The Sharpe Ratio

Sharpe, William F.

doi:10.3905/jpm.1994.409501

Cited by 2,047 publications

(917 citation statements)

References 5 publications

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“…Then, we have the following: The worst-case MPRA problem (25) is equivalent to the min-max problem (28), which is in turn equivalent to the convex problem (30). This proposition shows that the TP of the least-favorable model (μ , Σ ) solves the worst-case SR maximization problem (24). The saddle-point property (32) means that the portfolio w in (33) is the TP of the least-favorable model (μ , Σ ).…”

Section: Seung-jean Kim and Stephen Boydmentioning

confidence: 86%

“…The SR achieved by this portfolio is called the market price of risk. The TP plays an important role in asset pricing theory and practice (see, e.g., [8,19,24]). If the n risky assets with (single period) returns follow a ∼ N (μ, Σ), then…”

Section: Mean-variance Asset Allocationmentioning

confidence: 99%

“…satisfies the budget constraint and is admissible (i.e., w ∈ W); i.e., it is a solution to the worst-case SR maximization (24). Moreover, it is the unique solution to the worst-case SR maximization (24).…”

Section: Seung-jean Kim and Stephen Boydmentioning

confidence: 99%

“…Moreover, it is the unique solution to the worst-case SR maximization (24). The case of 1 T x = 0 may arise when the set W is unbounded.…”

Section: Seung-jean Kim and Stephen Boydmentioning

confidence: 99%

“…The case of 1 T x = 0 may arise when the set W is unbounded. In this case, the worst-case SR maximization problem (24) has no solution, so the game involving the SR has no saddle point.…”

Section: Seung-jean Kim and Stephen Boydmentioning

confidence: 99%

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A minimax theorem with applications to machine learning, signal processing, and finance

Kim

Boyd

2007

2007 46th IEEE Conference on Decision and Control

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Abstract. This paper concerns a fractional function of the form x T a/ √ x T Bx, where B is positive definite. We consider the game of choosing x from a convex set, to maximize the function, and choosing (a, B) from a convex set, to minimize it. We prove the existence of a saddle point and describe an efficient method, based on convex optimization, for computing it. We describe applications in machine learning (robust Fisher linear discriminant analysis), signal processing (robust beamforming and robust matched filtering), and finance (robust portfolio selection). In these applications, x corresponds to some design variables to be chosen, and the pair (a, B) corresponds to the statistical model, which is uncertain.

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Section: Seung-jean Kim and Stephen Boydmentioning

confidence: 86%

Section: Mean-variance Asset Allocationmentioning

confidence: 99%

Section: Seung-jean Kim and Stephen Boydmentioning

confidence: 99%

“…Moreover, it is the unique solution to the worst-case SR maximization (24). The case of 1 T x = 0 may arise when the set W is unbounded.…”

Section: Seung-jean Kim and Stephen Boydmentioning

confidence: 99%

“…The case of 1 T x = 0 may arise when the set W is unbounded. In this case, the worst-case SR maximization problem (24) has no solution, so the game involving the SR has no saddle point.…”

Section: Seung-jean Kim and Stephen Boydmentioning

confidence: 99%

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A minimax theorem with applications to machine learning, signal processing, and finance

Kim

Boyd

2007

2007 46th IEEE Conference on Decision and Control

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Performance functions and reinforcement learning for trading systems and portfolios

Moody

Liao

et al. 1998

Journal of Forecasting

239

208

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We propose to train trading systems and portfolios by optimizing objective functions that directly measure trading and investment performance. Rather than basing a trading system on forecasts or training via a supervised learning algorithm using labelled trading data, we train our systems using recurrent reinforcement learning (RRL) algorithms. The performance functions that we consider for reinforcement learning are profit or wealth, economic utility, the Sharpe ratio and our proposed differential Sharpe ratio. The trading and portfolio management systems require prior decisions as input in order to properly take into account the effects of transactions costs, market impact, and taxes. This temporal dependence on system state requires the use of reinforcement versions of standard recurrent learning algorithms. We present empirical results in controlled experiments that demonstrate the efficacy of some of our methods for optimizing trading systems and portfolios. For a long/short trader, we find that maximizing the differential Sharpe ratio yields more consistent results than maximizing profits, and that both methods outperform a trading system based on forecasts that minimize MSE. We find that portfolio traders trained to maximize the differential Sharpe ratio achieve better risk‐adjusted returns than those trained to maximize profit. Finally, we provide simulation results for an S&P 500/TBill asset allocation system that demonstrate the presence of out‐of‐sample predictability in the monthly S&P 500 stock index for the 25 year period 1970 through 1994. Copyright © 1998 John Wiley & Sons, Ltd.

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Good‐Deal Bounds

Hodges

2010

Encyclopedia of Quantitative Finance

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Good‐deal bounds provide a range of prices within which an instrument must trade if it is not to offer a surprisingly good reward‐for‐risk opportunity. This approach to valuation provides an important middle course between finding a unique value and finding probably weak bounds based on super‐replication. In a world where derivatives are difficult to hedge precisely, good‐deal bounds reflect this; they depend on model assumptions and on the prices of the securities that would be used to exploit mispricing. Good‐deal bounds have two interpretations: we can think of them either as establishing normative bid and ask forward prices for a particular trader, or as predicting a range in which we expect the market price to lie. We cover the main issues without going too deeply into mathematical technicalities, describing the nature of the construction and giving insights into the analysis, including the use of duality in the solutions. We also sketch the history of the topic, including that of the closely related generalized Sharpe ratio, and the link to coherent risk measures. There is also a discussion of the role of the utility function. The article concludes with a short account of the more recent and prospective literature.

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The Sharpe Ratio

Cited by 2,047 publications

References 5 publications

A minimax theorem with applications to machine learning, signal processing, and finance

A minimax theorem with applications to machine learning, signal processing, and finance

Performance functions and reinforcement learning for trading systems and portfolios

Good‐Deal Bounds

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