On the Relative Accuracy of Discounting Based on Risk-Free and Risky Portfolios

The degree of risk that should be incorporated into the net discount rate that is used to estimate the present value of future lost earnings has been the subject of controversy. While some forensic economists insist that a risk-free discount rate must be used, others have offered economic arguments that support use of a risk-adjusted rate. Historical simulation studies have found that, when the discount rate is based on risk-free or low-risk securities, the historical averages method of estimating present value is subject to large forecast errors due to significant changes in net discount rates over time. This study explores whether basing the discount rate on mixed portfolios of equities, intermediate- term government bonds, and Treasury bills might result in more accurate estimation. Using the historical averages method with data covering the period 1926-2008, results are generated for four mixed portfolios of varying degrees of risk, and these results are compared to the results obtained with Treasury bills, intermediate-term government bonds and long-term corporate bonds. The historical simulations do show that the mixed portfolios often provide more accurate estimates. These results should be of considerable interest to forensic economists who believe that some degree of risk should be incorporated into the discount rate

Using Historical Simulation to Compare the Accuracy of Nine Alternative Methods of Estimating the Present Value of Future Lost Earnings

To estimate the present value of future lost earnings, forensic economists must employ some method to determine the interest rate and the earnings growth rate, or the net discount rate derived from them, to use in that estimation. Historical simulation can be used to determine how accurate any such method would have been had it been used in the past. In this paper, historical simulation is used to compare the accuracy of nine different methods of choosing the net discount rate to estimate present value for numerous 30-, 20- and 10-year loss periods. These methods include historical averages, current rates, recent rates, total offset, and a number of methods that combine historical averages with current or recent rates. While no one method is obviously superior in all cases, the results do provide some support for blending historical averages with current or recent rates

The thinning of lamellae in surfactant-free foams with non-Newtonian liquid phase

Thinning rates of liquid lamellae in surfactant-free non-Newtonian gas–liquid foams, appropriate for ceramic or polymer melts and also in metals near the melting point, are derived in two dimensions by matched asymptotic analysis valid at small capillary number. The liquid viscosity is modelled (i) as a power-law function of the shear rate and (ii) by the Ellis law. Equations governing gas–liquid interface dynamics and variations in liquid viscosity are derived within the lamellar, transition and plateau border regions of a corner of the liquid surrounding a gas bubble. The results show that the viscosity varies primarily in the very short transition region lying between the lamellar and the Plateau border regions where the shear rates can become very large. In contrast to a foam with Newtonian liquid, the matching condition which determines the rate of lamellar thinning is non-local. In all cases considered, calculated lamellar thinning rates exhibit an initial transient thinning regime, followed by a t−2 power-law thinning regime, similar to the behaviour seen in foams with Newtonian liquid phase. In semi-arid foam, in which the liquid fraction is O(1) in the small capillary number, results explicitly show that for both the power-law and Ellis-law model of viscosity, the thinning of lamella in non-Newtonian and Newtonian foams is governed by the same equation, from which scaling laws can be deduced. This result is consistent with recently published experimental results on forced foam drainage. However, in an arid foam, which has much smaller volume fraction of liquid resulting in an increase in the Plateau border radius of curvature as lamellar thinning progresses, the scaling law depends on the material and the thinning rate is not independent of the liquid viscosity model parameters. Calculations of thinning rates, viscosities, pressures, interface shapes and shear rates in the transition region are presented using data for real liquids from the literature. Although for shear-thinning fluids the power-law viscosity becomes infinite at the boundaries of the internal transition region where the shear rate is zero, the interface shape, the pressure and the internal shear rates calculated by both rheological models are indistinguishable