Risk Parity Return Trade-off in Relaxed Risk Parity Portfolio Optimization PDF Download

Author: Vaughn Edward Gambeta
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
This paper formulates a relaxed risk parity optimization model to control the balance of risk parity violation against the total portfolio performance. Risk parity is criticized as being conservative and it is improved by re-introducing the asset expected returns into the model and permitting the portfolio to violate the risk parity condition. The incorporation of an explicit target return goal into a second-order-cone model of a risk parity optimization is proposed. When the target return is greater than risk parity return a violation to risk parity allocations occurs that is controlled using a computational construct to obtain near risk parity portfolios to retain risk parity like traits. This model is used to demonstrate empirically that higher returns can be achieved without the risk contributions deviating dramatically from the risk parity allocations. This study also reveals that the relaxed risk parity model exhibits advantageous traits of robustness to expected returns.

Author: Giorgio Costa
Publisher:
ISBN:
Category :
Languages : en
Pages : 35

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Book Description
The risk parity solution to the asset allocation problem yields portfolios where the risk contribution from each asset is made equal. We consider a generalized approach to this problem. First, we set an objective that seeks to maximize the portfolio expected return while minimizing portfolio risk. Second, we relax the risk parity condition and instead bound the risk dispersion of the constituents within a predefined limit. This allows an investor to prescribe a desired risk dispersion range, yielding a portfolio with an optimal risk-return profile that is still well-diversified from a risk-based standpoint. We add robustness to our framework by introducing an ellipsoidal uncertainty structure around our estimated asset expected returns to mitigate estimation error. Our proposed framework does not impose any restrictions on short selling. A limitation of risk parity is that allowing of short sales leads to a non-convex problem. However, we propose an approach that relaxes our generalized risk parity model into a convex semi-definite program. We proceed to tighten this relaxation sequentially through the alternating direction method of multipliers. This procedure iterates between the convex optimization problem and the non-convex problem with a rank constraint. In addition, we can exploit this structure to solve the non-convex problem analytically and efficiently during every iteration. Numerical results suggest that this algorithm converges to a higher quality optimal solution when compared to the competing non-convex problem, and can also yield a higher ex post risk-adjusted rate of return.

Author: Edward E. Qian
Publisher: CRC Press
ISBN: 149873880X
Category : Business & Economics
Languages : en
Pages : 245

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Book Description
Written by an experienced researcher and portfolio manager who coined the term "risk parity," this book provides readers with a practical understanding of the risk parity investment approach. It uses fundamental, quantitative, and historical analysis to address the merit of risk parity as well as the practical and underlying aspects of risk parity investing. Requiring no advanced degrees in quantitative fields, the book analyzes risk parity performance from historical periods and more recent market environments.

Author: Thierry Roncalli
Publisher:
ISBN:
Category :
Languages : en
Pages : 19

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Book Description
Risk parity is an allocation method used to build diversified portfolios that does not rely on any assumptions of expected returns, thus placing risk management at the heart of the strategy. This explains why risk parity became a popular investment model after the global financial crisis in 2008. However, risk parity has also been criticized because it focuses on managing risk concentration rather than portfolio performance, and is therefore seen as being closer to passive management than active management. In this article, we show how to introduce assumptions of expected returns into risk parity portfolios. To do this, we consider a generalized risk measure that takes into account both the portfolio return and volatility. However, the trade-off between performance and volatility contributions creates some difficulty, while the risk budgeting problem must be clearly defined. After deriving the theoretical properties of such risk budgeting portfolios, we apply this new model to asset allocation. First, we consider long-term investment policy and the determination of strategic asset allocation. We then consider dynamic allocation and show how to build risk parity funds that depend on expected returns.

Author: Giorgio Costa Del Pozo
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
Risk parity is an asset allocation strategy that seeks to equalize the risk contributions of the constituent assets in a portfolio. The resulting portfolio is fully diversified from a risk perspective. However, like other asset allocation strategies, risk parity is susceptible to estimation errors. Moreover, its mathematical formulation imposes some fundamental limitations. This thesis aims to modernize risk parity by addressing all of the aforementioned issues. We address the susceptibility to estimation errors through three different frameworks. First, we introduce a robust framework that quantifies estimation error and embeds this information during optimization to construct a robust risk parity portfolio. Our second framework takes a different approach, introducing robustness during the parameter estimation step. This is formulated as a game-theoretic minimax problem to make an optimal investment decision against the most adversarial estimate of our parameters. Our third framework improves the quality of our estimated parameters before optimization takes place. We posit that we can embed the cyclical information of financial markets directly into our estimates, resulting in risk parity portfolios aligned with the current market regime. The result is a Markov regime-switching factor model of asset returns from which we can naturally derive regime-dependent parameters for use during optimization. The final component of this thesis addresses the fundamental limitations of risk parity: its lack of accountability for the investor's risk and reward appetite and its prohibition of short sales. We propose a generalized risk parity framework where the investor's risk and reward appetite define our objective, while still enforcing a desirable degree of risk-based diversification. Moreover, we propose an algorithm that allows us to consider portfolios with short positions. Thus, our generalized framework addresses the fundamental limitations of risk parity while retaining the desirable property of risk-based diversification. The frameworks proposed in this thesis can be used independently or in tandem, depending on the investor's needs and goals. The unifying subject of this thesis is to advance risk parity by addressing its fundamental weaknesses. This is achieved by proposing different frameworks and algorithms, with the overarching property of preserving the interpretability and computational tractability of our solutions.

Author: Denis B. Chaves
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
In this article, the authors conduct a horse race between representative risk parity portfolios and other asset allocation strategies, including equal weighting, minimum variance, mean-variance optimization, and the classic 60/40 equity/bond portfolio. They find that the traditional risk parity portfolio construction does not consistently outperform (in terms of risk-adjusted return) equal weighting or a model pension fund portfolio anchored to the 60/40 equity/bond portfolio structure. However, it does significantly outperform such optimized allocation strategies as minimum variance and mean-variance efficient portfolios. Over the last 30 years, the Sharpe ratios of the risk parity and the equal-weighting portfolios have been much more stable across decade-long subperiods than either the 60/40 portfolio or the optimized portfolios. Although risk parity performs on par with equal weighting, it does provide better diversification in terms of risk allocation and thus warrants further consideration as an asset allocation strategy. The authors show, however, that the performance of the risk parity strategy can be highly dependent on the investment universe. Thus, to execute risk parity successfully, the careful selection of asset classes is critical, which, for the time being, remains an art rather than a formulaic exercise based on theory.

Author: Joel Goh
Publisher:
ISBN:
Category :
Languages : en
Pages : 31

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Book Description
We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using simulated data, the PVaR approach always generates better risk-return tradeoffs in the optimal portfolios when compared to traditional Markowitz mean-variance approach. When using real financial data, our approach also outperforms the Markowitz approach in the risk-return tradeoff. Given that the PVaR measure is also a robust risk measure, our new approach can be very useful for optimal portfolio allocations when asset return distributions are asymmetrical.

Author: Saul Sala Peñalver
Publisher:
ISBN:
Category :
Languages : en
Pages : 29

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Book Description
Capitalization-weighted indexes are the most common way to gain access to broad equity market performance. However, interest in risk based investing has grown steadily in the recent post-crisis years as investors seek to overcome the limitations of traditional approaches to asset allocation. Despite the interest, there remains confusion about how to implement these strategies in any investor's portfolio, and even more when we want to implement it into a particular asset class. This paper compares some risk-based indexation methodologies, where risk parity takes an important role, and illustrates these issues as it applies to the Ibex 35 universe. We also use the typical capitalization-weighted index as a benchmark. Using 10 years of data, we show that risk parity portfolios outperform all the underlying portfolios on an absolute and risk adjusted basis.

Author: Peter Williams
Publisher:
ISBN:
Category :
Languages : en
Pages : 11

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Book Description
This paper finds that factor based risk parity portfolios are able to outperform other standard asset allocation approaches, including 60/40 and long-only risk parity. By using a group of factors which have negligible correlations with each other and the market, this portfolio generates a stable return stream with little exposure to macroeconomic risks. If these factors are dynamically scaled according to their conditional volatility the portfolio's performance markedly increases. While this portfolio is composed of well known factors it exhibits 'alpha through construction' by scaling out of strategies when their expected returns are lowest and using minimally correlated components.

Author: Bai, Xi
Publisher:
ISBN:
Category :
Languages : en
Pages : 27

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Book Description
The risk parity optimization problem aims to find such portfolios for which the contributions of risk from all assets are equally weighted. Portfolios constructed using risk parity approach are a compromise between two well-known diversification techniques: minimum variance optimization approach and the equal weighting approach. In this paper, we discuss the problem of finding portfolios that satisfy risk parity of either individual assets or groups of assets. We describe the set of all risk parity solutions by using convex optimization techniques over orthants and we show that this set may contain exponential number of solutions. We then propose an alternative nonconvex least-square model whose set of optimal solutions includes all risk parity solutions, and propose a modified formulation which aims at selecting the most desirable risk parity solution (according to some criteria). When general bounds are considered, a risk parity solution may not exist. The nonconvex least-square model then seeks a feasible portfolio which is as close to risk parity as possible. Furthermore, we propose an alternating linearization framework to solve this nonconvex model. Numerical experiments indicate the effectiveness of our technique in terms of both speed and accuracy.