On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important

The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to subsequent lows. Motivated by the fact that this issue is of paramount concern to conservative investors, we dispense with the classical variance as the risk metric and work with drawdown and mean return as the risk-reward pair. In this setting, the main results in this paper address the so-called "efficiency" of linear time-invariant (LTI) investment feedback strategies which correspond to Markowitz-style schemes in the finance literature. Our analysis begins with the following principle which is widely used in finance: Given two investment opportunities, if one of them has higher risk and lower return, it will be deemed to be inefficient or strictly dominated and generally rejected in the marketplace. In this framework, with risk-reward pair as described above, our main result is that classical Markowitz-style strategies are inefficient. To establish this, we use a new investment strategy which involves a time-varying linear feedback block K(k), called the drawdown modulator. Using this instead of the original LTI feedback block K in the Markowitz scheme, the desired domination is obtained. As a bonus, it is also seen that the modulator assures a worst-case level of drawdown protection with probability one.Comment: This paper has been published in Proceedings of 56th IEEE Conference on Decision and Control (CDC) 201

Kelly Betting Can Be Too Conservative

Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes arguments that the theory often leads to bets which are "too aggressive" with respect to various risk metrics. To remedy this problem, many papers include prescriptions for scaling down the bet size. Such schemes are referred to as Fractional Kelly Betting. In this paper, we take the opposite tack. That is, we show that in many cases, the theoretical Kelly-based results may lead to bets which are "too conservative" rather than too aggressive. To make this argument, we consider a random vector X with its assumed probability distribution and draw m samples to obtain an empirically-derived counterpart Xhat. Subsequently, we derive and compare the resulting Kelly bets for both X and Xhat with consideration of sample size m as part of the analysis. This leads to identification of many cases which have the following salient feature: The resulting bet size using the true theoretical distribution for X is much smaller than that for Xhat. If instead the bet is based on empirical data, "golden" opportunities are identified which are essentially rejected when the purely theoretical model is used. To formalize these ideas, we provide a result which we call the Restricted Betting Theorem. An extreme case of the theorem is obtained when X has unbounded support. In this situation, using X, the Kelly theory can lead to no betting at all.Comment: Accepted in 2016 IEEE 55th Conference on Decision and Control (CDC

Addressing Cultural Pluralism from an Evangelical Christian Perspective

The complex issues surrounding cultural pluralism are rapidly turning the public square into a battlefield that divides our country. As Charles Haynes summarized, “At issue for this nation, as for much of the world, is the simple but profound question that runs through modern experience: How will we live with our deepest differences?” (Haynes, 1994). At a time when many citizens of our diverse nation have become disillusioned with the motto e pluribus unum, the Christian higher education community deals with issues involving race, ethnicity, and gender through a variety of responses ranging from isolationism to unqualified inclusion. Evangelical institutions of higher learning are not new to the discussion of multiculturalism. They have rather a rich history of commitment to living out Christ’s commandment to love one’s neighbor as oneself (Mk 12:31) regarding each other through the unity of faith in Christ (Gal 3:28). This paper addresses the historical context for understanding cultural pluralism together with the scriptural and religious imperatives for engaging Christian and secular audiences on this issue. It identifies several of the issues surrounding cultural pluralism faced by evangelicals today, while also developing criteria for celebrating and confronting pluralism. Finally, it articulates strategies for pursuing common ground in the public arena and discusses implications for Christian higher education in addressing cultural pluralism within and beyond the college classroom

Distributed allocation of mobile sensing swarms in gyre flows

We address the synthesis of distributed control policies to enable a swarm of homogeneous mobile sensors to maintain a desired spatial distribution in a geophysical flow environment, or workspace. In this article, we assume the mobile sensors (or robots) have a "map" of the environment denoting the locations of the Lagrangian coherent structures or LCS boundaries. Based on this information, we design agent-level hybrid control policies that leverage the surrounding fluid dynamics and inherent environmental noise to enable the team to maintain a desired distribution in the workspace. We establish the stability properties of the ensemble dynamics of the distributed control policies. Since realistic quasi-geostrophic ocean models predict double-gyre flow solutions, we use a wind-driven multi-gyre flow model to verify the feasibility of the proposed distributed control strategy and compare the proposed control strategy with a baseline deterministic allocation strategy. Lastly, we validate the control strategy using actual flow data obtained by our coherent structure experimental testbed.Comment: 10 pages, 14 Figures, added reference