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- Bermin, Hans Peter, et al.
(författare)
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The geometry of risk adjustments
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Ingår i: Decisions in Economics and Finance. - 1593-8883.
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Tidskriftsartikel (refereegranskat)abstract
- We present a geometric approach to portfolio theory with a focus on risk-adjusted returns, in particular Jensen’s alpha. We find that while the alpha/beta approach has severe limitations, especially in higher dimensions, only minor conceptual modifications (e.g., using orthogonal Sharpe ratios rather than risk-adjusted returns) are needed to identify the efficient trading strategies. We further show that, in a complete market, the so-called market price of risk vector is identical to the growth optimal Kelly vector, albeit expressed in coordinates of a different basis. This implies that a derivative, having an orthogonal Sharpe ratio of zero, has a price given by the minimal martingale measure.
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| 2. |
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| 3. |
- Fabretti, Annalisa, et al.
(författare)
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Convex incentives in financial markets: an agent-based analysis
- 2017
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Ingår i: Decisions in Economics and Finance. - : Springer Science and Business Media LLC. - 1593-8883 .- 1129-6569. ; 40:1-2, s. 375-395
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Tidskriftsartikel (refereegranskat)abstract
- © 2017, Springer-Verlag Italia S.r.l. We investigate whether convex incentive contracts are a source of instability of financial markets as indicated by the results of a continuous double-auction asset market experiment performed by Holmen et al. (J Econ Dyn Control 40:179–194, 2014). We develop a model to replicate the setting of the experiment and perform an agent-based simulation where agents have linear or convex incentives. Extending the simulation by varying features of actual asset markets that were not studied in the experiment, our main results show that increasing the number of convex incentive contracts increases prices and volatility and decreases market liquidity, measured both as bid–ask spreads and volumes. We also observe that the influence of risk aversion on traders’ decisions decreases when there are convex contracts and that increasing the differences in initial wealth among the traders has similar effects as increasing number of convex incentive contracts.
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| 4. |
- LINDBERG, CARL, 1978
(författare)
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Investing equally in risk
- 2013
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Ingår i: Decisions in Economics and Finance. - : Springer Science and Business Media LLC. - 1593-8883 .- 1129-6569. ; 36:1, s. 39-46
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Tidskriftsartikel (refereegranskat)abstract
- Classical optimal strategies are notorious for producing remarkably volatile portfolio weights over time when applied with parameters estimated from data. This is predominantly explained by the difficulty to estimate expected returns accurately. In Lindberg (Bernoulli 15:464-474, 2009), a new parameterization of the drift rates was proposed with the aim to circumventing this difficulty, and a continuous time mean-variance optimal portfolio problem was solved. This approach was further developed in Alp and Korn (Decis Econ Finance 34:21-40, 2011a) to a jump-diffusion setting. In the present paper, we solve a different portfolio problem under the market parameterization in Lindberg (Bernoulli 15:464-474, 2009). Here, the admissible investment strategies are given as the amounts of money to be held in each stock and are allowed to be adapted stochastic processes. In the references above, the admissible strategies are the deterministic and bounded fractions of the total wealth. The optimal strategy we derive is not the same as in Lindberg (Bernoulli 15:464-474, 2009), but it can still be viewed as investing equally in each of the n Brownian motions in the model. As a consequence of the problem assumptions, the optimal final wealth can become non-negative. The present portfolio problem is solved also in Alp and Korn (Submitted, 2011b), using the L 2 -projection approach of Schweizer (Ann Probab 22:1536-1575, 1995). However, our method of proof is direct and much easier accessible.
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| 5. |
- Shternshis, Andrey, 1995-, et al.
(författare)
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Variance of entropy for testing time-varying regimes with an application to meme stocks
- 2024
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Ingår i: Decisions in Economics and Finance. - : Springer. - 1593-8883 .- 1129-6569.
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Tidskriftsartikel (refereegranskat)abstract
- Shannon entropy is the most common metric for assessing the degree of randomness of time series in many fields, ranging from physics and finance to medicine and biology. Real-world systems are typically non-stationary, leading to entropy values fluctuating over time. This paper proposes a hypothesis testing procedure to test the null hypothesis of constant Shannon entropy in time series data. The alternative hypothesis is a significant variation in entropy between successive periods. To this end, we derive an unbiased sample entropy variance, accurate up to the order O(n^(-4)) with n the sample size. To characterize the variance of the sample entropy, we first provide explicit formulas for the central moments of both binomial and multinomial distributions describing the distribution of the sample entropy. Second, we identify the optimal rolling window length to estimate time-varying Shannon entropy. We optimize this choice using a novel self-consistent criterion based on counting significant entropy variations over time. We corroborate our findings using the novel methodology to assess time-varying regimes of entropy for stock price dynamics by presenting a comparative analysis between meme and IT stocks in 2020 and 2021. We show that low entropy values correspond to periods when profitable trading strategies can be devised starting from the symbolic dynamics used for entropy computation, namely periods of market inefficiency.
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