Ralph Vince

Financial time series and other human-driven, non-natural processes are known to exhibit fat-tailed outcome distributions. That is, such processes demonstrate a greater tendency for extreme outcomes than the normal distribution or other natural distributional processes would predict. We examine the mathematical expectation, or simply “expectation”,...

Financial time series and other human-driven, non-natural processes are known to exhibit fat-tailed outcome distributions. That is, such processes demonstrate a greater tendency for extreme outcomes than the normal distribution or other natural distributional processes would predict. We examine the mathematical expectation, or simply "expectation,"...

The Growth-Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz’s mean-variance or risk parity. The GOP literature typically considers risk-neutral investors with an infinite investment horizon. In th...

The mathematically correct growth-optimal fraction of resources to commit to a risky proposition for all circumstances, not simply the asymptotic Kelly Criterion solution. This also requires the correct, non-asymptotic calculation for "Expectation," not merely the asymptotic, classical probability-weighted mean expectation, and shows how one conver...

Growth Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. How it is also known in practice GOP is too risky. We explain in this talk that the reason is in practice the investment horizon is finite and practitioners account for risk more explicitly. We develop risk adjusted growth portfolio and discuss ho...

Inflection points in the the function for determining estimated geometric gain with respect to capital committed emerge when planning an investment for a finite time horizon. These are points where marginal increases in reward with respect to risk peaks. We analyze the properties of inflection points for a mix of one risky asset and one risk-free a...

Growth Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz's mean-variance or risk parity. The GOP literature typically considers risk-neutral investors with an infinite investment horizon. In this p...

We develop the theory of Kelly and Thorp in analyzing the optimal bet sizes for blackjack by incorporating the practical considerations of players wherein only a finite number of plays shall occur as well as pursuing maximizing risk-adjusted returns. We show that the ratio of return to bet size is approximately proportional to the return / drawdown...

We discuss here a dynamic implementation of the leverage space portfolio theory in the form of DJ-LSP position sizing index implemented the Dow Jones indexes. Our emphasis in this case study is on the practical issues related to the implementation.