Optimal Trading with an Unobservable Mean-Reverting Trend

Summary

This paper studies portfolio choice when an asset’s price trend follows an unobserved Ornstein–Uhlenbeck process. It derives optimal strategies for a trader with logarithmic utility under two information settings: one in which the trend is known and one in which it must be inferred from available information. The comparison addresses how incomplete knowledge of the trend affects investment performance.

For both strategies, the paper gives asymptotic expectations and variances of logarithmic returns as functions of the signal-to-noise ratio and the trend’s mean-reversion speed. It also compares asymptotic Sharpe ratios to quantify the performance cost of partial information. The provided description does not state the resulting formulas or numerical size of that cost, and it gives no empirical evaluation, so the findings are framed within the specified stochastic model.

Key ideas

• The asset price trend is modeled as an unobservable mean-reverting process.
• The paper compares logarithmic-utility strategies under full and partial information.
• Asymptotic return expectations and variances depend on signal quality and trend mean reversion.
• Sharpe ratios are used to measure the performance loss associated with partial information.
• The supplied description gives no numerical results or empirical validation.

Tags

# Performance analysis of the optimal strategy under partial information


# Performance analysis of the optimal strategy under partial information









The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein-Uhlenbeck process. We focus on the optimal strategy with a logarithmic utility function under full or partial information. For both cases, we provide the asymptotic expectation and variance of the logarithmic return as functions of the signal-to-noise ratio and of the trend mean reversion speed. Finally, we compare the asymptotic Sharpe ratios of these strategies in order to quantify the loss of performance due to partial information.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.