Discounting and Consumption Over an Uncertain Horizon: Draw-Down Plans for Family Trusts

Individuals, endowments and trusts face uncertain lifetimes. When the planning horizon of an entity is stochastic and Pareto distributed, hyperbolic discounting and time-varying consumption rates are optimal. We derive expressions for the optimal rate of consumption (draw-down) from wealth for family trusts facing positive probabilities of extinction at each generation. Using birth statistics for the UK, we compute family extinction probabilities and show that they are well-approximated by a Pareto distribution, hence family trusts will discount hyperbolically. Numerically optimised consumption paths for family trusts with CRRA preferences are decreasing but always higher than for infinitely-lived trusts.family extinction; hyperbolic discounting; inter-temporal choice

Modeling style rotation: switching and re-switching

The purpose of this paper is to investigate the dynamics and statistics of style rotation based on the Barberis-Shleifer model of style switching. Investors in stocks regard the forecasting of style-relative performance, especially style rotation, as highly desirable but difficult to achieve in practice. Whilst we do not claim to be able to do this in an empirical sense, we do provide a framework for addressing these issues. We develop some new results from the Barberis-Shleifer model which allows us to understand some of the time series properties of style relative price performance and determine the statistical properties of the time until a switch between styles. We apply our results to a set of empirical data to get estimates of some of the model parameters including the level of risk aversion of market participants

Bayesian Analysis of the Black-Scholes Option Price

This paper investigates the statistical properties of the Black-Scholes option price under a Bayesian approach. We incorporate randomness, both in the price process and in volatility, to derive the prior and posterior densities of a European call option. Expressions for the density of the option price conditional on the sample estimates of volatility and on the asset price respectively, are also derived. Numerical results are presented to compare how the dispersion of the option price changes in the transition from prior to posterior information, where information may be price or sample variance or both

Scenario Analysis with Recursive Utility: Dynamic Consumption Plans for Charitable Endowments

We determine optimal consumption paths under a series of returns scenarios for charitable endowments with distinct tastes over investment risk and inter-temporal substitution. Charities typically prefer smooth consumption paths but are investment-risk tolerant. Using a recursive, Kreps-Porteus utility function, we model the optimal disbursement from an infinitely-lived charitable trust, then, allowing a general form for the returns density, we apply stochastic dominance relations to estimate income/substitution effects whereby a change in future returns influences the current consumption rate. The elasticity of intertemporal substitution rather than risk aversion is key: optimal consumption rises or falls as the elasticity diverges from one.recursive utility; stochastic dominance; inter-temporal choice

Valuation of Options in a Setting with Happiness-Augmented Preferences

We derive a pricing formula for a European call option written on equity in a framework where returns and consumption covary with external happiness. Being a non-tradable variable, happiness is regarded as an extra variable in a parameterised version of state dependent utility. We derive an extended version of the Black-Scholes (BS) formula and find that, in an optimistic environment (that is, where a high growth rate of happiness is expected), the standard BS formula may underestimate the value of the call option, and overestimate its sensitivity to changes in the underlying parameters. Under the assumption of lognormality of the happiness distribution, testable hypotheses for quality of hedging strategies can also be implemented.

Are there bubbles in the art market? The detection of bubbles when fair value is unobservable

The purpose of this paper is to look for bubbles in the Art Market using a structure based on steady state results for TAR models and appropriate definitions of bubbles recently put forward by Knight, Satchell and Srivastava (2011). The usual method for investigating bubbles is to measure prices as deviations from fair value. We assess whether it is meaningful to define a fair value of art and conclude that it is very challenging empirically to implement any definition. We then treat fair value as zero in one instance and unobservable in the other case and in both cases provide evidence of bubbles in the art market

Improved testing for the efficiency of asset pricing theories in linear factor models

This paper suggests a refinement of the standard T2 test statistic used in testing asset pricing theories in linear factor models. The test is designed to have improved power characteristics and to deal with the empirically important case where there are many more assets than time periods. This is necessary because the case of too few time periods invalidates the conventional T2. Furthermore, the test is shown to have reasonable power in cases where common factors are present in the residual covariance matrix

The properties of double-blind Dutch auctions in a clearing house; some new results for the Mendelson Model

In this paper, we re-examine Mendelson’s model for the equilibrium price of a double-blind Dutch auction with Poisson-distributed stochastic demand and supply. We present a number of new results. We focus on the various ways that demand and supply cross. We identify four different categories of crossing, extending Mendelson’s results which are based on a single category of crossing. Secondly, conditioning on quantity, we derive the joint distribution of the relevant demand and supply prices associated with such two-sided markets originally described by Bohm-Bawerk (1891). The distributional result is extended to the case where the limit orders on different sides of the market arrive at different rates. Finally, we derive the distributional properties of the price elasticities