Tracking Error and Information Ratio

Author(s):  
Mikkel Rasmussen
2020 ◽  
Vol 13 (8) ◽  
pp. 171
Author(s):  
Paskalis Glabadanidis

I investigate the question of how to construct a benchmark replicating portfolio consisting of a subset of the benchmark’s components. I consider two approaches: a sequential stepwise regression and another method based on factor models of security returns’ first and second moments. The first approach produces the standard hedge portfolio that has the maximum feasible correlation with the benchmark. The second approach produces weights that are proportional to a “signal-to-noise” ratio of factor beta to idiosyncratic volatility. Using a factor model of securities returns allows the use of a larger number of securities than the number of time periods used to estimate the parameters of the factor model. I also consider a second objective that maximizes expected returns subject to a target tracking error variance. The security selection criterion naturally extends to the product of the information ratio and the signal-to-noise ratio. The optimal tracking portfolio is either a one-fund or a two-fund portfolio rule consisting of the optimal hedging portfolio, the tangent portfolio or the global minimum variance portfolio, depending on what constraints are imposed on the objective function. I construct buy-and-hold replicating portfolios using the algorithms presented in the paper to track a widely followed stock index with very good results both in-sample and out-of-sample.


2019 ◽  
Vol 10 (3) ◽  
pp. 466-487 ◽  
Author(s):  
Salman Ahmed Shaikh ◽  
Mohd Adib Ismail ◽  
Abdul Ghafar Ismail ◽  
Shahida Shahimi ◽  
Muhammad Hakimi Mohd. Shafiai

Purpose This study aims to comparatively analyze the performance of Islamic and conventional income and equity funds using various performance evaluation methods. Design/methodology/approach The authors comparatively analyze the performance of mutual funds using measures, such as tracking error, Sharpe ratio (1966), Treynor ratio (1965), M-square measure by Modigliani and Modigliani (1997) and information ratio. The authors also use market timing and selection measures, such as Treynor and Mazuy model (1966), Henriksson and Merton (1981) model and Fama’s decomposition approach (1973). Findings The authors find that Islamic equity funds are as much competitive as conventional equity funds. All Islamic equity funds have positive Sharpe ratio, Treynor ratio and net selectivity measure. Islamic equity funds are slightly less risky in general. Islamic equity and income funds generally have positive Jensen's Alpha and a positive market timing ability. However, the authors find that Islamic income funds generally underperform the market due to less Shari’ah-compliant investment class assets in the market. Practical implications It will help the industry players to assess their strategic positioning with regard to the commercial competitiveness of Islamic investments. Originality/value The authors take considerably large sample of 60 funds in Pakistan as compared to previous studies and also cover recent period (2006-16). For income funds, the authors construct an original benchmark index based on price and dividend data and use that in performance assessment.


2016 ◽  
Vol 24 (4) ◽  
pp. 557-589
Author(s):  
Woo-baik Lee

Commodity ETF, Cumulative Return, Tracking Error, Information Ratio, Inverse ETF


2016 ◽  
Vol 24 (4) ◽  
pp. 525-555
Author(s):  
Dong Hyun Choi ◽  
Junesuh Yi

This study analyses empirically the Granger causality between commodity ETFs listed in KRX (Korea Stock Exchange) and the price determinants of the underlying commodities as well as the KOSPI200 index and the underlying indices, and compares the performance of four commodity ETFs : gold futures, oil futures, soybean futures and the copper price. The main findings are as follows : First, the commodity ETFs tracking gold futures, oil futures and soybean futures prices in the sample from the inception to June 2015 were not directly related to the price determinants of the underlying commodities except for the copper ETF which was affected by the oil price as one of the price determinants of copper. In addition, all four ETFs were not related to the KOSPI200 index while they were affected by the underlying indices. Second, the soybean futures ETF outperformed the KOSPI200 index in terms of the cumulative returns and the oil futures ETF recorded the worst performance in terms of the cumulative returns and IR (information ratio). Third, the average tracking error of each ETF except for the oil futures ETF showed a positive value and the price of each ETF except for the soybean futures ETF has been undervalued compared to its net asset value. From the above findings, we can infer that investors in the copper ETF should closely watch the movement of the oil price to enhance the return and investors in the commodity ETFs should first consider agriculture-related ETFs rather than oil-related ETFs considering the price volatility. In addition, the inverse ETFs for copper and agriculture-related products should be introduced following the oil and gold futures inverse ETFs to protect against negative returns in a declining period of commodity prices.


2019 ◽  
Vol 65 (9) ◽  
pp. 4440-4450 ◽  
Author(s):  
Shomesh E. Chaudhuri ◽  
Andrew W. Lo

The value added by an active investor is traditionally measured using alpha, tracking error, and the information ratio. However, these measures do not characterize the dynamic component of investor activity, nor do they consider the time horizons over which weights are changed. In this paper, we propose a technique to measure the value of active investment that captures both the static and dynamic contributions of an investment process. This dynamic alpha is based on the decomposition of a portfolio’s expected return into its frequency components using spectral analysis. The result is a static component that measures the portion of a portfolio’s expected return resulting from passive investments and security selection and a dynamic component that captures the manager’s timing ability across a range of time horizons. Our framework can be universally applied to any portfolio and is a useful method for comparing the forecast power of different investment processes. Several analytical and empirical examples are provided to illustrate the practical relevance of this decomposition. This paper was accepted by Gustavo Manso, finance.


The authors study the impact of the inclusion of the momentum and size factors, and the selectiveness in stock screening, on the performance and implementation cost of a multifactor strategy. Whereas the cost of implementing a stand-alone momentum strategy is quite high because of its extraordinarily high turnover, adding momentum to a mix of the value, low beta, profitability, investment, and size factors helps lower tracking error and improves the information ratio without a significant increase in implementation cost because offsetting trades cancel each other out. Contrary to conventional wisdom, the inclusion of the size factor does not negatively affect the multifactor strategy’s trading costs in light of its relatively low turnover. Additionally, including the size factor improves the performance and coverage of the multifactor strategy, which otherwise would be constructed with only large and mid-size companies. As expected, by using factor portfolios with more concentrated holdings, investors can improve the performance of a multifactor strategy, but these benefits come at the expense of high turnover and high trading costs. The authors specify portfolio design as a conscious choice made on the trade-off between the effective harvesting of the factor premium and low-cost implementation. They highlight the importance of the thoughtful portfolio construction work required to deliver a smart beta multifactor strategy that serves investors’ needs.


2012 ◽  
Vol 132 (3) ◽  
pp. 347-356 ◽  
Author(s):  
Yuta Nabata ◽  
Tatsuya Nakazaki ◽  
Tokoku Ogata ◽  
Kiyoshi Ohishi ◽  
Toshimasa Miyazaki ◽  
...  

2016 ◽  
Vol 9 (5) ◽  
pp. 324 ◽  
Author(s):  
Zain Retas ◽  
Lokman Abdullah ◽  
Syed Najib Syed Salim ◽  
Zamberi Jamaludin ◽  
Nur Amira Anang

Author(s):  
G. N. Maltsev ◽  
A. V. Evteev

Introduction: Radio information transmission systems with noise-like phase-shift keyed signals based on pseudo-random sequences have potential noise immunity provided by accurately tracking the delay of the received signal in the correlation receiver. When working with moving objects, the delay of the received signal varies continuously, and the reception quality for noise-like phase-shifted signals highly depends on the synchronization system operation and on the accuracy of estimating the received signal delay by the tracking system. To ensure the required signal reception quality, it is necessary to provide an informed choice of tracking system parameters, taking into account their effects, which are the random and systematic components of the delay tracking error, on the selected noise immunity indicator.Purpose: Analyzing how the errors in tracking the delay of a received phase-shift keyed signal based on a pseudorandom sequence by the synchronization system of a radio information transmission system can affect the probability of erroneous reception of an information symbol.Results: The calculation method was used to obtain families of dependencies of the probability of erroneous reception of an information symbol on the signal-noise ratio (SNR), and the values of the random and systematic components of the delay tracking error which are normalized to the capture band of the correlation receiver. It has been shown that at a fixed SNR, the values of the random and systematic components of the delay tracking error are critical for the erroneous reception probability. In all the cases discussed, all the dependencies are characterized by a slow change of the erroneous reception probability while the synchronization errors within the area of small SNR have fixed values. As the SNR value grows, the erroneous reception probability rapidly drops. To ensure the specified signal reception quality and the reliability of the selection of information symbols and messages in a radio information transmission system with noise-like phase-manipulated signals, its synchronization system requires a joint selection of the tracking system parameters, taking into account the limitations imposed by the operating conditions and technical implementation features.Practical relevance: The obtained results can be used in noise immunity analysis of radio information transmission systems with noise-like phase-shift keyed signals in a wide range of communication conditions, and in providing technical solutions for synchronization systems ensuring the required quality of signal reception.


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