Sydney Howell

Trading Constraints and Illiquidity Discounts

Acting as the source of exogenous illiquidity, trading constraints prevent free trading of shares and discount their value relative to freely traded counterparts with identical dividends and voting rights. This paper numerically solves the theoretical illiquidity discounts for the restricted shares with long constraint horizon and then reconciles the contradictions in the results of various theoretical models. With control of leveraged positions, illiquidity discounts increase with the volatility, and their size is greatly diminished. We also empirically test the theories within the unique setting of China, which has the largest population of restricted shares worldwide. Large discounts are documented in two forms of occasional transactions in restricted shares: namely auctions and transfers. The results empirically verify the theoretical findings by showing that illiquidity discounts in auctions increase with both the volatility and constraint horizons. The results from transfers, however, are not always significant as the transfers are made privately and may be subject to price manipulation when the involved parties are related.

A statistical investigation of inventory shrinkage in a large retail chain

Abstract In a large retail chain, we used statistical regression to relate shrinkage to explanatory variables such as staffing, security, store layout and catchment-area demographics. There were large measurement errors in the retailers estimates of shrinkage, together with high correlations among the potential causal variables. These effects caused our models to give poor predictions of shrinkage for individual stores, but the models were highly statistically significant, which means that they can accurately forecast the average (and hence the aggregate) effects of policy changes affecting hundreds of stores. Factors associated with lower shrinkage included high turnover of stock, and high densities on the sales floor of staff, pay-points and customers. Our results suggest that crowding among staff and customers may be a more effective inhibitor of shrinkage than many traditional formal security precautions, such as CCTV and store detectives.

The expected lifetime of an extraction project

When a mining company begins extraction from a finite resource, it does so in the presence of numerous uncertainties. One key uncertainty is the future price of the commodity being extracted, since a large enough drop in price can make a resource no longer cost-effective to extract, resulting in the mine being closed down. By specifying a stochastic price process, and implementing a financial-type model which leads to the use of partial differential equations, this paper creates the framework for efficiently capturing the probability of a mine remaining open throughout its planned extraction period, and derives the associated expected lifetime of extraction. An approximation to the abandonment price is described, which enables a closed-form solution to be derived for the probability of operational success and expected lifetime. This approximation compares well with the full solution obtained using a semi-Lagrangian numerical technique.

The Determination of a Dynamic Cut-Off Grade for the Mining Industry

Prior to extraction from a mine, a pit is usually divided up into 3-D ‘blocks’ which contain varying levels of estimated ore-grades. From these, the order (or ‘pathway’) of extraction is decided, and this order of extraction can remain unchanged for several years. However, because commodity prices are uncertain, once each block is extracted from the mine, the company must decide in real-time whether the ore grade is high enough to warrant processing the block further in readiness for sale, or simply to waste the block. This paper first shows how the optimal cut-off ore grade—the level below which a block should be wasted—is not simply a function of the current commodity price and the ore grade, but also a function of the ore-grades of subsequent blocks, the costs of processing, and the bounds on the rates of processing and extraction. Secondly, the paper applies a stochastic price uncertainty, and shows how to derive an efficient mathematical algorithm to calculate and operate a dynamic optimal cut-off grade criterion throughout the extraction process, allowing the mine operator to respond to future market movements. The model is applied to a real mine composed of some 60,000 blocks, and shows that an extra 10% of value can be created by implementing such an optimal regime.

The evaluation of real options by managers: a potential aspect of the audit of management skills

Reports on a survey which asked 82 experienced managers from various functions, business levels, and industries to value case studies which were in effect real options on growth. Compares these empirical valuations with theoretical values derived from a specific real options model (European non‐dividend paying). In a questionnaire survey, participating managers showed high levels of agreement with various statements needed as assumptions in the real options model. They also accepted as realistic most of the parameter settings used in the experiment. Results imply that training is needed and likely to be acceptable to managers, and underinvestment could be explained by an inability to perceive option values. Choosing teams of decision makers may reduce the variance (but not the bias) of intuitive option valuations.

Parameter instability in learning curve models: Invited comments on papers by Towill and by Sharp and Price

Abstract Towill, and Sharp and Price, have confirmed that the Time Constant/Wiltshire learning curve model is relevant to wider aspects of learning, and over longer time horizons, than it was designed for. However in many contexts the model shows paradoxical properties; it is non-robust in estimation, due to instability in its parameter estimates, but robustly good at forecasting, whether the parameters are unstable or not. Researchable causes and estimation remedies are suggested, but it is also pointed out that this model should not converge in all circumstances, and failure to converge can be informative.

Modelling the number of customers as a birth and death process

Birth and death may be a better model than Brownian motion for many physical processes, which real options models will increasingly need to deal with. In this paper, we value a perpetual American call option, which gives the monopoly right to invest in a market in which the number of active customers (and hence the sales rate) follows a birth and death process. The problem contains a singular point, and we develop a mixed analytic/numeric method for handling this singular point, based on the method of Frobenius. The method may be useful for other cases of singular points. The birth and death model gives lower option values than the geometric Brownian motion model, except at very low volatilities, so that if a firm incorrectly assumes a geometric Brownian motion process in place of a birth and death process, it will invest too seldom and too late.

Pattern analysis of data for control system diagnosis

The accounts of a large retailer showed statistical evidence that shrinkage (stock loss) was being measured with serious error. As a result, profit itself in many departments was seriously in error. These errors tended to wash out over large areas of the business, but at local level, serious mistakes could be made in commercial decisions, motivation, discipline and firing. Pattern analysis revealed a set of errors that occur only one per million transactions.

Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage

A mixed financial/physical partial differential equation (PDE) can optimize the joint earnings of a single wind power generator (WPG) and a generic energy storage device (ESD). Physically, the PDE includes constraints on the ESD’s capacity, efficiency and maximum speeds of charge and discharge. There is a mean-reverting daily stochastic cycle for WPG power output. Physically, energy can only be produced or delivered at finite rates. All suppliers must commit hourly to a finite rate of delivery C, which is a continuous control variable that is changed hourly. Financially, we assume heavy ‘system balancing’ penalties in continuous time, for deviations of output rate from the commitment C. Also, the electricity spot price follows a mean-reverting stochastic cycle with a strong evening peak, when system balancing penalties also peak. Hence the economic goal of the WPG plus ESD, at each decision point, is to maximize expected net present value (NPV) of all earnings (arbitrage) minus the NPV of all expected system balancing penalties, along all financially/physically feasible future paths through state space. Given the capital costs for the various combinations of the physical parameters, the design and operating rules for a WPG plus ESD in a finite market may be jointly optimizable. This article is part of the themed issue ‘Energy management: flexibility, risk and optimization’.

Optimal costless extraction rate changes from a non-renewable resource

This paper considers the role of costless decisions relating to the extraction of a non-renewable resource in the presence of uncertainty. We begin by deriving a size scale of the extractable resource, above which the solution to the valuation and optimal control strategy can be described by analytic solutions; we produce solutions for a general form of operating cost function. Below this critical resource size level the valuation and optimal control strategy must be solved by numerical means; we present a robust numerical algorithm that can solve such a class of problem. We also allow for the embedding of an irreversible investment decision (abandonment) into the optimisation. Finally, we conduct experimentation for each of these two approaches (analytical and numerical), and show how they are consistent with one another when used appropriately. The extensions of this papers techniques to renewable resources are explored.