A Comparison of Cointegration & Tracking Error Models for Mutual Funds & Hedge Funds

We present a detailed study of portfolio optimisation based on cointegration, a statistical tool that here exploits a long-run equilibrium relationship between stock prices and an index price. We compare the theoretical and empirical properties of cointegration optimal equity portfolios with those of portfolios optimised on the tracking error variance. From an eleven year out of sample performance analysis we find that for simple index tracking the additional feature of cointegration between the tracking portfolio and the index has no clear advantages or disadvantages relative to the tracking error variance (TEV) minimization model. However ensuring a cointegration relationship does pay off when the tracking task becomes more difficult. Cointegration optimal portfolios clearly dominate the TEV equivalents for all of the statistical arbitrage strategies based on enhanced indexation, in all market circumstancescointegration, tracking error, index tracking, statistical arbitrage

Index Mutual Fund Replication

This paper discusses the application of an index tracking technique to mutual fund replication problems. By using a tracking error (TE) minimization method and two tactical rebalancing strategies (i.e. the calendar based strategy and the tolerance triggered strategy), a multi-period fund tracking model is developed that replicates S&P 500 mutual fund returns. The impact of excess returns and loss aversion on overall tracking performance is also discussed in two extended cases of the original TE optimization respectively. An evolutionary method, namely Differential Evolution, is used for optimizing the asset weights. According to the experiment results, it is found that the proposed model replicates the first two moments of the fund returns by using only five equities. The TE optimization strategy under loss aversion with tolerance triggered rebalancing dominates other combinations studied with regard to tracking ability and cost efficiency.Passive Portfolio Management, Fund Tracking, MultiPeriod Optimization, Differential Evolution

Sources of Over-performance in Equity Markets: Mean Reversion, Common Trends and Herding

In the field of optimisation models for passive investments, we propose a general portfolio construction model based on principal component analysis. The portfolio is designed to replicate the first principal component of a group of stocks, instead of a traditional benchmark, thus capturing only the common trend in the stock returns. The main advantage of this approach is that the reduction of the noise present in stock returns facilitates the replication task considerably and the optimal portfolio structure is very stable. We analyse the portfolio performance over different time horizons and in different international equity markets. The strategy over-performs both equally weighted and price weighted benchmarks, even after transaction costs. A market premium, a value premium associated with mean reversion in stock returns, and a volatility premium which give the strategy characteristics of a benchmark enhancer, all explain the over-performance, but have time-varying contributions to it. A behavioural explanation for the mean reversion mechanism leads to the conclusion that the portfolio performance is influenced by the extent of investors herding towards the common trend in stock returns.common trends, mean revrsion, herding, principal component analysis, abnormal returns, value strategies, behavioural finance

Do Business Cycles Exhibit Beneficial Information for Portfolio Management? An Empirical Application of Statistical Arbitrage

An advantageous statistical arbitrage strategy should exhibit a zero-cost trading strategy for which the expected payoff should be positive. In practical applications, however, the abnormal returns often are out-of-sample not significant. The statistical model being suggested here results in an estimated portfolio exhibiting in-sample a cointegration relationship with the artificial stock index. The portfolio returns exhibited out-of-sample a mean of 10.44% p.a., whereas the volatility was one third lower in comparison to the benchmark's volatility. Accounting for trading costs of 2.94% p.a. on average, the annual returns of the estimated portfolio are out-of-sample still 6.83% higher than the market returns. As a result, the model involves implicitly advantageous market timing.

Optimal composition of hybrid/blended real estate portfolios

Purpose: The purpose of this paper is to establish an optimum mix of liquid, publicly traded assets that may be added to a real estate portfolio, such as those held by open-ended funds, to provide the liquidity required by institutional investors such as UK defined contribution pension funds. This is with the objective of securing liquidity while not unduly compromising the risk-return characteristics of the underlying asset class. This paper considers the best mix of liquid assets at different thresholds for a liquid asset allocation, with the performance then evaluated against that of a direct real estate benchmark index. Design/Methodology/Approach: The authors employ a mean-tracking error optimisation approach in determining the optimal combination of liquid assets that can be added to a real estate fund portfolio. The returns of the optimised portfolios are compared to the returns for portfolios that employ the use of either cash or listed real estate alone as a liquidity buffer. Multivariate Generalised Autoregressive models are used along with rolling correlations and tracking errors to gauge the effectiveness of the various portfolios in tracking the performance of the benchmark index. Findings: The results indicate that applying formal optimisation techniques leads to a considerable improvement in the ability of the returns from blended real estate portfolios to track the underlying real estate market. This is the case at a number of different thresholds for the liquid asset allocation and in cases where a minimum return requirement is imposed. Practical Implications: The results suggest that real estate fund managers can realise the liquidity benefits of incorporating publicly traded assets into their portfolios without sacrificing the ability to deliver real estate-like returns. However, in order to do so, a wider range of liquid assets must be considered, not just cash. Originality/value: Despite their importance in the real estate investment industry, comparatively few studies have examined the structure and operation of open-ended real estate funds. To the authors’ knowledge, this is the first study to analyse the optimal composition of liquid assets within blended or hybrid real estate portfolios

Low volatility alternative equity indices

In recent years, there has been an increasing interest in constructing low volatility portfolios. These portfolios have shown significant outperformance when compared with the market capitalization-weighted portfolios. This study analyses the low volatility portfolios in South Africa using sectors instead of individual stocks as building blocks for portfolio construction. The empirical results from back-testing these portfolios show significant outperformance when compared with their market capitalization weighted equity benchmark counterpart (ALSI). In addition, a further analysis of this study delves into the construction of the low volatility portfolios using the Top 40 and Top 100 stocks. The results also show significant outperformance over the market-capitalization portfolio (ALSI), with the portfolios constructed using the Top 100 stocks having a better performance than portfolio constructed using the Top 40 stocks. Finally, the low volatility portfolios are also blended with typical portfolios (ALSI and the SWIX indices) in order to establish their usefulness as effective portfolio strategies. The results show that the Low volatility Single Index Model (SIM) and the Equally Weight low-beta portfolio (Lowbeta) were the superior performers based on their Sharpe ratios

Portfolio optimization and index tracking for the shipping stock and freight markets using evolutionary algorithms

This paper reproduces the performance of an international market capitalization shipping stock index and two physical shipping indexes by investing only in US stock portfolios. The index-tracking problem is addressed using the differential evolution algorithm and the genetic algorithm. Portfolios are constructed by a subset of stocks picked from the shipping or the Dow Jones Composite Average indexes. To test the performance of the heuristics, three different trading scenarios are examined: annually, quarterly and monthly rebalancing, accounting for transaction costs where necessary. Competing portfolios are also assessed through predictive ability tests. Overall, the proposed investment strategies carry less risk compared to the tracked benchmark indexes while providing investors the opportunity to efficiently replic ate the performance of both the stock and physical shipping indexes in the most cost-effective way

Equity Indexing: Conitegration and Stock Price Dispersion: A Regime Switiching Approach to market Efficiency

This paper examines the performance of a general dynamic equity indexing strategy based on cointegration, from a market efficiency perspective. A consistent return in excess of the benchmark is demonstrated over different time horizons and in different, real world and simulated stock markets. A measure of stock price dispersion is shown to be a leading indicator for the excess return, and their relationship is modelled as a Markov switching process of two market regimes. We find that the entire ‘abnormal return’ is associated with the high volatility regime, so the presence of a latent risk factor cannot be ruled out. Moreover, any market inefficiencies identified by the dynamic indexing model are temporary and occur only in special market circumstances. Our results have implications for equity fund managers: we shown how, without any stock selection, solely through smart optimisation and market timing, the benchmark performance can be significantly enhanced.cointegration, dispersion, efficient market hypothesis equity markets, index tracking, Markov switching

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