An Entropy-Based Approach to Portfolio Optimization

Recent literature shows that many testing procedures used to evaluate asset pricing models result in spurious rejection probabilities. Model misspecification, the strong factor structure of test assets, or skewed test statistics largely explain this. In this paper we use the relative entropy of pricing kernels to provide an alternative framework for testing asset pricing models. Building on the fact that the law of one price guarantees the existence of a valid pricing kernel, we study the relationship between the mean-variance efficiency of a model’s factor-mimicking portfolio, as measured by the cross-sectional generalized least squares (GLS) R 2 statistic, and the relative entropy of the pricing kernel, as determined by the Kullback–Leibler divergence. In this regard, we suggest an entropy-based decomposition that accurately captures the divergence between the factor-mimicking portfolio and the minimum-variance pricing kernel resulting from the Hansen-Jagannathan bound. Our results show that, although GLS R 2 statistics and relative entropy are strongly correlated, the relative entropy approach allows us to explicitly decompose the explanatory power of the model into two components, namely, the relative entropy of the pricing kernel and that corresponding to its correlation with asset returns. This makes the relative entropy a versatile tool for designing robust tests in asset pricing.

Section: Discussionmentioning

confidence: 99%

Relative Entropy and Minimum-Variance Pricing Kernel in Asset Pricing Model Evaluation

Rojo-Suárez

Alonso‐Conde

2020

“…Using the same combinatorial technique that was employed for REPO [ 1 ], the Shannon entropy of portfolio returns can be estimated empirically via probability generating functions. For a collection of n discrete return assets over time period

, let

denote the cross-sectional n -dimensional vector of outcomes across one observational row of data, and let them be uniquely represented by the collection of

’s such that

.…”

Section: Minimum Relative Entropymentioning

confidence: 99%

“…When selecting a portfolio of securities, the objective was to minimize the discrete entropy of portfolio returns, as seen in REPO [ 1 ] (i.e., to minimize entropy, and maximize expected returns). Low entropy means low risk.…”

Section: Minimum Relative Entropymentioning

confidence: 99%

“…In our previous paper (Mercurio et al [ 1 ]), a new class of portfolio optimization problems was introduced called return-entropy portfolio optimization (REPO). REPO uses Shannon entropy (Shannon, 1948) [ 2 , 3 ] as the discriminatory risk measure for portfolio selection for assets with continuous returns, as opposed to variance used by Markowitz [ 4 ] in mean-variance portfolio optimization (MVPO).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Portfolio Optimization for Binary Options Based on Relative Entropy

Mercurio

Xie

2020

Self Cite

The portfolio optimization problem generally refers to creating an investment portfolio or asset allocation that achieves an optimal balance of expected risk and return. These portfolio returns are traditionally assumed to be continuous random variables. In An Entropy-Based Approach to Portfolio Optimization, we introduced a novel non-parametric optimization method based on Shannon entropy, called return-entropy portfolio optimization (REPO), which offers a simple and fast optimization algorithm for assets with continuous returns. Here, in this paper, we would like to extend the REPO approach to the optimization problem for assets with discrete distributed returns, such as those from a Bernoulli distribution like binary options. Under a discrete probability distribution, portfolios of binary options can be viewed as repeated short-term investments with an optimal buy/sell strategy or general betting strategy. Upon the outcome of each contract, the portfolio incurs a profit (success) or loss (failure). This is similar to a series of gambling wagers. Portfolio selection under this setting can be formulated as a new optimization problem called discrete entropic portfolio optimization (DEPO). DEPO creates optimal portfolios for discrete return assets based on expected growth rate and relative entropy. We show how a portfolio of binary options provides an ideal general setting for this kind of portfolio selection. As an example we apply DEPO to a portfolio of short-term foreign exchange currency pair binary options from the NADEX exchange platform and show how it outperforms leading Kelly criterion strategies. We also provide an additional example of a gambling application using a portfolio of sports bets over the course of an NFL season and present the advantages of DEPO over competing Kelly criterion strategies.

“…The mean-entropy portfolios are consistent with the full covariance and the single-index models. Many progresses have been made in exploring entropy of the portfolio weights as a maximization objective to encourage diversification levels ([ 31 , 32 , 33 , 34 , 35 , 36 , 37 ]). Lassance [ 38 ] used the R

nyi entropy discussed the portfolio optimization.…”

Section: Introductionmentioning

confidence: 99%

Maximum Varma Entropy Distribution with Conditional Value at Risk Constraints

Liu

Chang

2020

It is well known that Markowitz’s mean-variance model is the pioneer portfolio selection model. The mean-variance model assumes that the probability density distribution of returns is normal. However, empirical observations on financial markets show that the tails of the distribution decay slower than the log-normal distribution. The distribution shows a power law at tail. The variance of a portfolio may also be a random variable. In recent years, the maximum entropy method has been widely used to investigate the distribution of return of portfolios. However, the mean and variance constraints were still used to obtain Lagrangian multipliers. In this paper, we use Conditional Value at Risk constraints instead of the variance constraint to maximize the entropy of portfolios. Value at Risk is a financial metric that estimates the risk of an investment. Value at Risk measures the level of financial risk within a portfolio. The metric is most commonly used by investment bank to determine the extent and occurrence ratio of potential losses in portfolios. Value at Risk is a single number that indicates the extent of risk in a given portfolio. This makes the risk management relatively simple. The Value at Risk is widely used in investment bank and commercial bank. It has already become an accepted standard in buying and selling assets. We show that the maximum entropy distribution with Conditional Value at Risk constraints is a power law. Algebraic relations between the Lagrangian multipliers and Value at Risk constraints are presented explicitly. The Lagrangian multipliers can be fixed exactly by the Conditional Value at Risk constraints.