Factor investing stands as a cornerstone methodology in the sphere of portfolio management, where the selection of securities is guided by identifiable and quantifiable characteristics—referred to as factors—that are empirically linked to potential excess returns. These factors, among which value, size, momentum, quality, and volatility are most prominent, serve as the bedrock for constructing investment strategies that aim to achieve superior risk-adjusted performance compared to the broader market benchmarks.

Single factor models are strategies that concentrate on exploiting the return potential of one specific factor. The advantage of such a focused approach lies in its clarity and ease of implementation where investors can distinctly attribute the performance of their portfolio to the behavior of the selected factor. Moreover, the simplicity inherent in single factor models allows for straightforward attribution analysis and rebalancing procedures. However, these models are not without their limitations. The reliance on a singular factor exposes the investor to a heightened degree of cyclical risk, whereby the factor may exhibit varying degrees of performance through different economic phases. This can potentially lead to periods of significant underperformance. Furthermore, such models harbor concentration risks, as the portfolio may be unduly exposed to sector-specific shocks or macroeconomic trends that disproportionately affect the chosen factor.

In contrast, multi-factor models present a more nuanced and sophisticated investment strategy. By combining various factors, the multi-factor models strive to construct a portfolio that captures a more comprehensive set of factor risk premiums, potentially leading to a more consistent and stable performance over time. The diversification achieved through the combination of low-correlated factors reduces overall portfolio volatility, thereby offering a smoother investment journey. Nonetheless, the intricate nature of multi-factor models introduces complexity to the investment process. The risk of overfitting, a scenario where a model is excessively tailored to historical data, thus impairing its future predictive power is a pertinent concern. Additionally, the interplay between different factors may lead to a dilution effect, where the strong performance of one factor is offset by the weaker performance of another, potentially muting the overall return profile of the portfolio.

The adaptation of factor-based investing strategies within the Indian equity markets requires an astute recognition of our market's intricacies. The challenges are manifold: constructing robust factor parameters is a nuanced exercise, particularly in Indian markets characterized by a different microstructure compared to the developed markets such as the US where much of the factor investing research has originated from. The Indian market, with its shorter history of available data and issues surrounding data quality, compels investment professionals to undertake a meticulous process of model validation and adaptation. Another pivotal challenge is that of liquidity. Unlike the more mature markets, a significant segment of the Indian market lacks the depth of liquidity necessary for the seamless implementation of factor strategies. This necessitates an adjustment of academic models to ensure they are not only investable but also capable of capturing the factor premiums under real-world trading conditions.

In summary, the choice between single and multi-factor models is a function of the investor's risk profile, investment horizon, and the intricacies of the market environment. In emerging markets like India, this choice is compounded by additional layers of complexity. These include the necessity for localized factor parameter construction, the reconciliation of academic research with practical investability, and the continuous adaptation to market idiosyncrasies. As such, while factor investing can provide a structured path towards achieving enhanced returns, it demands a comprehensive understanding of both the factors in play and the economic backdrop against which they operate.