{Solo-Authored Research Program.}

"One man writes a novel. One man writes a symphony. It is essential that one man make a film." --Stanley Kubrick

[> Submitted Research Papers.

Garivaltis, A., 2022. Recursive Overbetting of a Satellite Investment Account. Submitted.

  • Announced on arXiv: June 22, 2022.

  • Spreadsheet Model.

  • Abstract: This paper builds a core-satellite model of semi-static Kelly betting and log-optimal investment. We study the problem of a saver whose core portfolio consists in unlevered (1x) retirement plans with no access to margin debt. However, the agent has a satellite investment account with recourse to significant, but not unlimited, leverage; accordingly, we study optimal controllers for the satellite gearing ratio. On a very short time horizon, the best policy is to overbet the satellite, whereby the overriding objective is to raise the aggregate beta toward a growth-optimal level. On an infinite horizon, by contrast, the correct behavior is to blithely ignore the core and optimize the exponential growth rate of the satellite, which will anyways come to dominate the entire bankroll in the limit. For time horizons strictly between zero and infinity, the optimal strategy is not so simple: there is a key trade-off between the instantaneous growth rate of the composite bankroll, and that of the satellite itself, which suffers ongoing volatility drag from the overbetting. Thus, a very perspicacious policy is called for, since any losses in the satellite will constrain the agent's access to leverage in the continuation problem. We characterize the optimal feedback controller, and compute it in earnest by solving the corresponding HJB equation recursively and backward in time. This solution is then compared to the best open-loop controller, which, in spite of its relative simplicity, is expected to perform similarly in practical situations.

  • Keywords: Stochastic Control; Kelly Criterion; Asymptotic Capital Growth; Log-Optimal Portfolios; Geared Investment; Leveraged ETFs; Controlled Diffusion Processes; Markov Decision Processes; Lattice-Based Models; Lifecycle Investing; Leverage Constraints.

  • JEL Classification Codes: C44; C61; D14; D15; D81; G00; G10; G11.

Garivaltis, A., 2021. Grade Inflation and Stunted Effort in a Curved Economics Course. Submitted.

  • Announced on arXiv: August 8, 2021.

  • Spreadsheet Model.

  • Abstract: To protect his teaching evaluations, an economics professor uses the following exam curve: if the class average falls below a known target, m, then all students will receive an equal number of free points so as to bring the mean up to m. If the average is above m then there is no curve; curved grades above 100% will never be truncated to 100% in the gradebook. The n students in the course all have Cobb-Douglas preferences over the grade-leisure plane; effort corresponds exactly to earned (uncurved) grades in a 1:1 fashion. The elasticity of each student's utility with respect to his grade is his ability parameter, or relative preference for a high score. I find, classify, and give complete formulas for all the pure Nash equilibria of my own game, which my students have been playing for some eight semesters. The game is supermodular, featuring strategic complementarities, negative spillovers, and nonsmooth payoffs that generate non-convexities in the reaction correspondence. The n+2 types of equilibria are totally ordered with respect to effort and Pareto preference, and the lowest n+1 of these types are totally ordered in grade-leisure space. In addition to the no-curve ("try-hard") and curved interior equilibria, we have the "k-don't care" equilibria, whereby the k lowest-ability students are no-shows. As the class size becomes infinite in the curved interior equilibrium, all students increase their leisure time by a fixed percentage, i.e., 14%, in response to the disincentive, which amplifies any pre-existing ability differences. All students' grades inflate by this same (endogenous) factor, say, 1.14 times what they would have been under the correct standard.

  • Keywords: Economics of Education; Supermodular Games; Strategic Complementarity; Grade Inflation; Continuous Games; Increasing Returns; Negative Spillovers; Ordered Comparative Statics; Coordination Games.

  • JEL Classification Codes: A20; A22; C62; C70; C72; I20; I21; I23.

Garivaltis, A., 2021. Waiting to Borrow From a 457(b) Plan. Under Review.

  • Announced on arXiv: July 9, 2021.

  • Historical Contribution Limits.

  • Abstract: This paper formulates and solves the optimal stopping problem for a loan made to one's self from a tax-advantaged retirement account such as a 401(k), 403(b), or 457(b) plan. If the plan participant has access to an external asset with a higher expected rate of return than the investment funds and indices that are available within the retirement account, then he must decide how long to wait before exercising the loan option. On the one hand, taking the loan quickly will result in many years of exponential capital growth at the higher (external) rate; on the other hand, if we wait to accumulate more funds in the 457(b), then we can make a larger deposit into the external asset (albeit for a shorter period of time). I derive a variety of cutoff rules for optimal loan control; in general, the investor must wait until he accumulates a certain amount of money (measured in contribution-years) that depends on the disparate yields, the loan parameters, and the date certain at which he will liquidate the retirement account. Letting the horizon tend to infinity, the optimal (horizon-free) policy gains in elegance, simplicity, and practical robustness to different life outcomes. When asset prices and returns are stochastic, the (continuous time) cutoff rule turns into a "wait region," whereby the mean of terminal wealth is rising and the variance of terminal wealth is falling. After his sojourn through the wait region is over, the participant finds himself on the mean-variance frontier, at which point his subsequent behavior is a matter of personal risk preference.

  • Keywords: Retirement Accounts; Defined Contribution Plans; Tax Planning; Mean-Variance Frontier; 401(k) Plans; Optimal Stopping; Financial Decision Making; Asset Management; Household Finance; Consumer Finance.

  • JEL Classification Codes: D14; D15; G11; G19; G23; G28; G29; H26.

Garivaltis, A., 2021. Long Run Feedback in the Broker Call Money Market. Submitted.

  • Announced on arXiv: June 24, 2019.

  • Abstract: I unravel the basic long run dynamics of the broker call money market, which is the pile of cash that funds margin loans to retail clients (read: continuous time Kelly gamblers). Call money is assumed to supply itself perfectly inelastically, and to continuously reinvest all principal and interest. I show that the relative size of the money market (that is, relative to the Kelly bankroll) is a martingale that nonetheless converges in probability to zero. The margin loan interest rate is a submartingale that converges in mean square to the choke price r:= ν−σ^2/2, where ν is the asymptotic compound growth rate of the stock market and σ is its annual volatility. In this environment, the gambler no longer beats the market asymptotically a.s. by an exponential factor (as he would under perfectly elastic supply). Rather, he beats the market asymptotically with very high probability (think 98%) by a factor (say 1.87, or 87% more final wealth) whose mean cannot exceed what the leverage ratio was at the start of the model (say, 2:1). Although the ratio of the gambler’s wealth to that of an equivalent buy-and-hold investor is a submartingale (always expected to increase), his realized compound growth rate converges in mean square to ν. This happens because the equilibrium leverage ratio converges to 1:1 in lockstep with the gradual rise of margin loan interest rates.

  • Keywords: Interest Rates; Margin Loans; Kelly Criterion; Risk Sharing.

  • JEL Classification Codes: D14; D53; E41; E43; G11; G17; G24.

Garivaltis, A., 2021. Rational Pricing of Leveraged ETF Expense Ratios. Accepted at Annals of Finance.

  • Announced on arXiv: June 28, 2021.

  • Leveraged ETF Data.

  • Abstract: This paper studies the general relationship between the gearing ratio of a Leveraged ETF and its corresponding expense ratio, viz., the investment management fees that are charged for the provision of this levered financial service. It must not be possible for an investor to combine two or more LETFs in such a way that his (continuously-rebalanced) LETF portfolio can match the gearing ratio of a given, professionally managed product and, at the same time, enjoy lower weighted-average expenses than the existing LETF. Given a finite set of LETFs that exist in the marketplace, I give necessary and sufficient conditions for these products to be undominated in the price-gearing plane. In an application of the duality theorem of linear programming, I prove a kind of two-fund theorem for LETFs: given a target gearing ratio for the investor, the cheapest way to achieve it is to combine (uniquely) the two nearest undominated LETF products that bracket it on the leverage axis. This also happens to be the implementation with the lowest annual turnover. For completeness, we supply a second proof of the Main Theorem on LETFs that is based on Carathéodory's theorem in convex geometry. Thus, say, a triple-leveraged ("UltraPro") exchange-traded product should never be mixed with cash, if the investor is able to trade in the underlying index. In terms of financial innovation, our two-fund theorem for LETFs implies that the introduction of new, undominated 2.5x products would increase the welfare of all investors whose preferred gearing ratios lie between 2x ("Ultra") and 3x ("UltraPro"). Similarly for a 1.5x product.

  • Keywords: Leveraged ETFs; Margin Loans; Expense Ratios; Investment Management; Cost of Leverage; Volatility Decay.

  • JEL Classification: C44; D24; D81; G11; G23; G51; G53.

[> Published Research Papers.

  1. Garivaltis, A., 2021. Cover’s Rebalancing Option with Discrete Hindsight Optimization. The Journal of Derivatives, 29(2), pp.8-29.

  • Announced on arXiv: March 3, 2019.

  • DOI: https://doi.org/10.3905/jod.2021.1.135.

  • Author's Copy.

  • Editor's Letter.

  • Maple Code and Maple Output.

  • Abstract: The author studies T. Cover’s rebalancing option (Ordentlich and Cover (1998)) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to an initial deposit of 1 unit of the numéraire into the best of some finite set of (perhaps levered) rebalancing rules determined in hindsight. A rebalancing rule (or fixed-fraction betting scheme) amounts to fixing an asset allocation (i.e., 200% equities and −100% bonds) and then continuously executing rebalancing trades so as to counteract allocation drift. Restricting the hindsight optimization to a small number of rebalancing rules (i.e., 2) has some advantages over the pioneering approach taken by Cover & Company in their theory of universal portfolios (1986, 1991, 1996, 1998), wherein one’s trading performance is benchmarked relative to the final wealth of the best unlevered rebalancing rule (of any kind) in hindsight. Our approach lets practitioners express an a priori view that one of the favored asset allocations (“bets”) in the set {b1,…,bn} will turn out to have performed spectacularly well in hindsight. In limiting our robustness to some discrete set of asset allocations (rather than all possible asset allocations) we reduce the price of the rebalancing option and guarantee that we will achieve a correspondingly higher percentage of the hindsight-optimized wealth at the end of the planning period. A practitioner who lives to delta-hedge this variant of Cover’s rebalancing option through several decades is guaranteed to see the day that his realized compound-annual capital growth rate is very close to that of the best bi in hindsight. Hence the point of the rock-bottom option price.

  • Keywords: Adaptive Asset Allocation; Continuously-Rebalanced Portfolios; Exchange Options; Kelly Criterion; Lookback Options; On-Line Portfolio Selection; Rainbow Options; Robust Procedures; Universal Portfolios.

  • JEL Classification Codes: C44; D80; D81; G11.

  1. Garivaltis, A., 2019. Exact Replication of the Best Rebalancing Rule in Hindsight. The Journal of Derivatives, 26(4), pp.35-53.

  • Announced on arXiv: October 5, 2018.

  • DOI: https://doi.org/10.3905/jod.2019.26.4.035.

  • Author's Copy.

  • Editor's Letter.

  • Maple Code and Maple Output.

  • Presentation Slides.

  • Abstract: This paper prices and replicates the financial derivative whose payoff at T is the wealth that would have accrued to a $1 deposit into the best continuously-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. For the single-stock Black-Scholes market, Ordentlich and Cover (1998) only priced this derivative at time-0, giving C0=1+σ*sqrt[T/(2*π)]. Of course, the general time-t price is not equal to 1+σ*sqrt[T/(2π)]. I complete the Ordentlich-Cover (1998) analysis by deriving the price at any time t. By contrast, I also study the more natural case of the best levered rebalancing rule in hindsight. This yields C(S,t)=sqrt(T/t)*exp[r*t+σ^2*b(S,t)^2*t/2], where b(S,t) is the best rebalancing rule in hindsight over the observed history [0,t]. I show that the replicating strategy amounts to betting the fraction b(S,t) of wealth on the stock over the interval [t,t+dt]. This fact holds for the general market with n correlated stocks in geometric Brownian motion: we get C(S,t)=(T/t)^(n/2)*exp(r*t+b'Σb*t/2), where Σ is the covariance of instantaneous returns per unit time. This result matches the O(T^(n/2)) “cost of universality” derived by Cover in his “universal portfolio theory” (1986, 1991, 1996, 1998), which super-replicates the same derivative in discrete-time. The replicating strategy compounds its money at the same asymptotic rate as the best levered rebalancing rule in hindsight, thereby beating the market asymptotically. Naturally enough, we find that the American-style version of Cover’s Derivative is never exercised early in equilibrium.

  • Keywords: Exotic Options; Lookback Options; Correlation Options; Continuously-Rebalanced Portfolios; Kelly Criterion; Universal Portfolios; Dynamic Replication.

  • JEL Classification Codes: C44; D53; D81; G11; G13.

  1. Garivaltis, A., 2019. Two Resolutions of the Margin Loan Pricing Puzzle. Research in Economics, 73(2), pp.199-207.

  • Announced on arXiv: June 3, 2019.

  • DOI: https://doi.org/10.1016/j.rie.2019.04.006.

  • Author's Copy.

  • Abstract: This paper supplies two possible resolutions of Fortune’s (2000) margin loan pricing puzzle. Fortune (2000) noted that the margin loan interest rates charged by stock brokers are very high in relation to the actual (low) credit risk and the cost of funds. If we live in the Black-Scholes world, the brokers are presumably making arbitrage profits by shorting dynamically precise amounts of their clients’ portfolios. First, we extend Fortune’s (2000) application of Merton’s (1974) no-arbitrage approach to allow for brokers that can only revise their hedges finitely many times during the term of the loan. We show that extremely small differences in the revision frequency can easily explain the observed variation in margin loan pricing. In fact, four additional revisions per three-day period serve to explain all of the currently observed heterogeneity. Second, we study monopolistic (or oligopolistic) margin loan pricing by brokers whose clients are continuous-time Kelly gamblers. The broker solves a general stochastic control problem that yields simple and pleasant formulas for the optimal interest rate and the net interest margin. If the author owned a brokerage, he would charge an interest rate of (r+ν)/2−σ^2/4, where r is the cost of funds, ν is the compound-annual growth rate of the S&P 500 index, and σ is the volatility.

  • Keywords: Margin Loan Pricing; Arbitrage Pricing; Super-Hedging; Net Interest Margin; Continuous-Time Kelly Rule.

  • JEL Classification Codes: C44; D42; D43; D53; D81; E43; G11; G13; G24.

  1. Garivaltis, A., 2019. Game-Theoretic Optimal Portfolios in Continuous Time. Economic Theory Bulletin, 7(2), pp.235-243.

  • Announced on arXiv: June 5, 2019.

  • DOI: https://doi.org/10.1007/s40505-018-0156-5.

  • Author's Copy.

  • Maple Code and Maple Output.

  • Abstract: We consider a two-person trading game in continuous time where each player chooses a constant rebalancing rule b that he must adhere to over [0,t]. If V(t,b) denotes the final wealth of the rebalancing rule b, then Player 1 (the “numerator player”) picks b so as to maximize E[V(t,b)/V(t,c)], while Player 2 (the “denominator player”) picks c so as to minimize it. In the unique Nash equilibrium, both players use the continuous-time Kelly rule b*=c*=(Σ^−1)*(µ−r1), where Σ is the covariance of instantaneous returns per unit time, µ is the drift vector, and 1 is a vector of ones. Thus, even over very short intervals of time [0,t], the desire to perform well relative to other traders leads one to adopt the Kelly rule, which is ordinarily derived by maximizing the asymptotic exponential growth rate of wealth. Hence, we find agreement with Bell and Cover’s (1988) result in discrete time.

  • Keywords: Optimal Portfolio Choice; Continuously-Rebalanced Portfolios, Continuous-Time Kelly Rule; Minimax.

  • JEL Classification Codes: C44; D80; D81; G11.

  1. Garivaltis, A., 2021. Universal Risk Budgeting. Annals of Financial Economics, p.2150014.

  • Announced on arXiv: June 18, 2021.

  • DOI: https://doi.org/10.1142/s2010495221500147.

  • Author's Copy.

  • Abstract: I juxtapose Cover’s vaunted universal portfolio selection algorithm (Cover 1991) with the modern representation (Qian 2016; Roncalli 2013) of a portfolio as a certain allocation of risk among the available assets, rather than a mere allocation of capital. Thus, I define a Universal Risk Budgeting scheme that weights each risk budget (instead of each capital budget) by its historical performance record (á la Cover). I prove that my scheme is mathematically equivalent to a novel type of Cover and Ordentlich 1996 universal portfolio that uses a new family of prior densities that have hitherto not appeared in the literature on universal portfolio theory. I argue that my universal risk budget, so-defined, is a potentially more perspicuous and flexible type of universal portfolio; it allows the algorithmic trader to incorporate, with advantage, his prior knowledge (or beliefs) about the particular covariance structure of instantaneous asset returns. Say, if there is some dispersion in the volatilities of the available assets, then the uniform (or Dirichlet) priors that are standard in the literature will generate a dangerously lopsided prior distribution over the possible risk budgets. In the author’s opinion, the proposed “Garivaltis prior” makes for a nice improvement on Cover’s timeless expert system (Cover 1991), that is properly agnostic and open (from the very get-go) to different risk budgets. Inspired by Jamshidian 1992, the universal risk budget is formulated as a new kind of exotic option in the continuous time Black and Scholes 1973 market, with all the pleasure, elegance, and convenience that that entails.

  • Keywords: Risk Decomposition; Risk Contributions; Risk Budgeting; Risk Parity; On-Line Portfolio Selection; Portfolio Construction; Universal Portfolios; Correlation Options, Expert Systems; Multi-Armed Bandit Problem.

  • JEL Classification Codes: D80; D81; D83; G11; G13; G17.

  1. Garivaltis, A., 2021. A Note on Universal Bilinear Portfolios. International Journal of Financial Studies, 9(1), 11.

  • Announced on arXiv: July 23, 2019.

  • DOI: https://doi.org/10.3390/ijfs9010011.

  • Author's Copy.

  • Maple Code and Maple Output.

  • Abstract: This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of “universal portfolios”. I generalize Cover’s benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hindsight for the realized sequence of asset prices. A bilinear trading strategy is a mini two-period active strategy whose final capital growth factor is linear separately in each period’s gross return vector for the asset market. I apply Thomas Cover’s ingenious performance-weighted averaging technique to construct a universal bilinear portfolio that is guaranteed (uniformly for all possible market behavior) to compound its money at the same asymptotic rate as the best bilinear trading strategy in hindsight. Thus, the universal bilinear portfolio asymptotically dominates the original (1-linear) universal portfolio in the same technical sense that Cover’s universal portfolios asymptotically dominate all constant-rebalanced portfolios and all buy-and-hold strategies. In fact, like so many Russian dolls, one can get carried away and use these ideas to construct an endless hierarchy of ever more dominant H-linear universal portfolios.

  • Keywords: On-Line Portfolio Selection (OPS); Universal Portfolios; Robust Procedures; Model Uncertainty; Constant-Rebalanced Portfolios; Asymptotic Capital Growth; Kelly Criterion.

  • JEL Classification Codes: D81; D83; G11.

  1. Garivaltis, A., 2019. The Laws of Motion of the Broker Call Rate in the United States. International Journal of Financial Studies, 7(4), 56.

  • Announced on arXiv: June 3, 2019.

  • DOI: https://doi.org/10.3390/ijfs7040056.

  • Author's Copy.

  • Abstract: In this paper, which is the third installment of the author’s trilogy on margin loan pricing, we analyze 1,367 monthly observations of the U.S. broker call money rate, e.g., the interest rate at which stockbrokers can borrow to fund their margin loans to retail clients. We describe the basic features and mean-reverting behavior of this series and juxtapose the empirically-derived laws of motion with the author’s prior theories of margin loan pricing (Garivaltis 2019a, 2019b). This allows us to derive stochastic differential equations that govern the evolution of the margin loan interest rate and the leverage ratios of sophisticated brokerage clients (namely, continuous-time Kelly gamblers). Finally, we apply Merton’s (1974) arbitrage theory of corporate liability pricing to study theoretical constraints on the risk premia that could be generated in the market for call money. Apparently, if there is no arbitrage in the U.S. financial markets, the implication is that the total volume of call loans must constitute north of 70% of the value of all leveraged portfolios.

  • Keywords: Broker Call Rate; Call Money Rate; Margin Loans; Net Interest Margin; Risk Premium; Mean-Reverting Processes; Vasicek Model; Kelly Criterion; Monopoly Pricing; Arbitrage Pricing.

  • JEL Classification Codes: C22; C58; D42; D53; E17; E31; E41; G17; G21.

  1. Garivaltis, A., 2019. Nash Bargaining Over Margin Loans to Kelly Gamblers. Risks, 7(3), 93.

  • Announced on arXiv: April 14, 2019.

  • DOI: https://doi.org/10.3390/risks7030093.

  • Author's Copy.

  • Abstract: I derive practical formulas for optimal arrangements between sophisticated stock market investors (continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e., the market portfolio). Rather than, say, the broker posting a monopoly price for margin loans, the gambler agrees to use a greater quantity of margin debt than he otherwise would in exchange for an interest rate that is lower than the broker would otherwise post. The gambler thereby attains a higher asymptotic capital growth rate and the broker enjoys a greater rate of intermediation profit than would be obtained under non-cooperation. If the threat point represents a complete breakdown of negotiations (resulting in zero margin loans), then we get an elegant rule of thumb: rL=(3/4)*r+(1/4)*(ν−σ^2/2), where r is the broker’s cost of funds, ν is the compound-annual growth rate of the market index, and σ is the annual volatility. We show that, regardless of the particular threat point, the gambler will negotiate to size his bets as if he himself could borrow at the broker’s call rate.

  • Keywords: Nash Bargaining; Margin Loans; Kelly Betting; Log-Optimal Portfolios; Continuously-Rebalanced Portfolios; Net Interest Margin.

  • JEL Classification Codes: C78; D42; G11; G21; G24.

  1. Garivaltis, A., 2019. Game-Theoretic Optimal Portfolios for Jump Diffusions. Games, 10(1), 8.

  • Announced on arXiv: December 11, 2018.

  • DOI: https://doi.org/10.3390/g10010008.

  • Author's Copy.

  • Abstract: This paper studies a two-person trading game in continuous time that generalizes Garivaltis (2018) to allow for stock prices that both jump and diffuse. Analogous to Bell and Cover (1988) in discrete time, the players start by choosing fair randomizations of the initial dollar, by exchanging it for a random wealth whose mean is at most 1. Each player then deposits the resulting capital into some continuously rebalanced portfolio that must be adhered to over [0,t]. We solve the corresponding “investment ϕ-game”, namely the zero-sum game with payoff kernel E[ϕ{W1*V(t,b)/(W2*V(t,c))}], where Wi is player i's fair randomization, V(t,b) is the final wealth that accrues to a one dollar deposit into the rebalancing rule b, and ϕ() is any increasing function meant to measure relative performance. We show that the unique saddle point is for both players to use the (leveraged) Kelly rule for jump diffusions, which is ordinarily defined by maximizing the asymptotic almost-sure continuously compounded capital growth rate. Thus, the Kelly rule for jump diffusions is the correct behavior for practically anybody who wants to outperform other traders (on any time frame) with respect to practically any measure of relative performance.

  • Keywords: Optimal Portfolio Choice; Continuously Rebalanced Portfolios; Kelly Criterion; Log-Optimal Investment; Minimax; Jump Processes.

  • JEL Classification Codes: C44; D80; D81; G11.

  1. Garivaltis, A., 2019. Super-Replication of the Best Pairs Trade in Hindsight. Cogent Economics & Finance, 7(1), 1568657.

  • Announced on arXiv: October 4, 2018.

  • DOI: https://doi.org/10.1080/23322039.2019.1568657.

  • Author's Copy.

  • Abstract: This paper derives a robust online equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target fraction of wealth in each of the two. After each discrete market fluctuation, a pairs rebalancing rule will sell a precise amount of the outperforming stock and put the proceeds into the underperforming stock. Under typical conditions, in hindsight one can find pairs rebalancing rules that would have spectacularly beaten the market. Our trading strategy, which extends Ordentlich and Cover’s “max-min universal portfolio,” guarantees to achieve an acceptable percentage of the hindsight-optimized wealth, a percentage which tends to zero at a slow (polynomial) rate. This means that on a long enough investment horizon, the trader can enforce a compound-annual growth rate that is arbitrarily close to that of the best pairs rebalancing rule in hindsight. The strategy will “beat the market asymptotically” if there turns out to exist a pairs rebalancing rule that grows capital at a higher asymptotic rate than the market index. The advantages of our algorithm over the Ordentlich and Cover strategy are twofold. First, their strategy is impossible to compute in practice. Second, in considering the more modest benchmark (instead of the best all-stock rebalancing rule in hindsight), we reduce the “cost of universality” and achieve a higher learning rate.

  • Keywords: Super-Replication; Pairs Trading; Correlation Options; Constant-Rebalanced Portfolios; Universal Portfolios; Kelly Criterion; Robust Procedures; Minimax.

  • JEL Classification Codes: C44; D81; D83; G11; G12; G13.

[> Working Papers.

  • "Does the NBA Pay Structure Favor Superstar Players? A Non-Parametric Investigation." [with Milivoje Davidovic] [Abstract]

  • "Margin Loan Pricing Analytics."

  • "Multilinear Superhedging of Lookback Options."

  • "The Geometry of Historical Stock Prices."

  • "Kelly Betting on Hidden Markov Models of the Stock Market."

  • "Some Notes on Jamshidian's Universal Portfolio."

  • "[REDACTED]."

  • "[REDACTED]."

  • "[REDACTED]."

[> Handbook Proposals, Editorial & Referee Activity.

  • "Handbook of Portfolio Optimization and On-Line Portfolio Selection," solicited by Walter de Gruyter GmbH.

  • Member of the Editorial Board, International Journal of Financial Studies (IJFS). Editor of the Special Issue "Leveraged, Inverse, and Specialty ETFs."

  • Referee for The Journal of Derivatives (JoD); Managerial & Decision Economics (MDE); Annals of Operations Research (ANOR), Annals of Finance (AOFI), Computational Economics (CSEM); Risks; Economies; International Journal of Financial Studies (IJFS); Operational Research: an International Journal; Expert Systems with Applications: an International Journal (ESWA); Annals of Financial Economics (AFE).

[> Grant Proposals.

  • “Waiting to Borrow From a 457(b) Plan: Large Scale Modelling and Simulation of Retirement Plan Loans.” Steven H. Sandell Grant Proposal, The Center for Retirement Research at Boston College.