There is an ongoing debate about how idiosyncratic volatility (IV) and momentum returns are related to each other and whether that helps to improve the returns of an investment strategy for investors. However, interestingly, this has not been studied in the Indian stock market. In this paper, we investigate the relationship between average expected momentum returns and IV, and the possible role being played by IV in explaining the abnormal momentum returns. The study employs data of 473 companies taken from Bloomberg for the BSE 500 index for the time period 2008 -- 2018, on a daily basis. The study also uses characteristic data such as market capitalisation and book-to-market ratio. BSE-200 index data are also used as the proxy of market returns. The methodology of Fama-French (1993), Jegadeesh and Titman (1993), and Ang et al. (2006) is used in the formation of mimicking portfolios, momentum based portfolios, and estimation of idiosyncratic volatility, respectively. The empirical results show that there is a significant positive relationship between average expected returns on momentum and IV, as high IV portfolios have high returns and low IV portfolios have low returns. It is also found that two prominent risk models such as CAPM and FFTFM fail to capture the abnormal returns. Further, it is also found that idiosyncratic volatilities have a significant impact on momentum returns on all three short-term trading strategies (3-3, 6-6 and 12-12) and the two long-term trading strategies (36-36 and 60-60) as the resulting alphas are non-zeros and statistically significant. Further, to maximise their returns on portfolios, investors can short the past losers with low IV and hold (buy) past winners with high IV. Even holding the past losers with high idiosyncratic volatilities is a profitable avenue although it is riskier in the case of short-term trading strategies. In the case of long-term trading strategies, investors can invest in any stock as all the stocks generate positive returns.
