Capital budgeting and Kelly betting

Abstract

Capital investments are easily interpreted as bets and vice versa. The mathematical theory of betting, often known as ‘Kelly betting’, has implications for all financial decision-making under uncertainty. There have been attempts to exploit Kelly betting methods in financial portfolio optimization, but there has been little analysis of conventional capital budgeting methods against a Kelly framework. A simple comparison between methods reveals that capital budgeting decisions made using conventional finance methods can embed the error that Kelly theorists call ‘overbetting’. The outcome of overbetting is that the firm reduces its expected compound capital growth rate while simultaneously adding to the volatility of its anticipated growth path. That unfortunate pairing is mathematically precluded under Kelly betting rules but is implicitly, albeit unknowingly, sanctioned by accepted capital budgeting practices in finance. JEL Classification: G11, G12, G31