Carbon portfolio management

The aim of the European Union's Emissions Trading Scheme (EU ETS) is that by 2020, emissions from sectors covered by the EU ETS will be 21% lower than in 2005. In addition to large CO 2 emitting companies covered by the scheme, other participants have entered the market with a view of using emission allowances for the diversification of their investment portfolios. The performance of this asset as a stand alone investment and its portfolio diversification implications will be investigated in this paper. Our results indicate that the market views Phases 1, 2, and 3 European Union allowance futures as unattractive as stand alone investments. In a portfolio context, in Phase 1, once the short-selling option is added, there are considerable portfolio benefits. However, our results indicate that these benefits only existed briefly during the pilot stage of the EU ETS. There is no evidence to suggest portfolio diversification benefits exist for Phase 2 or the early stages of Phase 3

A Robust Statistics Approach to Minimum Variance Portfolio Optimization

We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available market returns is often of similar order to the number of assets, so that the sample covariance matrix performs poorly as a covariance estimator. Additionally, financial market data often contain outliers which, if not correctly handled, may further corrupt the covariance estimation. We address these shortcomings by studying the performance of a hybrid covariance matrix estimator based on Tyler's robust M-estimator and on Ledoit-Wolf's shrinkage estimator while assuming samples with heavy-tailed distribution. Employing recent results from random matrix theory, we develop a consistent estimator of (a scaled version of) the realized portfolio risk, which is minimized by optimizing online the shrinkage intensity. Our portfolio optimization method is shown via simulations to outperform existing methods both for synthetic and real market data

Performance analysis and optimal selection of large mean-variance portfolios under estimation risk

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings

When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between estimation period T and number of stocks N, on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than the one obtained with the sample covariance method. This is particularly true when T/N is close to one. Moreover many estimators reduce the fraction of negative portfolio weights, while little improvement is achieved in the degree of diversification. On the contrary when short selling is not allowed and T>N, the considered methods are unable to outperform the sample covariance in terms of realized risk but can give much more diversified portfolios than the one obtained with the sample covariance. When T<N the use of the sample covariance matrix and of the pseudoinverse gives portfolios with very poor performance.Comment: 30 page

Large-scale portfolios using realized covariance matrix: evidence from the Japanese stock market

The objective of this paper is to examine effects of realized covariance matrix estimators based on intraday returns on large-scale minimum-variance equity portfolio optimization. We empirically assess out-of-sample performance of portfolios with different covariance matrix estimators: the realized covariance matrix estimators and Bayesian shrinkage estimators based on the past monthly and daily returns. The main results are: (1) the realized covariance matrix estimators using the past intraday returns yield a lower standard deviation of the large-scale portfolio returns than the Bayesian shrinkage estimators based on the monthly and daily historical returns; (2) gains to switching to strategies using the realized covariance matrix estimators are higher for an investor with higher relative risk aversion; and (3) the better portfolio performance of the realized covariance approach implied by ex-post returns in excess of the risk-free rate, the standard deviations of the excess returns, the return per unit of risk (Sharpe ratio) and the switching fees seems to be robust to the level of transaction costs.Large-scale portfolio selection; Realized covariance matrix; Intraday data

Multiple tests for the performance of different investment strategies

In the context of modern portfolio theory, we compare the out-of-sample performance of 8 investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the traditional sample-based approach, several minimum-variance techniques, a shrinkage, and a minimax approach. In contrast to similar studies in the literature, we also consider shortselling constraints and a risk-free asset. We provide a way to extend the concept of minimum-variance strategies in the context of short-selling constraints. A main drawback of most empirical studies on that topic is the use of simple-testing procedures which do not account for the effects of multiple testing. For that reason we conduct several hypothesis tests which are proposed in the multiple-testing literature. We test whether it is possible to beat a trivial strategy by at least one of the non-trivial strategies, whether the trivial strategy is better than every non-trivial strategy, and which of the non-trivial strategies are significantly outperformed by naive diversification. In our empirical study we use monthly US stock returns from the CRSP database, covering the last 4 decades. --Asset allocation,Certainty equivalent,Investment strategy,Markowitz,Multiple tests,Naive diversification,Out-of-sample performance,Portfolio optimization,Sharpe ratio

Calibration of shrinkage estimators for portfolio optimization

Shrinkage estimators is an area widely studied in statistics. In this paper, we contemplate the role of shrinkage estimators on the construction of the investor's portfolio. We study the performance of shrinking the sample moments to estimate portfolio weights as well as the performance of shrinking the naive sample portfolio weights themselves. We provide a theoretical and empirical analysis of different new methods to calibrate shrinkage estimators within portfolio optimizationPortfolio choice, Estimation error, Shrinkage estimators, Smoothed bootstrap