Abstract
This empirical study is an endeavor to assess the impact of the number of securities in a risk parity portfolio on its performance. The study focuses on performance analysis of fifty, seventy-five and hundred stocks risk parity portfolio for emerging markets—India and China—and the developed market—the USA. Alpha of the risk parity portfolio has shown sensitivity to the change in the size as a number of holdings of the portfolio. The findings of this empirical study reveal that seventy-five stocks risk parity portfolio is in a sweet-spot for the full sample time period from Dec 2002 to Dec 2014. It not only generates statistically significant superior alpha, but also achieves a similar level of risk diversification as to fifty and hundred stocks portfolio. Testing of sub-periods of the full sample time period, which is coinciding with interest rate cycle, suggests that during the crucial period of financial crisis of 2008, seventy-five stocks portfolio shows the superior performance of alpha, Sharpe ratio and Treynor ratio over fifty stocks and hundred stocks portfolio with a similar level of risk diversification. However, the possibility of superior risk parity portfolio with a marginally higher or lower number than seventy-five stock portfolio cannot be denied.
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Notes
Gini index is a statistical measure of distribution which ranges between zero to one, where zero indicates full diversification and one being full concentration. Here, the Gini index is calculated based on weights distribution among assets in the portfolio. The lower Gini index for weights for portfolio means better distribution of weights within portfolio leading to less concentration in the portfolio.
Maximum drawdown is an indicator of maximum % loss of a portfolio value from the previous peak of the portfolio to the trough of a portfolio over a specified time period. It is a measure of downside risk for a portfolio, so bigger the maximum drawdown, larger the loss of the portfolio value.
For India and the USA, both RP50 and RP100 portfolio excess returns time series are modified as at the level both series have shown the existence of unit root, but modified series as resulted from first difference which has no unit root is used for testing of serial correlation. Again to improve Durbin-Watson stat, the second-order autoregressive process is run on this modified time series. Exhibit 2 shows the outcome of a modified time series for regression analysis.
For China, the second-order autoregressive process is run on time series of both RP50 and RP100 with respective indices to remove serial correlation from the series and resultantly improving Durbin–Watson stat.
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Shah, T., Parikh, A. Does the number of holdings in a risk parity portfolio matter?. J Asset Manag 20, 124–133 (2019). https://doi.org/10.1057/s41260-019-00110-y
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DOI: https://doi.org/10.1057/s41260-019-00110-y