Does the low-risk anomaly exist in the Indian equity market? A test using alternative risk measures

PurposeThis study aims to investigate the risk-return trade-off in the Indian equity market at both the aggregate equity market level and in the cross-sections of stock return using alternative risk measures.Design/methodology/approachThe study uses weekly and monthly data of 3,085 Bombay Stock Exchange-listed stocks spanning over 20 years from January 2000 to December 2019. The study evaluates the risk-return trade-off at the aggregate equity market level using the value-weighted and the equal-weighted broader portfolios. Eight different risk proxies belonging to the conventional, downside and extreme risk categories are considered to analyse the cross-sectional risk-return relationship.FindingsThe results show a positive equity premium on the value-weighted portfolio; however, the equal-weighted portfolio of these stocks shows an average return lower than the return on the 91-day Treasury Bills. The inverted size premium mainly causes this anomaly in the Indian equity market as the small stocks have lower returns than big stocks. The study presents a strong negative risk-return relationship across different risk proxies. However, under the subsample of more liquid stocks, the low-risk anomaly regarding other risk proxies becomes moderate except the beta-anomaly. This anomalous relationship seems to be caused by small and less liquid stocks having low institutional ownership and higher short-selling constraints.Practical implicationsThe findings have important implications for investors, managers and practitioners. Investors can incorporate the effects of different highlighted anomalies in their investment strategies to fetch higher returns. Managers can also use these findings in their capital budgeting decisions, resource allocations and other diverse range of direct and indirect decisions, particularly in emerging markets such as India. The findings provide insights to practitioners while valuing the firms.Originality/valueThe study is among the earlier attempts to examine the risk-return trade-off in an emerging equity market at both the aggregate equity market level and in the cross-sections of stock returns using alternative measures of risk and expected returns.

ON PORTFOLIO OPTIMIZATION: ARE THERE FINANCIAL GAINS OF USING ALTERNATIVE COVARIANCE METHODS?

Purpose: The study evaluates the performance of alternative variance-covariance estimators as a fundamental ingredient to portfolio optimization. Methodology: The study estimates eleven covariance matrices on the data of Pakistan stock exchange's non-financial sector firms covering the period from July 2006 to June 2020. The accuracy and efficiency of covariance estimators are assessed through two evaluation parameters: root mean square error and minimum variance portfolios (risk behavior). Main findings: Empirical findings based on evaluation parameters suggest that more complex covariance estimators in the equity market of Pakistan yield no additional financial gains than the equally weighted portfolio of estimators. Application of the study: As the estimation of the variance-covariance matrix is one of the essential elements of portfolio construction, this study guides investor(s) on selecting an appropriate covariance estimator among eleven estimators endorsed by literature. Novelty/ originality of the study: Based on detailed analysis, the study documents that investor(s) of the Pakistan stock exchange cannot gain any additional benefit from more complex and tricky methods of variance-covariance estimators compared to a portfolio of estimators for the non-financial sector. Investors are advised to consider the equally weighted portfolio of estimators when formulating their investment strategy.

Mean–variance combining rules that outperform naïve diversification

The mean–variance framework developed by Markowitz (1952). Portfolio selection, The Journal of Finance, 7(1), 77–91 is still the major model used nowadays in asset allocation and active portfolio management. However, the estimated mean–variance rules often fail to deliver superior performance compared with the simple naïve rule (the equally weighted portfolio) due to the problem of estimation errors. In this paper, I propose a portfolio construction method that is effective in dealing with estimation errors in the optimization process. Particularly, I specify the portfolio weights as an optimal combination of the equally weighted portfolio and a sample zero-investment portfolio. I show analytically that the proposed method alleviates the problem of estimation errors and dominates naïve diversification. I suggest two implementable versions of the combining method and show, empirically, their good performances relative to the naïve rule. The newly developed rules work well, particularly, for portfolios with a medium and high number of assets. Moreover, the outperformance persists generally even in the presence of transaction costs. Since the combinations are theory-based, my study may be interpreted as reaffirming the usefulness of the Markowitz portfolio theory in practice.

Fundamentals-weighting vs. Capitalization-weighting: An Empirical Comparison

Following the criticism surrounding capitalization-weighting, both academic and practitioner communities have developed alternative approaches to portfolio construction. We analyze one of these approaches, fundamentals-based weighting, which identifies the weights of portfolio constituents on the basis of their market multiples and accounting ratios. Our analysis is carried out on four fundamentals-weighted portfolios (FW) based on four different weighting variants, the capitalization-weighted portfolio (CW), and the equally-weighted (EW) portfolio, from January 2004 to December 2020, and in two subperiods (2004–2011 and 2011–2020). We find that in the first subperiod, the EW portfolio shows the highest risk-adjusted performance, followed by the FW portfolios. In contrast, in the second subperiod and in the period as a whole, the CW portfolio outperforms the other portfolios in terms of risk-adjusted performance. Overall, we conclude that both FW portfolios and the EW portfolio do not exhibit superior results when compared with the classic CW portfolio. Therefore, we have shown that FW and EW techniques provide superior risk-adjusted performance only during a period of exceptional financial turmoil. However, under normal conditions, they cannot be recommended as a rational investment strategy. JEL classification numbers: G11, G14. Keywords: Fundamental weighting, Capitalization weighting, Equal weighting, Value investing, Indexed investing.

Out-of-sample performance of the Black-Litterman model

The aim of this paper is to test the out-of-sample performance of the Black Litterman (BL) model for a German stock portfolio compared to the traditional mean-variance optimized (MV) portfolio, the German stock index DAX, a reference portfolio, and an equally weighted portfolio. The BL model was developed as an alternative approach to portfolio optimization many years ago and has gained attention in practical portfolio management. However, in the literature, there are not many studies that analyze the out-of-sample performance of the model in comparison to other asset allocation strategies. The BL model combines implied returns and subjective return forecasts. In this study, for each stock, sample means of historical returns are employed as subjective return forecasts. The empirical analysis shows that the BL portfolio performs significantly better than the DAX, the reference portfolio and the equally weighted portfolio. However, overall, it is slightly outperformed by the MV portfolio. Nevertheless, the BL portfolio may be of greater interest to investors because -according to this study, where the subjective return forecasts are based on historical returns of a rather long past period of time-it could lead in most cases to lower absolute (normalized) values for the stock weights and for all stocks to smaller fluctuations in the (normalized) weights compared to the MV portfolio. JEL classification numbers: C61, G11. Keywords: Black-Litterman, Mean-variance, Portfolio optimization, Performance.

Factor-Based Optimization of a Fundamentally-Weighted Portfolio in the Illiquid and Undeveloped Stock Market

In this paper, the possibility of using fundamental weighting as a tool to intentionally tilt a portfolio toward specific and unobservable risk factors in the illiquid and undeveloped Croatian stock market is explored. Thus far, fundamental-weighting has been shown to be able to outperform the cap-weighted index in such environments but no attempt regarding control for implicit factor exposure of such portfolios has been reported. Therefore, in this study principal component analysis is performed to capture the underlying risk factors of the fundamentally-weighted portfolio in order to optimize the portfolio’s performance by minimizing its volatility. Previous attempts focusing purely on portfolio risk reduction by estimating minimum variance portfolios failed both from an in-sample and out-of-sample perspective. Results in this study are based on 22 in-sample and out-of-sample tests in the period from March 2009 till March 2020. On the in-sample estimation basis, the proposed approach significantly improves the portfolio’s performance and, if restrictions to weights are imposed, it can outperform the cap-weighted benchmark. However, out-of-sample testing yielded poor results both in terms of risk and return. Such results are in contrast to findings for the developed markets but corroborate the claim that a broad investment base is needed for successful risk exposure in the long run.

Forecasting multivariate VaR and ES using MC-GARCH-Copula model

Purpose This study aims to use a novel methodology to investigate the performance of several multivariate value at risk (VaR) and expected shortfall (ES) models implemented to assess the risk of an equally weighted portfolio consisting of high-frequency (1-min) observations for five foreign currencies, namely, EUR/USD, GBP/USD, EUR/JPY, USD/JPY and GBP/JPY. Design/methodology/approach By applying the multiplicative component generalised autoregressive conditional heteroskedasticity (MC-GARCH) model on each return series and by modelling the dependence structure using copulas, the 95 per cent intraday portfolio VaR and ES are forecasted for an out-of-sample set using Monte Carlo simulation. Findings In terms of VaR forecasting performance, the backtesting results indicated that four out of the five models implemented could not be rejected at 5 per cent level of significance. However, when the models were further evaluated for their ES forecasting power, only the Student’s t and Clayton models could not be rejected. The fact that some ES models were rejected at 5 per cent significance level highlights the importance of selecting an appropriate copula model for the dependence structure. Originality/value To the best of the authors’ knowledge, this is the first study to use the MC-GARCH and copula models to forecast, for the next 1 min, the VaR and ES of an equally weighted portfolio of foreign currencies. It is also the first study to analyse the performance of the MC-GARCH model under seven distributional assumptions for the innovation term.

Dependence Structure Analysis and VaR Estimation Based on China’s and International Gold Price: A Copula Approach

Since 2013, China has become the world’s largest gold producer and consumer. To gain the corresponding global pricing power in gold, many actions have been taken by China in recent years, including the International Board at Shanghai Gold Exchange, Shanghai-Hong Kong Gold Connect and Shanghai Gold Fix. Our work studies the dependence structure between China’s and international gold price and examines whether these moves are changing the dependence structure. We use GARCH-copula models to detect the dynamic dependence and tail dependence. The research period is set to contain the Financial Crisis in 2008, the dramatical plunge of gold price in 2013 and a series of black swan events in 2016. The empirical study shows that some event driven dependence structure breaks are statistically insignificant. And the time-varying Symmetrized Joe-Clayton copula is the best copula to model the dependence structure based on AIC value. Finally, an example of applications of this dependence structure is given by estimating the VaR of an equally weighted portfolio with a simulation-based method.