Long-Tail Distributions And Total Returns On Risk-Based Investment Products

Abstract

<p>Use of target date funds (TDFs) in retirement plans increased in popularity following the 2007-2008 financial crisis. However, some argued that TDFs do not provide an acceptable level of protection against market downturns and long-tail events. This study assesses the ability of TDFs to deal with long-tail events. It builds a system of equations for seven asset classes that are used to build four hypothetical TDFs, and compares simulated total returns for four hypothetical TDFs over a 50-year horizon, where the stochastic terms for each of the underlying asset classes is based on the normal distribution and a long-tail distributions (the Laplace distribution). Simulations are repeated 2000 times. Total returns for four TDFs are calculated over non-overlapping 1-, 2- 3-, and 5-year horizons over the 50-year span for the 2000 simulations. Results show that about half the time the risk measure for the long-tail distribution are wider than the normal, and about half the time the opposite holds. It seems that the processes of asset diversification along with calculating returns over horizons of at least one year mitigates effects of long-tail characteristics. Even so, results do not bode well for those nearing retirement. Negative returns over 1- and 2-year investment horizons are possible 17% of the time for a conservative allocation over a 50-year period.</p>

Many-Body Quantum Chemistry on Massively Parallel Computers

“…Recent emergence of heterogeneous architectures as costefficient compute platforms has spurred efforts to utilize such platforms in the context of electronic structure. 325 Due to the complexity of programming heterogeneous computers and the large memory footprint of many-body methods (which prevents fitting all data to accelerator memory) the deployment of many-body methods onto heterogeneous platforms has been slow and usually did not target heterogeneous distributed memory platforms. The pioneering efforts in this area utilized accelerators only for tensor contractions, implemented by matricizing the argument tensors followed by dense matrix multiplication on the device using the vendorprovided BLAS library.…”

Bond-Order Time Series Analysis for Detecting Reaction Events in Ab Initio Molecular Dynamics Simulations

“…More recently, modern advances in electronic structure methods and accelerated hardware implementations have resulted in speed-ups of 2-3 orders of magnitude for Hartree-Fock and density functional theory (DFT) calculations, [24][25][26][27][28][29][30][31][32][33][34][35] placing AIMD simulations on the threshold of discovering reaction mechanisms that occur on nanosecond or longer timescales. [36][37][38][39][40][41] Because reaction rates are exponentially decreasing functions of the activation barrier, it is still highly challenging to map the chemically interesting reaction pathways in an unbiased AIMD simulation.…”