025 · Parametric design is a design methodology that relies on parameters and rules to define relationships between different elements within a model.
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The History of Rhino - McNeel Wiki
Feb 2007 - Rhino 4.0 released. Dec 2007 - Penguin 2.0 released. Mar 2008 - Added Grasshopper to Rhino for Windows. Sep 2010 - First RhinoFabLab opened. Apr ...
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Design Parameters to Parametric Design - Patrik Schumacher
Jan 5, 2024 · Parametric Design is a computer based design approach that treats the geometric properties of the design as variables. The dimensions, angles ...
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Parametric Design: a Brief History - arcCA Digest
Applying similar morphological simulations in architecture, designers in the late 1980s to mid-1990s began to use the computer alongside software developed for ...
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A History of Parametric - Daniel Davis
Aug 6, 2013 · The term parametric originates in mathematics, but there is debate as to when designers initially began using the word. David Gerber (2007, 73), ...
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How Parametric Design Is Revolutionizing Modern Architecture And ...
Dec 2, 2024 · Structural efficiency: Parametric design principles optimize material use and load distribution, lowering building costs while ensuring safety ...
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Parametric Design: What's Gotten Lost Amid the Algorithms
Jul 11, 2013 · “Imagined or perceived parameters” sounds pretty arbitrary. Indeed, the algorithms that underlie parametric modeling are altered seemingly at ...<|separator|>
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https://parametric-architecture.com/wp-content/uploads/2018/11/The-Challenges-of-Parametric-Design-in-Architecture-Today.pdf
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[2208.09591] Diffusion Models Beat GANs on Topology Optimization
Aug 20, 2022 · By introducing diffusion models to topology optimization, we show that conditional diffusion models have the ability to outperform GANs in ...<|separator|>
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Diffusion Models Beat GANs on Topology Optimization
Aug 6, 2025 · Our work demonstrates the potential of using diffusion models in topology optimization and suggests a general framework for solving engineering ...
[95]
Democratising Computational Design via Cloud Based Applications
May 8, 2025 · By leveraging cloud-based platforms like ShapeDiver, we can turn parametric models into accessible, interactive applications; tools that anyone ...
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Three Ways Additive Manufacturing is Changing Supply Chain ...
Feb 26, 2025 · According to an MIT study on the impact of 3D printing on the Global Supply Chain in 2020, the move to 3D printing allows companies to save 85% ...Missing: surge parametric
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Complete Guide to Parametric Energy Modeling: From Concept to ...
Parametric energy modeling empowers designers to explore and refine building performance from the earliest stages of design. According to the U.S. ...
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The Algorithm's Revenge: How Parametric Design Promises to ...
Sep 3, 2025 · Energy Reality: Parametric “optimization” typically reduces energy consumption by 8–15% while increasing embodied carbon by 35–60% due to ...
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Review on parametric building information modelling and forward ...
Feb 8, 2025 · Scalability proving robustness handling continent-scale production models remains unproven. ... Cost Overruns: The high initial investment in BIM ...Missing: criticisms | Show results with:criticisms<|control11|><|separator|>