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박재훈투영인 프로필 사진박재훈투영인
Finding the Optimal Stock Selling Timing Based on Average Prices (Jul 15, 2008)
created At: 3/15/2025
Neutral
Neutral
This analysis was written from a neutral perspective. We advise you to always make careful and well-informed investment decisions.
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Fact
Study Focus: Optimal buy/sell timing based on price averages. Analysis Methods: Uses geometric and arithmetic averages to derive optimal strategies. Strategy Type: Optimal stopping problem using a bang-bang approach. Optimal Selling (Geometric Average): Hold until maturity if μ > σ²/2 Sell immediately if μ ≤ σ²/2 Optimal Buying (Geometric Average): Determined by a feedback function based on the price-to-running-average ratio. Arithmetic Average Strategy: No explicit formula, dynamically depends on price-to-average ratio and time until maturity.
Opinion
This study provides a clear and structured decision-making framework for timing stock sales based on average price comparisons. The geometric average approach offers an intuitive rule that helps investors determine whether to sell immediately or hold based on the stock’s expected return and volatility. The arithmetic average strategy, while more complex, allows for a dynamic and flexible response to market conditions. This framework helps investors manage market uncertainty rationally, avoiding emotional decision-making and enhancing long-term profitability.
Core Sell Point
The bang-bang selling strategy, based on average price comparisons, provides investors with a clear, rule-based framework for exiting positions. This approach minimizes emotional trading errors and enhances long-term profitability, even under uncertain market conditions.

A study titled "Optimal Stock Selling/Buying Strategy with Reference to the Ultimate Average" proposes an optimal decision rule for buying and selling stocks based on their ultimate average price. The study aims to determine the ideal timing for maximizing (selling) or minimizing (buying) the expected price ratio relative to the ultimate average over a given period.

Key Findings:

1. Problem Definition

  • Given stock price volatility, when is the optimal time to buy or sell based on its ultimate average price?

2. Theoretical Model

  • The problem is framed as an optimal stopping problem formulated using variational inequalities.

  • The study employs partial differential equation (PDE) methods to analyze optimal strategies.

3. Optimal Strategies

Using Geometric Average:

  • Optimal Selling Strategy:

    • If μ (expected return) > σ²/2 (half of squared volatility), hold until maturity.

    • If μ ≤ σ²/2, sell immediately.

  • Optimal Buying Strategy:

    • Based on a feedback mechanism, dependent on the price-to-running-average ratio.

Using Arithmetic Average:

  • Unlike geometric averaging, a clear-cut formula for selling decisions is not available.

  • However, analysis suggests that the optimal selling strategy depends on:

    • The price-to-running-average ratio

    • Time remaining until maturity

  • The threshold for selling is not fixed but varies dynamically based on the stock price and running average.

General Selling Criteria:

  • The study advocates a "bang-bang" strategy, where stocks are either sold immediately or held until maturity, based on predefined conditions.

  • Key factors influencing the selling decision:

    • Type of average used (geometric vs. arithmetic)

    • Expected return (μ)

    • Stock price volatility (σ)

    • Price-to-running-average ratio

Considerations & Limitations:

  • The results are derived from specific mathematical models and assumptions, which may differ from real market conditions.

  • Transaction costs and market liquidity are not accounted for in this model.

  • Optimal selling timing may vary based on an investor’s risk tolerance and objectives.

[Compliance Note]

  • All posts by Sellsmart are for informational purposes only. Final investment decisions should be made with careful judgment and at the investor’s own risk.

  • The content of this post may be inaccurate, and any profits or losses resulting from trades are solely the responsibility of the investor.

  • Core16 may hold positions in the stocks mentioned in this post and may buy or sell them at any time.

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