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Register a new userIs being `Robust beneficial?: A perspective from the Indian market
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Added by
Siddhartha Chakrabarty
Publication date
2019
fields
Financial
and research's language is
English
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The problem of data uncertainty has motivated the incorporation of robust optimization in various arenas, beyond the Markowitz portfolio optimization. This work presents the extension of the robust optimization framework for the minimization of downside risk measures, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We perform an empirical study of VaR and CVaR frameworks, with respect to their robust counterparts, namely, Worst-Case VaR and Worst-Case CVaR, using the market data as well as the simulated data. After discussing the practical usefulness of the robust optimization approaches from various standpoints, we infer various takeaways. The robust models in the case of VaR and CVaR minimization exhibit superior performance with respect to their ba
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The emergence of robust optimization has been driven primarily by the necessity to address the demerits of the Markowitz model. There has been a noteworthy debate regarding consideration of robust approaches as superior or at par with the Markowitz model, in terms of portfolio performance. In order to address this skepticism, we perform empirical analysis of three robust optimization models, namely the ones based on box, ellipsoidal and separable uncertainty sets. We conclude that robust approaches can be considered as a viable alternative to the Markowitz model, not only in simulated data but also in a real market setup, involving the Indian indices of S&P BSE 30 and S&P BSE 100. Finally, we offer qualitative and quantitative justification regarding the practical usefulness of robust optimization approaches from the point of view of number of stocks, sample size and types of data.
We study the continuous time portfolio optimization model on the market where the mean returns of individual securities or asset categories are linearly dependent on underlying economic factors. We introduce the functional $Q_gamma$ featuring the expected earnings yield of portfolio minus a penalty term proportional with a coefficient $gamma$ to the variance when we keep the value of the factor levels fixed. The coefficient $gamma$ plays the role of a risk-aversion parameter. We find the optimal trading positions that can be obtained as the solution to a maximization problem for $Q_gamma$ at any moment of time. The single-factor case is analyzed in more details. We present a simple asset allocation example featuring an interest rate which affects a stock index and also serves as a second investment opportunity. We consider two possibilities: the interest rate for the bank account is governed by Vasicek-type and Cox-Ingersoll-Ross dynamics, respectively. Then we compare our results with the theory of Bielecki and Pliska where the authors employ the methods of the risk-sensitive control theory thereby using an infinite horizon objective featuring the long run expected growth rate, the asymptotic variance, and a risk-aversion parameter similar to $gamma$.
The paper predicts an Efficient Market Property for the equity market, where stocks, when denominated in units of the growth optimal portfolio (GP), have zero instantaneous expected returns. Well-diversified equity portfolios are shown to approximate the GP, which explains the well-observed good performance of equally weighted portfolios. The proposed hierarchically weighted index (HWI) is shown to be an even better proxy of the GP. It sets weights equal within industrial and geographical groupings of stocks. When using the HWI as proxy of the GP the Efficient Market Property cannot be easily rejected and appears to be very robust.
In this study, we have investigated empirically the effects of market properties on the degree of diversification of investment weights among stocks in a portfolio. The weights of stocks within a portfolio were determined on the basis of Markowitzs portfolio theory. We identified that there was a negative relationship between the influence of market properties and the degree of diversification of the weights among stocks in a portfolio. Furthermore, we noted that the random matrix theory method could control the properties of correlation matrix between stocks; this may be useful in improving portfolio management for practical application.
A Higher Order Markovian (HOM) model to capture the dynamics of commodity prices is proposed as an alternative to a Markovian model. In particular, the order of the former model, is taken to be the delay, in the response of the industry, to the market information. This is then empirically analyzed for the prices of Copper Mini and four other bases metals, namely Aluminum, Lead, Nickel and Zinc, in the Indian commodities market. In case of Copper Mini, the usage of the HOM approach consistently offer improvement, over the Markovian approach, in terms of the errors in forecasting. Similar trends were observed for the other base metals considered, with the exception of Aluminum, which can be attributed the volatility in the Asian market during the COVID-19 outbreak.
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