Volatility-induced financial growth

Abstract

We show that the volatility of a price process, which is usually regarded as an impediment to financial growth, can serve as an endogenous factor in its acceleration.

Keywords:

• Volatility
• Constant proportions strategies
• Financial markets
• Investment
• Exponential growth
• Transaction costs

Acknowledgements

We are indebted to numerous colleagues who had enough patience to participate in our ‘intuition tests’, the results of which are discussed in section 4 of this paper. Our comparative analysis of volatility-induced growth and arbitrage (also contained in section 4) was motivated by Walter Schachermayer's comments at a conference on Mathematical Finance in Paris in 2003. Albert N. Shiryaev deserves our thanks for a helpful discussion of some mathematical questions related to this work. Financial support by the Swiss National Centre of Competence in Research ‘Financial Valuation and Risk Management’ (NCCR FINRISK) is gratefully acknowledged.

Notes

†In connection with the discussion of relevant literature, we can mention a strand of publications dealing with Parrondo games (Harmer and Abbott 1999). Models considered in those publications are based on the analysis of lotteries whose odds depend on the investor's wealth. It is pointed out that losing lotteries, being played in a randomized alternating order, can become winning. In spite of some similarity, there are no obvious direct links between this phenomenon and that studied in the present paper.

†For the optimal timing of rebalancing in markets with transaction costs see, e.g. Aurell and Muratore (2000).