Liquidity-Adjusted Sharpe Ratio

Modern Portfolio Theory, introduced by Harry Markowitz in 1952, and the Sharpe Ratio, proposed by William Sharpe in 1966, focus on portfolio optimization considering market return and risk. Markowitz and Sharpe developed these theories in the New York Stock Exchange (NYSE) context. However, in markets with different characteristics, such as the Mexican market, additional factors beyond returns and market risk play a crucial role in the performance of an investment portfolio. One of the major challenges in low-liquidity markets is the difficulty of quickly buying or selling assets due to liquidity constraints. This thesis introduces a novel approach to portfolio optimization in such environments: the LiquidityAdjusted Sharpe Ratio. This method seeks to maximize the risk-return profile of a portfolio while factoring in liquidity risk, using a liquidity shrinkage factor to penalize assets with low liquidity. By doing so, the model balances an asset’s return potential with its associated market risk and liquidity risk. Additionally, we propose a specific case of this approach, termed the Liquidity Variance Return Ratio (LVRR), which measures the Sharpe Ratio achieved per unit of liquidity risk taken in an investment. The higher the LVRR, the more efficiently the portfolio manages liquidity risk in relation to its returns. The goal, therefore, is to maximize the LVRR, making it a distinct case within the broader Liquidity-Adjusted Sharpe Ratio framework. This targeted optimization ensures that portfolios are not only risk-efficient but also liquid, which is crucial in constrained markets. Throughout this document, we present this method’s analytical and empirical solution and propose a Sharpe-Liquidity efficient frontier that considers the return, market risk, and liquidity risk of an investment portfolio. This new frontier offers a more ad hoc approach for investors facing liquidity constraints when trading. We demonstrated that the proposed method and its elements (such as the LVRR portfolio) fall within this front’s optimal and feasible region. Also, we found that to achieve lower liquidity risk in a portfolio, it is generally necessary to accept higher market risk. However, in most cases, and subject to the selection of portfolio assets, the returns of LVRR-optimized portfolios show lower kurtosis with higher positive skewness compared to optimal Maximum Sharpe portfolios. This means that although the volatility of a LVRR portfolio generally increases, this volatility is skewed towards gains, i.e., positive returns. Additionally, when implementing the method through the backtesting of portfolios with random asset selection, we found that our method often outperforms the traditional Sharpe ratio approach in the Mexican market. Specifically, our analysis reveals a 74% probability of achieving superior returns in static long-term portfolios and a 80% probability in dynamic portfolios that incorporate periodic rebalancing. We also found that in liquid markets, the method tends to converge to the Sharpe Ratio, making it better to adopt the classic approach in these contexts due to the low relevance of liquidity risk. After extensive research, it has been concluded that the LVRR method consistently delivers favorable outcomes within low-liquidity markets. This suggests that the proposed methodology can serve as a viable alternative for investors seeking to operate effectively in such environments.