1,721,057 research outputs found
Equal Risk Bounding is better than Risk Parity for portfolio selection
No full textRisk Parity (RP), also called equally weighted risk contribution, is a recent approach to risk diversification for portfolio selection. RP is based on the principle that the fractions of the capital invested in each asset should be chosen so as to make the total risk contributions of all assets equal among them. We show here that the Risk Parity approach is theoretically dominated by an alternative similar approach that does not actually require equally weighted risk contribution of all assets but only an equal upper bound on all such risks. This alternative approach, called Equal Risk Bounding (ERB), requires the solution of a nonconvex quadratically constrained optimization problem. The ERB approach, while starting from different requirements, turns out to be strictly linked to the RP approach. Indeed, when short selling is allowed, we prove that an ERB portfolio is actually an RP portfolio with minimum variance. When short selling is not allowed, there is a unique RP portfolio and it contains all assets in the market. In this case, the ERB approach might lead to the RP portfolio or it might lead to portfolios with smaller variance that do not contain all assets, and where the risk contributions of each asset included in the portfolio is strictly smaller than in the RP portfolio. We define a new riskiness index for assets that allows to identify those assets that are more likely to be excluded from the ERB portfolio. With these tools we then provide an exact method for small size nonconvex ERB models and a very efficient and accurate heuristic for larger problems of this type. In the case of a common constant pairwise correlation among all assets, a closed form solution to the ERB model is obtained and used to perform a parametric analysis when varying the level of correlation. The practical advantages of the ERB approach over the RP strategy are illustrated with some numerical examples. Computational experience on real-world and on simulated data confirms accuracy and efficiency of our heuristic approach to the ERB model also in comparison with some state-of-the-art local and global optimization codes
A Quick Tool to forecast VaR
No full textWe propose here a naive model to forecast ex-ante Value-at-Risk (VaR) using
a shrinkage estimator between realized volatility estimated on past return time
series, and implied volatility extracted from option pricing data. Implied volatility
is often indicated as the operators expectation about future risk, while the historical
volatility straightforwardly represents the realized risk prior to the estimation point,
which by definition is backward looking. In a nutshell, our prediction strategy for
VaR uses information both on the expected future risk and on the past estimated
risk.
We examine our model, called Shrinked Volatility VaR, both in the univariate
and in the multivariate cases, empirically comparing its forecasting power with that
of two benchmark VaR estimation models based on the Historical Filtered Bootstrap
and on the RiskMetrics approaches.
The performance of all VaR models analyzed is evaluated using both statistical
accuracy tests and efficiency evaluation tests, according to the Basel II and ESMAregulatory frameworks, on several major markets around the world over an out-ofsample
period that covers different financial crises.
Our results confirm the efficacy of the implied volatility indexes as inputs for
a VaR model, but combined together with realized volatilities. Furthermore, due
to its ease of implementation, our prediction strategy to forecast VaR could be
used as a tool for portfolio managers to quickly monitor investment decisions before
employing more sophisticated risk management systems
Improving the Risk Parity Approach to Portfolio Selection
No full textRisk Parity (RP), also called equally weighted risk contribution, is a recent approach to risk diversication in portfolio selection. RP is based on the principle that the fractions of the capital invested in each asset should be chosen so as to make the total risk contributions of all assets equal among them. We show here that the Risk Parity approach is theoretically dominated by an alternative similar approach that does not actually require equally weighted risk contribution of all assets but only an equal upper bound on all such risks. We call it the Equal Risk Bounding (ERB) approach. This alternative approach might, and actually does in some cases, select portfolios that do not contain all assets and where the risk contributions of all assets is strictly smaller than in the RP portfolio. We prove some relations between the solutions of the ERB and of the RP models and we use such relations to provide a finite method for finding an ERB portfolio. In the case of equal correlation, a closed form solution to the ERB model is also provided. Some numerical examples illustrate the advantages of the ERB approach over the RP approach
A Quick Tool to forecast VaR using Implied and Realized Volatilities
No full textWe propose here a naive model to forecast exante ValueatRisk (VaR) using a shrinkage estimator between
realized volatility estimated on past return time series, and implied volatility extracted from option pricing data.
Implied volatility is often indicated as the operators expectation about future risk, while the historical volatility
straightforwardly represents the realized risk prior to the estimation point, which by definition is backward looking.
In a nutshell, our prediction strategy for VaR uses information both on the expected future risk and on the past
estimated risk. We examine our model, called Shrinked Volatility VaR, both in the univariate and in the multivariate
cases, empirically comparing its forecasting power with that of two benchmark VaR estimation models based on the
Historical Filtered Bootstrap and on the RiskMetrics approaches. The performance of all VaR models analyzed is
evaluated using both statistical accuracy tests and efficiency evaluation tests, according to the Basel II and ESMA
regulatory frameworks, on several major markets around the world over an outof sample period that covers
different financial crises. Our results confirm the efficacy of the implied volatility indexes as inputs for a VaR model,
but combined together with realized volatilities. Furthermore, due to its ease of implementation, our prediction
strategy to forecast VaR could be used as a tool for portfolio managers to quickly monitor investment decisions
before employing more sophisticated risk management systems
Minimum Risk vs. Capital and Risk Diversification strategies for portfolio construction
No full textIn this paper we propose an extensive empirical analysis on three different categories of
portfolio selection models, each focused on different objectives: minimization of risk, maximization
of capital diversification, and uniform distribution of risk allocation. This latter approach,
also called Risk Parity (RP) or Equal Risk Contribution (ERC), is a recent strategy for asset
allocation, where the risk measure commonly used to select RP portfolios is volatility. We propose
here new developments on the ERC approach based on Conditional Value-at-Risk as risk
measure.
We investigate how these classes of portfolio models (Minimum-Risk, Capital and Risk Diversification)
work on seven investment universes, each with different sources of risk, which
consist of equities, bonds and mixed assets. Then we highlight some strengths and weaknesses
of all portfolio strategies in terms of various performance measures
Risk disparity is better than risk parity for portfolio selection
No full textThe Risk Parity approach to portfolio selection is based
on the principle that the fractions of the capital invested in each asset
should be chosen so as to make the total risk contributions of all asset
equal among them. We show that this approach is theoretically dominated by
an alternative similar approach that does not require such equality but only appropriate
inequalities
Optimally chosen small portfolios are better than large ones
No full textOne of the fundamental principles in portfolio selection models is minimization of risk through diversification of the
investment. However, this principle does not necessarily translate into a request for investing in all the assets of the
investment universe. Indeed, following a line of research started by Evans and Archer almost fifty years ago, we
provide here further evidence that small portfolios are sufficient to achieve almost optimal in-sample risk reduction
with respect to variance and to some other popular risk measures, and very good out-of-sample performances. While
leading to similar results, our approach is significantly different from the classical one pioneered by Evans and Archer.
Indeed, we describe models for choosing the portfolio of a prescribed size with the smallest possible risk, as opposed
to the random portfolio choice investigated in most of the previous works. We find that the smallest risk portfolios
generally require no more than 15 assets. Furthermore, it is almost always possible to find portfolios that are just 1%
more risky than the smallest risk portfolios and contain no more than 10 assets. Furthermore, the optimal small
portfolios generally show a better performance than the optimal large ones. Our empirical analysis is based on some
new and on some publicly available benchmark data sets often used in the literature
Optimally chosen small portfolios are better than large ones
Full text linkOne of the fundamental principles in portfolio selection models is minimization of risk through diversification of the investment. However, this principle does not necessarily translate into a request for investing in all the assets of the investment universe. Indeed, following a line of research started by Evans and Archer almost fifty years ago, we provide here further evidence that small portfolios are sufficient to achieve almost optimal in-sample risk reduction with respect to variance and to some other popular risk measures, and very good out-of-sample performances. While leading to similar results, our approach is significantly different from the classical one pioneered by Evans and Archer. Indeed, we describe models for choosing the portfolio of a prescribed size with the smallest possible risk, as opposed to the random portfolio choice investigated in most of the previous works. We find that the smallest risk portfolios generally require no more than 15 assets. Furthermore, it is almost always possible to find portfolios that are just 1% more risky than the smallest risk portfolios and contain no more than 10 assets. Furthermore, the optimal small portfolios generally show a better performance than the optimal large ones. Our empirical analysis is based on some new and on some publicly available benchmark data sets often used in the literature
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