The Kelly criterion for spread bets

The optimal betting strategy for a gambler betting on a discrete number of outcomes was determined by Kelly (1956, A new interpretation of information rate. J. Oper. Res. Soc., 57, 975–985). Here, the corresponding problem is examined for spread betting, which may be considered to have a continuous distribution of possible outcomes. Since the formulae for individual events are complicated, the asymptotic limit in which the gamblers edge is small is examined, which results in universal formulae for the optimal fraction of the bank to wager, the probability of bankruptcy and the distribution function of the gamblers total capital

The small-scale manufacturing sector in Ghana: a source of dynamism or of subsistence income?

Survey data from small-scale manufacturing enterprises in Central Region, Ghana permit analysis of factors affecting performance, and of economic dynamism. The majority of the firms were sole proprietorships, with most of the hired labour being apprentices. A high proportion of rural-based proprietors and many urban-based proprietors had secondary occupations. All but two of the industry groups were unprofitable when the legal minimum wage was used as a proxy for the value of proprietors' time. The implication of this is that the small-scale industries are principally a source of modest income and may not be financially and economically dynamic. However, the small enterprises surveyed do seem to represent part of a 'sustainable livelihoods' strategy of lowering economic risk by diversifying income sources. Copyright © 2007 John Wiley & Sons, Ltd.