Abstract

Improvement in Economic Position through Risk-Taking: An Attempt to Map Intertemporal Risk-Consumption

In this paper the possibility of overcoming an initial lack of sufficient economic assets through increased willingness to take risk (lower risk-aversion), is investigated. Compared are the situations of two investors, one of them possessing large, the other small economic assets. Both are risk-averters. In the computer model it is assumed that both investors can make their asset choices from the same opportunity set of m securities, which contains low as well as high risk securities. In each investment period optimal portfolios are selected. The condition is, however, that the investors have to egress after n investment periods from the security markets with assets equal to their initial ones. Because there is no net accumulation, the income streams emanating from the two portfolios result in differences in consumption levels. Inter-temporal consumption is a function of risk-aversion only. There are thus inter-temporal risk-consumption frontiers. These were computed in a simulation process and they were mapped in diagram 1. The conclusion of this study is that the possibility to compensate in a competitive world for a difference in initial wealth through increased risk-taking - a degree of freedom the less-wealthy has to improve his lot - is limited. The larger the wealth differential, the smaller the chance to catch up. This will be all the more so if the per unit investment cost (transaction cost, cost of obtaining information, etc.) which was assumed to be the same in this study, ıs higher for the small than the large investor. Finally, catching up becomes will-nigh impossible if with increased wealth goes, pari passu, a decreased risk-aversion, the rich man taking more risk because he can afford it.