Necessary and Sufficient Conditions for Frequency-Based Kelly Optimal Portfolio

Hsieh, Chung-Han

doi:10.1109/lcsys.2020.3002214

Cited by 7 publications

(11 citation statements)

References 21 publications

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“…Remark 2.1: (i) If α = 1, the double linear feedback scheme reduces to the classical single (pure long) linear feedback; see [18]- [20]. (ii) Indeed, as seen later in this paper, the parameter α is the key to guarantee the RPE property.…”

Section: Modified Sls: Double Linear Feedback Controlmentioning

confidence: 96%

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On Robust Optimal Linear Feedback Stock Trading

Hsieh¹

2022

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The take-off point for this paper is the Simultaneous Long-Short (SLS) control class, which is known to guarantee the so-called robust positive expectation (RPE) property. That is, the expected cumulative trading gain-loss function is guaranteed to be positive for a broad class of stock price processes. This fact attracts many new extensions and ramifications to the SLS theory. However, it is arguable that a "systematic" way to select an optimal decision variable that is robust in the RPE sense is still unresolved. To this end, we propose a modified SLS control structure, which we call the double linear feedback control scheme, that allows us to solve the issue above for stock price processes involving independent returns. In this paper, we go beyond the existing literature by not only deriving explicit expressions for the expected value and variance of cumulative gain-loss function but also proving various theoretical results regarding robust positive expected growth and monotonicity. Subsequently, we propose a new robust optimal gain selection problem that seeks a solution maximizing the expected trading gain-loss subject to the prespecified standard deviation and RPE constraints. Under some mild conditions, we show that the optimal solution exists and is unique. Moreover, a simple graphical approach that allows one to systematically determine the optimal solution is also proposed. Finally, some numerical and empirical studies using historical price data are also provided to support our theory.

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Section: Modified Sls: Double Linear Feedback Controlmentioning

confidence: 96%

“…Consistent with the existing literature; e.g., [4]- [6], [9]- [11], [18]- [20], we assume that stock trading occurs within an "idealized market," which plays an important role of benchmark for the practical trading. That is, we assume zero transaction costs and perfect liquidity conditions.…”

Section: A Idealized Market Assumptionsmentioning

confidence: 99%

On Robust Optimal Linear Feedback Stock Trading

Hsieh¹

2022

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“…That is, with K ∈ K, we have a guarantee that 100% of the account is invested. Moreover, we note that the constraint set K assures trader's survivability; i.e., no bankruptcy is guaranteed; see also [9] for a discussion of this important property.…”

Section: Admissible Set Of Portfolio Weightsmentioning

confidence: 99%

“…In this subsection, we review two technical notions called relative attractiveness and dominant asset that are useful for the later development. Indeed, according to [9,13], these two notions enable us to state a result called the Dominate Asset Theorem, which tells us that if a portfolio contains a dominant asset, then a log-optimal trader should invest all available funds on that asset. Definition 2.1 (Relative Attractiveness and Dominant Asset).…”

Section: Notion Of Relative Attractiveness and Dominant Assetmentioning

confidence: 99%

“…Compared with many of the recent papers that contributed to the ELG maximization problem and its application to stock trading, the effects of rebalancing frequency are arguably not heavily considered into the existing literature. Some initial results along this line regarding rebalancing frequency effects can be found in [6,7,9,11,13,15]. Specifically, in [15], a portfolio optimization with returns following a continuous geometric Brownian motion was considered.…”

Section: Introductionmentioning

confidence: 99%

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On Asymptotic Log-Optimal Buy-and-Hold Strategy

Hsieh

2021

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In this paper, we consider a frequency-based portfolio optimization problem with m ≥ 2 assets when the expected logarithmic growth (ELG) rate of wealth is used as the performance metric. With the aid of the notion called dominant asset, it is known that the optimal ELG level is achieved by investing all available funds on that asset. However, such an "all-in" strategy is arguably too risky to implement in practice. Motivated by this issue, we study the case where the portfolio weights are chosen in a rather ad-hoc manner and a buy-and-hold strategy is subsequently used. Then we show that, if the underlying portfolio contains a dominant asset, buy and hold on that specific asset is asymptotically log-optimal with a sublinear rate of convergence. This result also extends to the scenario where a trader either does not have a probabilistic model for the returns or does not trust a model obtained from historical data. To be more specific, we show that if a market contains a dominant asset, buy and hold a market portfolio involving nonzero weights for each asset is asymptotically log-optimal. Additionally, this paper also includes a conjecture regarding the property called high-frequency maximality. That is, in the absence of transaction costs, high-frequency rebalancing is unbeatable in the ELG sense. Support for the conjecture, involving a lemma for a weak version of the conjecture, is provided. This conjecture, if true, enables us to improve the log-optimality result obtained previously. Finally, a result that indicates a way regarding an issue about when should one to rebalance their portfolio, if needed, is also provided. Examples, some involving simulations with historical data, are also provided along the way to illustrate the theory.

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